Direct Detection of Black Hole-driven Turbulence in the Centers of Galaxy Clusters

Relaxed galaxy clusters often harbor a cool core, where radiative cooling of the intracluster medium (ICM) is expected to result in cooling flows of hundreds of ${M}_{\odot }\,{\mathrm{yr}}^{-1}$ in the absence of heating (Fabian 1994). Feedback from active galactic nuclei (AGNs) in forms of jets, radiation, and fast outflows is thought to provide the energy to balance radiative cooling and suppress star formation (McNamara et al. 2005). X-ray observations show that AGN feedback generates "bubbles" and "ripples" in the surrounding ICM (Fabian 2012). Based on X-ray measurements of line widths (Hitomi Collaboration et al. 2016) and surface brightness fluctuations (Zhuravleva et al. 2014, 2016), it is suggested that cluster cores are turbulent. However, current X-ray observatories have limited spatial and spectral resolutions, making it impossible to probe turbulence directly, let alone its drivers.

The centers of cool-core clusters also frequently exhibit extended filamentary structures that can be seen in the Hα (Conselice et al. 2001; Olivares et al. 2019) and sometimes CO (Edge 2001; McNamara et al. 2014). The existence of cold filaments has been linked to the activities of supermassive black holes (SMBHs) in the centers of galaxy clusters (Cavagnolo et al. 2008; Tremblay et al. 2016), and the ensemble velocity dispersion of the filaments has a similar amplitude as the mean line of sight velocity dispersion of the hot ICM (Gaspari et al. 2018; Gendron-Marsolais et al. 2018). The filaments often show perturbed kinematics and a lack of ordered motion on large scales (Sarzi et al. 2006; Olivares et al. 2019). In other words, the motion of the filaments appears turbulent.

In this work, we study the turbulent nature of multiphase filaments by measuring their velocity structure functions (VSFs) in three nearby galaxy clusters: Perseus, A2597, and Virgo. We describe the data and data processing in Section 2. In Section 3, we connect the turbulent motions of the filaments to the activities of SMBHs, and compare our measurements with the X-ray analysis. In Section 4, we discuss the puzzling features of the VSFs, the uncertainties of the analysis, and the implications of our results, including constraints on microscopic physics of the ICM. We conclude this work in Section 5.

The Perseus Hα filaments were observed using the optical imaging Fourier transform spectrometer SITELLE at the Canada–France–Hawaii Telescope (CFHT; Gendron-Marsolais et al. 2018). SITELLE has a spatial resolution of 0321 × 0321, and a spectral resolution of R = 1800. The original Perseus data cube was binned up by a factor of 2 to increase the signal-to-noise ratio. The ionized filaments in Virgo and A2597 was observed using the Multi Unit Spectroscopic Explorer (MUSE) with a spatial sampling of 02 and a spectral resolution of R = 3000 (Sarzi et al. 2018; Tremblay et al. 2018; Boselli et al. 2019). For Perseus and Virgo, the velocity in each pixel of the velocity map is obtained as the peak of a Gaussian profile fit to the Hα + N ii complex, and for A2597, only Hα is used in the fit. In Perseus, a small region in the center with a radius of 6'' is excluded from the fitting due to contamination from the AGN (Gendron-Marsolais et al. 2018). The molecular gas in A2597 and Virgo was observed using the Atacama Large Millimeter/submillimeter Array (ALMA) with a spatial resolution of 037 (Simionescu et al. 2018; Tremblay et al. 2018). See Table 1 for a summary of data.

To understand the nature of the motion of these filaments, we compute the VSFs for all three clusters. We first remove a small fraction (<20%) of pixels with large velocity errors, shown in the top panels of Figure 1. We have visually examined pixels with very large velocity errors, and found that they tend to be located either at the edge of filaments or in isolation with an appearance similar to noise (even though it could be from a real gas cloud that is very faint and poorly resolved). Therefore, it is sensible to remove these pixels. The value of the velocity error cut is chosen to be a few times the median velocity error for each cluster. We have verified that the results are not sensitive to the exact choice of this value. For Perseus, an additional flux cut is applied to remove pixels with low signal-to-noise (Gendron-Marsolais et al. 2018).

