Accretion-Driven Turbulence in the Circumgalactic Medium

Abstract

Both observations and hydrodynamic simulations suggest that turbulence is ubiquitous in the circumgalactic medium (CGM). We study the development and properties of CGM turbulence driven by accretion in halo masses of $10^{10}-10^{13}\,{\rm M}_\odot$ at redshifts $0\leq z\lesssim 2$, thus providing a baseline for additional turbulence driving processes such as galaxy feedback. Using analytic considerations and idealized hydrodynamical simulations we demonstrate that in halos with mass up to $\sim10^{12}\,{\rm M}_\odot$, even mild turbulent velocities near the virial radius of $σ_{\rm t}(R_{\rm vir})\sim 10\,{\rm km \, s^{-1}}$ are enhanced by the accretion process so that turbulent velocities are comparable to the virial velocity at inner CGM radii, with $σ_{\rm t}(0.1\,R_{\rm vir})\approx v_{\rm vir}\sim 100\,{\rm km \, s^{-1}}$. Rapid cooling at these inner radii further implies that thermal pressure support is small, and the gas is dominated by the cool and warm ($\sim10^4-10^5\,{\rm K}$) phases. Inner CGM energetics are thus dominated by turbulence, with gas density distributions and velocity structure functions similar to those seen in simulations of isothermal supersonic ISM turbulence, rather than those seen in subsonically turbulent stratified media such as the ICM. The gas accretion rate in these systems is regulated by the turbulence dissipation rate rather than by the cooling rate as in more massive halos. We argue that galaxy feedback is unlikely to qualitatively change our conclusions unless it continuously injects high specific energy material ($\gg v^2_{\rm vir}$) into the CGM. Such `turbulence-dominated' CGM can be identified in observations via the predicted wide lognormal ionization distributions and large velocity dispersions in UV absorption spectra, particularly in the inner CGM of $\sim L^\star$ and lower-mass halos.

Figures (14)

• Figure 1: Lagrangian evolution of the turbulent velocity in inflows, versus the ratio of the turbulent velocity to the mean inflow velocity. Calculation is based on eqn. (\ref{['eq:turbulence_combine']}) from Robertson & Goldreich (2012) assuming $\eta=1$. The turbulent velocity increases when it is lower than $|u_r|$ and decreases when it is higher than $|u_r|$, converging to $\sigma_{\rm t}=|u_r|$.
• Figure 2: Subsonic and supersonic turbulence in CGM inflows. Top: Cartoons of the subsonic and supersonic regimes versus halo mass. At high masses the hot phase ($T\approx T_{\rm vir}$) dominates the inflow, with subsonic inflow and turbulent velocities and an inflow velocity set by the cooling time (eqn. \ref{['eq:cooling_flow']}). At low masses the cool phase ($T\gtrsim T_{\rm eq}$) dominates so inflow and turbulence velocities are supersonic, and the inflow velocity is set by the turbulence dissipation time (eqn. \ref{['eq:ur cool solution']}). At intermediate masses CGM inflows have a sonic radius at halo radii separating the two regimes. Bottom: Sonic radius of CGM inflows relative to $R_{\rm vir}$ versus halo mass and redshift, calculated using eqn. (\ref{['eq:r_sonic']}) with $Z=0.3Z_\odot$ and a CGM mass relative to the halo baryon budget of $0.5$ (black lines) or $0.2$ (gray line). We mark the typical circularization radius of CGM inflows at which the inflow halts and within which the galaxy forms.
• Figure 3: Idealized GIZMO simulations of turbulent accretion flows in $z=1$ halos with different masses. Panels show temperature (top) and density (bottom) in snapshots after the flow becomes quasi-steady. Black circles mark the virial radius (solid) and the inflow sonic radius (dashed). Arrows in the top panels mark projected velocity vectors. At $r<R_{\rm sonic}$ the CGM is predominantly cool by mass and exhibits large density fluctuations at a given radius.
• Figure 4: Formation of a turbulent CGM accretion flow. Panels show profiles of the turbulent velocity (top), average inflow velocity (bottom left), and geometric average sound speed (bottom right) versus time in the $10^{11.5}\,\mathrm M_{\odot}$, $z=1$ simulation. Initial conditions (yellow lines) are hydrostatic with a low turbulent velocity of $\approx20\,{\rm km}\,{\rm s}^{-1}$ at large radii $\gtrsim 100\,\rm kpc$. Within $\sim2\,{\rm Gyr}$ the turbulent velocity increases to $\sigma_{\rm t}\approx 100\,{\rm km}\,{\rm s}^{-1}\approx V_{\rm c}$ at small radii of$r\lesssim 30\,{\rm kpc}\approx R_\mathrm{sonic}$. The bottom panels show that at these radii the flow initially cools and free-falls with $|u_r|\approx 150-200\,{\rm km}\,{\rm s}^{-1}$, and then slows down to $\sim50\,{\rm km}\,{\rm s}^{-1}$ as turbulence develops. After $\approx3\,\mathrm{Gyr}$ all three velocity profiles remain constant with time indicating that the flow is quasi-steady.
• Figure 5: Radial profiles of characteristic velocities in turbulent CGM accretion. Panels show turbulent velocity (black), average inflow velocity (blue), and geometric average sound-speed (red) for simulations of $z=1$ and $M_{\text{halo}}= 10^{10.5}\,{\rm M}_\odot$ (left), $10^{11.5}\,{\rm M}_\odot$ (middle), $10^{12.5}\,{\rm M}_\odot$ (right) at snapshots after the flow becomes quasi-steady. Horizontal lines indicate the circular velocity. The sonic radius is on CGM scales in the $10^{10.5}$ and $10^{11.5}\,{\rm M}_\odot$ simulations. Within than $R_{\rm sonic}$ the inflows have $\sigma_{\rm t}\approx V_{\rm c}$, cool gas temperatures and constant inflow speeds, implying that the inflow is dominated by turbulence. Note that $\sigma_{\rm t}$ follows $u_r$ up to an order-unity factor in the $10^{11.5}\,{\rm M}_\odot$ simulation, and at small radii in the $10^{12.5}\,{\rm M}_\odot$ and $10^{10.5}\,{\rm M}_\odot$ simulations.