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Register a new userGas Density Fluctuations in the Perseus Cluster: Clumping Factor and Velocity Power Spectrum
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X-ray surface brightness fluctuations in the core of the Perseus Cluster are analyzed, using deep observations with the Chandra observatory. The amplitude of gas density fluctuations on different scales is measured in a set of radial annuli. It varies from 8 to 12 per cent on scales of ~10-30 kpc within radii of 30-160 kpc from the cluster center and from 9 to 7 per cent on scales of ~20-30 kpc in an outer, 60-220 kpc annulus. Using a statistical linear relation between the observed amplitude of density fluctuations and predicted velocity, the characteristic velocity of gas motions on each scale is calculated. The typical amplitudes of the velocity outside the central 30 kpc region are 90-140 km/s on ~20-30 kpc scales and 70-100 km/s on smaller scales ~7-10 kpc. The velocity power spectrum is consistent with cascade of turbulence and its slope is in a broad agreement with the slope for canonical Kolmogorov turbulence. The gas clumping factor estimated from the power spectrum of the density fluctuations is lower than 7-8 per cent for radii ~30-220 kpc from the center, leading to a density bias of less than 3-4 per cent in the cluster core. Uncertainties of the analysis are examined and discussed. Future measurements of the gas velocities with the Astro-H, Athena and Smart-X observatories will directly measure the gas density-velocity perturbation relation and further reduce systematic uncertainties in these quantities.
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We investigate the power spectrum of velocity fluctuations in the universe, $V^2(k)$, starting from four different measures of velocity: (1) the power spectrum of velocity fluctuations from peculiar velocities of galaxies; (2) the rms peculiar velocity of galaxy clusters; (3) the power spectrum of velocity fluctuations from the power spectrum of density fluctuations in the galaxy distribution; (4) and the bulk velocity from peculiar velocities of galaxies. We show that measures (1) and (2) are not consistent with each other and either the power spectrum from peculiar velocities of galaxies is overestimated or the rms cluster peculiar velocity is underestimated. The amplitude of velocity fluctuations derived from the galaxy distribution (measure 3) depends on the parameter $beta$. We estimate the parameter $beta$ on the basis of measures (2) and (4). The power spectrum of velocity fluctuations from the galaxy distribution in the Stromlo-APM redshift survey is consistent with the observed rms cluster velocity and with the observed large-scale bulk flow when the parameter $beta$ is in the range 0.4-0.5. In this case the value of the function $V(k)$ at wavelength $lambda=120h^{-1}$Mpc is $sim 350$ km s$^{-1}$ and the rms amplitude of the bulk flow at the radius $r=60h^{-1}$ Mpc is $sim 340$ km s$^{-1}$. The velocity dispersion of galaxy systems originates mostly from the large-scale velocity fluctuations with wavelengths $lambda >100h^{-1}$ Mpc.
Extending the earlier measurements reported in Hitomi collaboration (2016, Nature, 535, 117), we examine the atmospheric gas motions within the central 100~kpc of the Perseus cluster using observations obtained with the Hitomi satellite. After correcting for the point spread function of the telescope and using optically thin emission lines, we find that the line-of-sight velocity dispersion of the hot gas is remarkably low and mostly uniform. The velocity dispersion reaches maxima of approximately 200~km~s$^{-1}$ toward the central active galactic nucleus (AGN) and toward the AGN inflated north-western `ghost bubble. Elsewhere within the observed region, the velocity dispersion appears constant around 100~km~s$^{-1}$. We also detect a velocity gradient with a 100~km~s$^{-1}$ amplitude across the cluster core, consistent with large-scale sloshing of the core gas. If the observed gas motions are isotropic, the kinetic pressure support is less than 10% of the thermal pressure support in the cluster core. The well-resolved optically thin emission lines have Gaussian shapes, indicating that the turbulent driving scale is likely below 100~kpc, which is consistent with the size of the AGN jet inflated bubbles. We also report the first measurement of the ion temperature in the intracluster medium, which we find to be consistent with the electron temperature. In addition, we present a new measurement of the redshift to the brightest cluster galaxy NGC~1275.