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For each clean velocity map, we compute the first-order VSF in the following way: for each pair of pixels, we record the projected physical separation ℓ of the pair and compute the velocity difference δv of the two pixels. The bottom panels of Figure 1 show the distribution of ℓ. We then compute the average absolute value of the velocity differences $\langle | \delta v| \rangle$ within bins of ℓ. The uncertainties in the VSFs are obtained by propagating the measurement errors.

The left panels of Figure 2 show the velocity maps of the Hα filaments in Perseus, A2597, and Virgo. The right panels show the corresponding VSFs. A broad power-law slope confirms the visual impression that the gas motion is turbulent. The VSFs of all three clusters show a flattening on scales above a characteristic pair separation, ranging from ∼10 kpc (for Perseus) to ∼1–2 kpc (for Virgo). The flattening of VSF indicates that this is the dominant driving scale of turbulence. Right below this characteristic scale, the slope of the VSF is ∼1/3, and is consistent with the expectation of classical Kolmogorov turbulence for an incompressible fluid. On smaller scales, the slopes appear to be steeper, and vary from cluster to cluster (see Section 4.1 for more discussions).

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To better reveal the driving source of turbulence, we divide the filaments in Perseus into inner (r < 12 kpc) and outer filaments (r > 12 kpc). We choose this dividing radius r = 12 kpc such that there are comparable total numbers of pixels in the inner and the outer regions. We have verified that the results are not sensitive to the exact value of this radius.

As the top-right panel of Figure 2 shows, the VSF of the inner filaments shows a similar shape as the VSF of all the filaments, but a larger amplitude and a more prominent break at r ≲ 10 kpc. This is roughly the size of the inner X-ray bubbles of Perseus (Fabian et al. 2003), suggesting that the driver of turbulence is AGN feedback. On the other hand, the VSF of the outer filaments does not show a clear break at such a scale. Instead, the power continues to rise toward larger scales. This suggests that the outer filaments likely probe turbulence driven on larger scales. The VSF shows a bump at 20–30 kpc, which is roughly the size of the outer bubble (Fabian et al. 2003). Thus it is possible that the turbulent motion of the outer filaments in Perseus is mainly caused by previous AGN outbursts. However, with current measurements, we cannot rule out the possibility that this area is dominated by turbulence driven by large-scale structure formation (e.g., sloshing; Ryu et al. 2008; ZuHone et al. 2018).

Hitomi has measured the line-of-sight velocity dispersion in the core of Perseus at much lower spatial resolution (Hitomi Collaboration et al. 2016). Our measured velocities at and above the driving scale for the inner and outer filaments agree with the Hitomi measurements of the inner and outer regions (Hitomi Collaboration et al. 2018) of the Perseus core (Figure 3). In addition, the VSF of the outer filaments shows remarkable agreement with that inferred from the analysis of X-ray surface brightness fluctuations of similar regions (Zhuravleva et al. 2014) (see Appendix for detail).

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The inner filaments of A2597 reveal a driving scale of ∼4 kpc (middle panels of Figure 2), which is also seen in the VSF of the molecular gas observed by ALMA. The driving scale is again consistent with the size of the inner X-ray bubbles filled with radio-emitting plasma (Tremblay et al. 2012). For the outer filaments of A2597, the power continues to rise toward larger separations. There is a clear bump between 20 and 30 kpc, which is roughly the distance to the outer X-ray bubbles that are visible on the X-ray map. This feature is also seen in the VSF of the molecular gas. The X-ray observations of A2597 show many shocks, bubbles, and ripples (Tremblay et al. 2012). It is likely that AGN-driven turbulence dominates the entire central region of A2597.

