Ram pressure stripping is a hydrodynamical process occurring when galaxies traverse through a dense medium, typically the hot, tenuous plasma known as the intracluster medium (ICM) in galaxy clusters. This phenomenon plays a crucial role in galaxy evolution within dense environments, affecting gas dynamics, star formation, and overall galactic morphology. The process is fundamentally a result of the interaction between the interstellar medium (ISM) of a galaxy and the ICM, mediated by the relative motion between the two.
Ram pressure is the pressure exerted on a body moving through a fluid medium. In the context of galaxies, it is the pressure experienced by a galaxy's gas as it moves through the ICM. Quantitatively, ram pressure is defined as:
$$ P_{\text{ram}} = \rho_{\text{ICM}} v^2 $$Where $\rho_{\text{ICM}}$ is the density of the ICM and $v$ is the velocity of the galaxy relative to the ICM. This formulation stems from the concept of dynamic pressure in fluid dynamics. The quadratic dependence on velocity underscores the significant impact of a galaxy's speed on the stripping process.
The physical basis for this equation can be understood by considering the momentum transfer from the ICM to the galaxy's gas. As the galaxy moves through the ICM, it experiences a force per unit area (pressure) proportional to the rate of change of momentum of the ICM particles it encounters. This rate is proportional to both the number of particles encountered per unit time (related to $\rho_{\text{ICM}}$) and the momentum change per particle (proportional to $v$).
Gunn & Gott (1972) proposed a simplistic yet insightful criterion for the onset of ram pressure stripping. Stripping occurs when the ram pressure exceeds the gravitational restoring force per unit area:
$$ \rho_{\text{ICM}} v^2 > 2\pi G \Sigma_{\text{disk}} \Sigma_{\text{gas}} $$Where $G$ is the gravitational constant, $\Sigma_{\text{disk}}$ is the surface density of the galactic disk, and $\Sigma_{\text{gas}}$ is the surface density of the gas. This condition, while simplistic, provides valuable insight into the competing forces at play: the ram pressure pushing the gas out versus the gravitational force holding it in.
However, this condition assumes a thin, face-on disk and neglects the multiphase nature of the ISM. In reality, the ISM consists of a complex mixture of cold, warm, and hot gas phases, each responding differently to ram pressure. The cold, dense molecular clouds are more resistant to stripping than the diffuse, hot gas.
At the interface between the ICM and the ISM, Kelvin-Helmholtz instabilities can develop, enhancing gas stripping. These instabilities occur when there is velocity shear in a continuous fluid, or at the interface between two fluids moving at different velocities. The growth rate of these instabilities is given by:
$$ \omega = k \sqrt{\frac{\rho_1 \rho_2}{(\rho_1 + \rho_2)^2}} (v_1 - v_2) $$Where $k$ is the wavenumber of the instability, $\rho_1$ and $\rho_2$ are the densities of the two fluids, and $v_1$ and $v_2$ are their respective velocities. These instabilities can lead to mixing of the ICM and ISM, accelerating the stripping process.
The presence of magnetic fields in both the ICM and ISM can significantly alter the stripping process. Magnetic pressure, given by:
$$ P_B = \frac{B^2}{2\mu_0} $$Where $B$ is the magnetic field strength and $\mu_0$ is the permeability of free space, can provide additional support against stripping. Furthermore, magnetic draping can create a protective layer around the galaxy, modifying the effective ram pressure.
The interaction between the galaxy's magnetic field and the ICM's field can lead to complex dynamics, including magnetic reconnection events that can heat the gas and potentially enhance or inhibit stripping depending on the field configuration.
The Reynolds number in the ICM-ISM interaction region is typically very high, indicating highly turbulent flow. Turbulent viscosity can be estimated using models like the Smagorinsky model:
$$ \nu_t = (C_s \Delta)^2 \sqrt{2S_{ij}S_{ij}} $$Where $\nu_t$ is the turbulent viscosity, $C_s$ is the Smagorinsky constant, $\Delta$ is the filter width, and $S_{ij}$ is the strain rate tensor. Turbulence can enhance mixing and stripping, but it can also lead to the formation of eddies that can temporarily trap gas, complicating the stripping process.
The stripping radius, beyond which gas is removed from the galaxy, can be estimated by equating the ram pressure to the gravitational restoring force:
$$ R_{\text{strip}} = \frac{G M_{\text{disk}}(R) \Sigma_{\text{gas}}(R)}{v^2 \rho_{\text{ICM}}} $$Where $M_{\text{disk}}(R)$ is the enclosed disk mass at radius $R$. This radius depends on the galaxy's mass distribution, gas surface density, and the ICM properties. The stripping process typically proceeds from the outside in, as the outer regions of galaxies have lower surface densities and are thus more susceptible to stripping.
The mass loss rate due to ram pressure stripping can be approximated as:
$$ \dot{M} \approx \pi R_{\text{strip}}^2 \rho_{\text{ISM}} v $$Where $\rho_{\text{ISM}}$ is the density of the stripped ISM. This rate can vary significantly depending on the galaxy's properties and its trajectory through the cluster.
The stripped gas, heated by shocks and mixing with the ICM, can emit in X-rays. The X-ray luminosity $L_X$ can be estimated using the bremsstrahlung emission:
$$ L_X \propto n_e^2 T^{1/2} V $$Where $n_e$ is the electron density, $T$ is the temperature, and $V$ is the emitting volume. X-ray observations can reveal the morphology of the stripped gas and provide insights into its temperature and density.
The distribution of neutral hydrogen (H I) and molecular gas (traced by CO) can be used to map the extent of stripping. The H I deficiency parameter is defined as:
$$ \text{DEF}_{\text{HI}} = \log[M_{\text{HI,expected}}/M_{\text{HI,observed}}] $$Where $M_{\text{HI,expected}}$ is calculated based on the galaxy's optical properties in isolation. This parameter quantifies the degree of gas loss due to environmental effects, including ram pressure stripping.
Modern hydrodynamical simulations, such as those using adaptive mesh refinement (AMR) or smoothed particle hydrodynamics (SPH), have greatly advanced our understanding of ram pressure stripping. These simulations solve the compressible Euler equations:
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 $$ $$ \frac{\partial (\rho \mathbf{v})}{\partial t} + \nabla \cdot (\rho \mathbf{v} \otimes \mathbf{v} + P\mathbf{I}) = \rho \mathbf{g} $$ $$ \frac{\partial E}{\partial t} + \nabla \cdot [(E + P)\mathbf{v}] = \rho \mathbf{v} \cdot \mathbf{g} $$Where $\rho$ is density, $\mathbf{v}$ is velocity, $P$ is pressure, $E$ is total energy density, and $\mathbf{g}$ is the gravitational acceleration. These simulations can capture the complex interplay between hydrodynamics, gravity, and other physical processes, providing detailed insights into the stripping process.
Ram pressure stripping is a complex phenomenon involving the interplay of various physical processes across multiple scales. While significant progress has been made in understanding this mechanism, several open questions remain: