Magnetohydrodynamic Precipitation

Abstract

Circumgalactic gas around massive galaxies generally has a volume-filling component -- an atmosphere -- with a temperature determined by the potential-well depth of the galaxy's halo. If the atmosphere is near hydrostatic equilibrium and is stable to convection, then it can remain nearly homogeneous, as long as it is not too dense. But if its density is great enough, it becomes prone to producing a rain of cold clouds that fall toward the galaxy's center and accrete onto its central black hole. Here we explain how relatively weak magnetic fields enhance a galactic atmosphere's tendency to produce cold clouds and how the cold gas becomes organized into vertically elongated, highly magnetized filaments descending at sub-Keplerian speeds. It is intended to complement recent numerical simulations of the process and to serve as a guide to interpreting both simulations and observations of the filamentary gas in hot galactic atmospheres.

Figures (10)

• Figure 1: Schematic illustration of an evolving entropy perturbation in a stratified atmosphere. Shading represents the background entropy gradient $\nabla \ln K_0$, which is vertical. A perturbation initially at location $\mathbf{r}_0$ begins with an entropy difference $\Delta_K$ relative to the background atmosphere at that location. Unperturbed gas starting at the same place would have moved with velocity $\tilde{\mathbf{v}}$ but the perturbed gas moves with velocity $\mathbf{v}$. The perturbation's displacement $\boldsymbol{\xi}$ relative to the unperturbed flow therefore changes with time, and so its entropy contrast $\delta_K$ relative to neighboring gas depends on evolution of both the intrinsic entropy difference $\Delta_K$ and the extrinsic entropy change $\boldsymbol{\xi} \cdot \nabla \ln K_0$.
• Figure 2: Schematic illustration of a thermally unstable entropy perturbation in a stratified atmosphere with $\tilde{\omega}_\mathrm{BV} > \omega_\mathrm{ti}$. Shading represents the background entropy gradient, which increases in a direction opposite to the effective gravitational acceleration $\mathbf{\tilde{g}}$. A low-entropy perturbation initially at location $\mathbf{r}_0$ accelerates downward and overshoots the layer at which its entropy contrast is zero $(\delta_K = 0)$. Its entropy contrast then becomes positive, and so it starts to accelerate upward, resulting in oscillations with a frequency approximately equal to $\tilde{\omega}_\mathrm{BV}$. As $\delta_K$ oscillates, the perturbation's intrinsic entropy difference $\Delta_K$ also oscillates, with an amplitude ratio $|\Delta_K|/|\delta_K| \sim \omega_\mathrm{ti}/\tilde{\omega}_\mathrm{BV}$, and thermal pumping causes the amplitudes of both $\delta_K$ and $\Delta_K$ to grow at a rate similar to $\omega_\mathrm{ti}$. However, nonlinear saturation ultimately limits growth of $\delta_K$ in atmospheres with $\tilde{\omega}_\mathrm{BV} \gg \omega_\mathrm{ti}$, for reasons discussed in Appendix \ref{['app:gMode_Saturation']}.
• Figure 3: Schematic illustration of linear magnetothermal drip in a stratified atmosphere with a uniform horizontal background magnetic field ($\mathbf{B}_0$, grey dotted line). Vertical displacement ($\xi_\parallel$, solid red line), entropy contrast ($\delta_K$), and vertical magnetic field strength ($B_\parallel$) all steadily grow on a thermal-instability timescale similar to the cooling time when magnetic acceleration ($k_\perp^2 v_{\rm A}^2 \xi_\parallel$) nearly offsets buoyant acceleration ($\tilde{g} \delta_K / \gamma$).
• Figure 4: Schematic illustration of nonlinear magnetothermal drip in a stratified atmosphere with a uniform horizontal magnetic field of strength $B_0$. A solid red line shows vertical displacement ($\xi_\parallel$), relative to the unperturbed background state. Growth and descent of a nonlinear density perturbation ($\delta \rho / \rho$) has pulled the magnetic field lines threading it downward, and simultaneous amplification of the vertical magnetic field ($B_\parallel$) has kept it strong enough to counteract negative buoyancy. Low-entropy gas in the perturbation has become more compressed because of both entropy losses and descent through higher-pressure layers. Meanwhile, higher entropy gas has become less compressed because it has ascended to lower-pressure layers. The magnetic field lines and displacements of an originally sinusoidal perturbation consequently become asymmetric.
• Figure 5: Schematic illustration of perturbations in a stratified atmosphere with a uniform vertical magnetic field of strength $B_0$ (dotted black lines). Solid red lines show horizontal displacement ($\xi_\perp$), relative to the unperturbed background state. Smaller red arrows show the pattern of horizontal and vertical displacements around the central pressure perturbation. Magnetic acceleration of magnitude $k_\parallel^2 v_{\rm A}^2 \xi_\perp$ is resisting the diverging horizontal flow. On the left side, showing a case with $\omega^2 < \omega_{\rm A,\perp}^2$, the central pressure perturbation is positive, because the vertical field successfully resists horizontal divergence. The pressure perturbation therefore inhibits descent of lower-entropy gas lying above it and enables its entropy contrast to grow. On the right side, showing a faster mode with $\omega^2 > \omega_{\rm A,\perp}^2$, horizontal divergence causes the central pressure perturbation to be negative, and it does not resist descent of the gas lying above it.