In Virgo (bottom panels of Figure 2), we again see a clear connection between AGN feedback and turbulence. The inferred driving scale in the center of Virgo is between 1 and 2 kpc, which is the size of the bright AGN jet (Marshall et al. 2002; the linear X-ray feature extending to the right) and also the jet-driven bubble. ALMA has observed a molecular complex located around the lower-left corner of the map (Simionescu et al. 2018), and the measured velocity dispersion is in good agreement with our results.

For all three clusters, the inferred driving scale is consistent with the scenario that AGN feedback is the main driver of turbulence in the centers of galaxy clusters. In addition, the amplitude of the turbulent motion revealed by the VSF is also consistent with this scenario. The largest velocity caused by AGN feedback is roughly the velocity of the post-shock material, which is $\tfrac{3}{2}(M-1){c}_{{\rm{s}}}$ with M being the Mach number of the shock and c_s being the sound speed of the ICM (Li et al. 2017). The measured M in these clusters is ∼1.1–1.2 (Tremblay et al. 2012; Forman et al. 2017), and c_s is a few hundred km s⁻¹. Therefore, the post-shock velocities are ∼100–200 km s⁻¹. If turbulence is driven by buoyantly rising bubbles, the largest velocities should be the velocities of the bubbles, which are also expected to be a fraction of the sounds speed (Robinson et al. 2004).

4.1. The Steepening of the VSF

4.2. Limitations and Uncertainties

4.3. Implications

Our results suggest that the motion of cold filaments is well-coupled with the hot ICM. The origin of the Hα filaments and their fate are still uncertain, but two scenarios would allow the filaments to share the same turbulent motion of the hot ICM: (1) if they originate from the hot gas, either due to thermal instabilities or induced cooling (McCourt et al. 2012; Li & Bryan 2014; Li et al. 2019), but are very short-lived (dissolve quickly) such that they keep the memory of the turbulent motion of the hot gas, and/or (2) if they are very "misty" and quickly become co-moving with the hot gas (McCourt et al. 2018) even if they are created independently of it (Qiu et al. 2019). On the other hand, if the cold gas is poorly coupled to the hot gas and follows ballistic trajectories, neighboring cold filaments would move independently and show little kinematic correlation. The measured VSF on small scales would be flatter than Kolmogorov, and certainly flatter than what is measured here.

In addition, we can use the turbulent motion of the cold gas to put constraints on microscopic transport processes in the hot ICM. Figure 4 shows velocities as a function of scales normalized by the Kolmogorov microscales. The Kolmogorov microscale where the turbulent kinetic energy is dissipated into heat, and is calculated as $\eta ={\left(\tfrac{{\nu }^{3}}{\epsilon }\right)}^{1/4}$, where ν is the kinematic viscosity and is the energy dissipation rate. The dynamic viscosity μ, which is related to the kinetic viscosity as μ = ρν, can be estimated as

$$\begin{eqnarray}&&\mu =5500\,{\rm{g}}\,{\mathrm{cm}}^{-1}\,{{\rm{s}}}^{-1}{\left(\displaystyle \frac{{T}_{{\rm{e}}}}{{10}^{8}{\rm{K}}}\right)}^{5/2}{\left(\displaystyle \frac{\mathrm{ln}{\rm{\Lambda }}}{40}\right)}^{-1}\end{eqnarray} \tag{ 1 }$$

where ln Λ is the Coulomb logarithm (Sarazin 1988). We estimate based on our measured VSF on small scales, which is slightly different from estimated using velocities at the driving scale because the slopes of the VSFs are steeper than Kolmogorov. For gas properties, we use T_e = 3 keV and ${n}_{{\rm{e}}}=0.02\,{\mathrm{cm}}^{-3}$ for Perseus (Churazov et al. 2004); for A2597, we use T_e = 2.7 keV and ${n}_{{\rm{e}}}=0.06\,{\mathrm{cm}}^{-3}$ (Tremblay et al. 2012); for Virgo, we use T_e = 1.6 keV and ${n}_{{\rm{e}}}=0.1\,{\mathrm{cm}}^{-3}$ (Zhuravleva et al. 2014).