We address the problem of evaluating the power spectrum of the velocity field of the ICM using only information on the plasma density fluctuations, which can be measured today by Chandra and XMM-Newton observatories. We argue that for relaxed clusters there is a linear relation between the rms density and velocity fluctuations across a range of scales, from the largest ones, where motions are dominated by buoyancy, down to small, turbulent scales: $(deltarho_k/rho)^2 = eta_1^2 (V_{1,k}/c_s)^2$, where $deltarho_k/rho$ is the spectral amplitude of the density perturbations at wave number $k$, $V_{1,k}^2=V_k^2/3$ is the mean square component of the velocity field, $c_s$ is the sound speed, and $eta_1$ is a dimensionless constant of order unity. Using cosmological simulations of relaxed galaxy clusters, we calibrate this relation and find $eta_1approx 1 pm 0.3$. We argue that this value is set at large scales by buoyancy physics, while at small scales the density and velocity power spectra are proportional because the former are a passive scalar advected by the latter. This opens an interesting possibility to use gas density power spectra as a proxy for the velocity power spectra in relaxed clusters, across a wide range of scales.
X-ray surface brightness fluctuations in the core ($650 times 650$ kpc) region of the Coma cluster observed with XMM-Newton and Chandra are analyzed using a 2D power spectrum approach. The resulting 2D spectra are converted to 3D power spectra of gas density fluctuations. Our independent analyses of the XMM-Newton and Chandra observations are in excellent agreement and provide the most sensitive measurements of surface brightness and density fluctuations for a hot cluster. We find that the characteristic amplitude of the volume filling density fluctuations relative to the smooth underlying density distribution varies from 7-10% on scales of $sim$500 kpc down to $sim$5% at scales $sim$ 30 kpc. On smaller spatial scales, projection effects smear the density fluctuations by a large factor, precluding strong limits on the fluctuations in 3D. On the largest scales probed (hundreds of kpc), the dominant contributions to the observed fluctuations most likely arise from perturbations of the gravitational potential by the two most massive galaxies in Coma, NGC4874 and NGC4889, and the low entropy gas brought to the cluster by an infalling group. Other plausible sources of X-ray surface brightness fluctuations are discussed, including turbulence, metal abundance variations, and unresolved sources. Despite a variety of possible origins for density fluctuations, the gas in the Coma cluster core is remarkably homogeneous on scales from $sim$ 500 to $sim$30 kpc.
Cores of relaxed galaxy clusters are often disturbed by AGN. Their Chandra observations revealed a wealth of structures induced by shocks, subsonic gas motions, bubbles of relativistic plasma, etc. In this paper, we determine the nature and energy content of gas fluctuations in the Perseus core by probing statistical properties of emissivity fluctuations imprinted in the soft- and hard-band X-ray images. About 80 per cent of the total variance of perturbations on ~ 8-70 kpc scales in the inner region have an isobaric nature, i.e., are consistent with slow displacements of the gas in pressure equilibrium with ambient medium. Observed variance translates to the ratio of non-thermal to thermal energy of ~13 per cent. In the region dominated by weak ripples, about half of the total variance is also associated with isobaric perturbations on scales ~ a few tens of kpc. If these isobaric perturbations are induced by buoyantly rising bubbles, then these results suggest that most of the AGN-injected energy should first go into bubbles rather than into shocks. Using simulations of a shock propagating through the Perseus atmosphere, we found that models reproducing the observed features of a central shock have more than 50 per cent of the AGN-injected energy associated with the bubble enthalpy and only about 20 per cent is carried away with the shock. Such energy partition is consistent with the AGN-feedback model, mediated by bubbles of relativistic plasma, and supports the importance of turbulence in the balance between gas heating and radiative cooling.
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