Velocity structure functions in multiphase turbulence: interpreting kinematics of Hα filaments in cool-core clusters

The central regions of cool-core galaxy clusters harbour multiphase gas, with gas temperatures ranging from $10$ to $10^7\, \mathrm{K}$. Feedback from active galactic nuclei jets prevents the gas from undergoing a catastrophic cooling flow. However, the exact mechanism of this feedback energy input is unknown, mainly due to the lack of velocity measurements of the hot-phase gas. However, recent observations have measured the velocity structure functions (VSFs) of the cooler molecular (${\sim} 10\, \mathrm{K}$) and Hα filaments (${\sim} 10^4\, \mathrm{K}$) and used them to indirectly estimate the motions of the hot phase. In the first part of this study, we conduct high-resolution (384³-1536³ resolution elements) simulations of homogeneous isotropic subsonic turbulence, without radiative cooling. We analyse the second-order velocity structure functions (VSF₂) in these simulations and study the effects of varying spatial resolution, the introduction of magnetic fields, and the effect of projection along the line of sight (LOS) on it. In the second part of the study, we analyse high-resolution (768³ resolution elements) idealized simulations of multiphase turbulence in the intracluster medium from the companion study Mohapatra et al. We compare the VSF₂ for both the hot ($T\sim 10^7\, \mathrm{K}$) and cold ($T\sim 10^4\, \mathrm{K}$) phases and find that their amplitude depends on the density contrast between the phases. They have similar scaling with separation, but introducing magnetic fields steepens the VSF₂ of only the cold phase. We also find that projection along the LOS steepens the VSF₂ for the hot phase and mostly flattens it for the cold phase.