论文标题
分层内培养基中的湍流密度和压力波动
Turbulent density and pressure fluctuations in the stratified intracluster medium
论文作者
论文摘要
在簇内培养基（ICM）中观察到湍流气体。 ICM是密度分层的，气体密度在簇的中心最高，并且向外降低。因此，Kolmogorov（均质，各向同性）湍流理论不适用于ICM。相反，气体运动是通过各向异性分层的湍流来解释的，分层由垂直的Froude编号（$ \ Mathrm {fr} _ \ perp $）量化。这些湍流运动与密度和压力波动有关，这些动作分别表现为ICM的X射线表面亮度图和热阳光Sunyaev-Zeldovich效应（SZ）波动的扰动。为了促进我们对这些波动和湍流气速之间关系的理解，我们进行了100个分层湍流的高分辨率流体动力模拟（$ 256^2 \ times 384 $ - $ 1024^2 \ times1536 $分辨率元素），我们在其中扫描了$ rms mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach Mach MACH MACH MACH MACE NUMBER的参数（M） $ \ mathrm {fr} _ \ perp $，以及与ICM相关的熵和压力比例高度的比率（$ r_p {ps} = h_p/h_s $）。我们在对数密度波动的标准偏差（$σ_s$，其中$ s = \ ln（ρ/\ left <ρ\ right>）$），$ \ mathcal {m} $之间，以及$ \ mathrm {fr} _ \ perp \ ll1 $：〜$σ_s^2 = \ ln \ left（1+b^2 \ mathcal {m}^4+0.10/（\ mathr m {fr} _ \ perp+0.25/\ sqrt {\ mathrm {fr} _ \ perp}）^2 \ mathcal {m}其中$ b \ sim1/3 $用于螺线管湍流驾驶。我们进一步发现，对数压力波动$σ_ {（\ ln {p}/\ left <p \ right>）} $独立于分层，并根据关系扩展$σ_ {（\ ln {\ bar {p}}）}^2 = \ ln \ left（1+b^2γ^2 \ Mathcal {m}^4 \ right）$，其中$ \ bar {p} = p/\ weft <p/\ weft <p \ p \ p \ p \ right> $ right> $ and $γ$是gasex的gasex exex exex exex exex。
Turbulent gas motions are observed in the intracluster medium (ICM). The ICM is density-stratified, with the gas density being highest at the centre of the cluster and decreasing radially outwards. As a result of this, Kolmogorov (homogeneous, isotropic) turbulence theory does not apply to the ICM. The gas motions are instead explained by anisotropic stratified turbulence, with the stratification quantified by the perpendicular Froude number ($\mathrm{Fr}_\perp$). These turbulent motions are associated with density and pressure fluctuations, which manifest as perturbations in X-ray surface brightness maps of the ICM and as thermal Sunyaev-Zeldovich effect (SZ) fluctuations, respectively. In order to advance our understanding of the relations between these fluctuations and the turbulent gas velocities, we have conducted 100 high-resolution hydrodynamic simulations of stratified turbulence ($256^2\times 384$ -- $1024^2\times1536$ resolution elements), in which we scan the parameter space of subsonic rms Mach number ($\mathcal{M}$), $\mathrm{Fr}_\perp$, and the ratio of entropy and pressure scale heights ($R_{PS}=H_P/H_S$), relevant to the ICM. We develop a new scaling relation between the standard deviation of logarithmic density fluctuations ($σ_s$, where $s=\ln(ρ/\left<ρ\right>)$), $\mathcal{M}$, and $\mathrm{Fr}_{\perp}$, valid till $\mathrm{Fr}_\perp\ll1$:~$σ_s^2=\ln\left(1+b^2\mathcal{M}^4+0.10/(\mathrm{Fr}_\perp+0.25/\sqrt{\mathrm{Fr}_\perp})^2\mathcal{M}^2R_{PS}\right)$, where $b\sim1/3$ for solenoidal turbulence driving studied here. We further find that logarithmic pressure fluctuations $σ_{(\ln{P}/\left<P\right>)}$ are independent of stratification and scale according to the relation $σ_{(\ln{\bar{P}})}^2=\ln\left(1+b^2γ^2\mathcal{M}^4\right)$, where $\bar{P}=P/\left<P\right>$ and $γ$ is the adiabatic index of the gas.