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According to direct numerical simulations (Ishihara et al. 2016), the gas viscosity affects pure hydrodynamic turbulence on scales that are larger than the Kolmogorov microscale (dashed gray line in Figure 4). Our detection of turbulence near and below the Kolmogorov microscale suggests that isotropic viscosity is suppressed in the ICM.

For comparison, we also plot in Figure 4 the measurement for Perseus using the X-ray surface brightness analysis, which assumes that density fluctuations follow the velocity field. Using the optical data, we are able to probe scales more than an order of magnitude smaller than X-ray observations of the same cluster. In fact, the electron mean free paths in the centers of Perseus and Virgo are ∼80 pc and ∼8 pc, respectively, about 1/3–1/2 the size of our resolution in the two clusters.

Figure 4 also includes the best X-ray constraint on viscosity obtained from deep Chandra observations of the Coma cluster (Zhuravleva et al. 2019), where the mean free paths and the Kolmogorov microscales are larger. Our analysis based on the optical data probes the velocity field directly, and shows remarkable agreement with the conclusion of the X-ray surface brightness analysis. Both measurements support suppressed effective viscosity in the bulk intergalactic plasma, suggesting that the microphysics of the ICM is driven by magnetic fields operating below the Coulomb mean free path.

4.4. Turbulence as a Heating Source

Our study demonstrates the power of high-resolution integral field unit observations in helping us understand the kinematics of multiphase gas. We show that AGN feedback is the main driver of turbulence in the centers of galaxy clusters. The result naturally serves as a test for numerical models of AGN feedback. In addition, it also serves as an excellent test for models of cool gas. Our detection of turbulence near the mean free path of the ICM supports suppressed effective viscosity. The slope of the VSF on small scales deviates from the classical Kolmogorov expectation, and points out directions for future theoretical and observational investigations.

We would like to thank Paul Duffell, Peng Oh, Christopher Reynolds, Anna McLeod, and Andrea Antoni for helpful discussions. This work was partly performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. We acknowledge the technical support from the Scientific Computing Core of the Simons Foundation.

We use deep Chandra observations of the Perseus cluster available in the archive. The initial data processing was done following the standard procedure (Vikhlinin et al. 2005) that includes the filtering of high background periods, calculating the background intensity in each observation and application of the latest calibration corrections. The point sources are detected using the wvdecomp tool, and their significance are verified (Zhuravleva et al. 2015). These point sources are excised from the image accounting for the Chandra point-spread function (PSF). The residual image of the cluster (the image of fluctuations) is obtained from the initial cluster image divided by the best-fitting model of the mean surface brightness profile. We calculate the power spectrum of the X-ray surface brightness fluctuations using the modified Δ-variance method, which is suitable for non-periodic images with gaps (Arévalo et al. 2012). We re-project the spectra, correct them for the PSF and the unresolved point sources (Churazov et al. 2012). For Perseus, we analyzed the images in the 0.5–3.5 keV band. In this band, the resulting spectrum of fluctuations gives the 3D power spectrum of density fluctuations. Using a statistical linear relation between the power spectrum of density fluctuations and velocity (Gaspari et al. 2014; Zhuravleva et al. 2014), we obtained the power spectrum of gas motions in Perseus.

The innermost $r\lesssim 25\,\mathrm{kpc}$ region is dominated by the prominent structures associated with the bubbles of relativistic plasma and shocks around them (Zhuravleva et al. 2015). Therefore, we carefully select the region where the dynamics of the hot X-ray gas is probed. This region is shown in Figure 5. We effectively use fluctuations in the annulus ∼25–40 kpc. We additionally check the nature of fluctuations in this region (Arévalo et al. 2016; Churazov et al. 2016; Zhuravleva et al. 2016) and confirm that most fluctuations in these regions are of isobaric nature.

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