Surface Brightness Fluctuations Research Articles

Constraining Gas Motions in the Intra-Cluster Medium

The detailed velocity structure of the diffuse X-ray emitting intra-cluster medium (ICM) remains one of the last missing key ingredients in understanding the microphysical properties of these hot baryons and constraining our models of the growth and evolution of structure on the largest scales in the Universe. Direct measurements of the gas velocities from the widths and shifts of X-ray emission lines were recently provided for the central region of the Perseus Cluster of galaxies by $Hitomi$, and upcoming high-resolution X-ray microcalorimeters onboard $XRISM$ and $Athena$ are expected to extend these studies to many more systems. In the mean time, several other direct and indirect methods have been proposed for estimating the velocity structure in the ICM, ranging from resonant scattering to X-ray surface brightness fluctuation analysis, the kinematic Sunyaev-Zeldovich effect, or using optical line emitting nebulae in the brightest cluster galaxies as tracers of the motions of the ambient plasma. Here, we review and compare the existing estimates of the velocities of the hot baryons, as well as the various overlapping physical processes that drive motions in the ICM, and discuss the implications of these measurements for constraining the viscosity and identifying the source of turbulence in clusters of galaxies.

Turbulence in the intracluster medium: simulations, observables, and thermodynamics

We conduct two kinds of homogeneous isotropic turbulence simulations relevant for the intracluster medium (ICM): (i) pure turbulence runs without radiative cooling; (ii) turbulent heating$+$radiative cooling runs with global thermal balance. For pure turbulence runs in the subsonic regime, the rms density and surface brightness (SB) fluctuations vary as the square of the rms Mach number ($\mathcal{M}_{\text{rms}}$). However, with thermal balance, the density and SB fluctuations $(\delta SB/SB)$ are much larger. These scalings have implications for translating SB fluctuations into a turbulent velocity, particularly for cool cores. For thermal balance runs with large (cluster core) scale driving, both the hot and cold phases of the gas are supersonic. For small scale (one order of magnitude smaller than the cluster core) driving, multiphase gas forms on a much longer timescale but $\mathcal{M}_{\text{rms}}$ is smaller. Both small and large scale driving runs have velocities larger than the Hitomi results from the Perseus cluster. Thus turbulent heating as the dominant heating source in cool cluster cores is ruled out if multiphase gas is assumed to condense out from the ICM. Next we perform thermal balance runs in which we partition the input energy into thermal and turbulent parts and tune their relative magnitudes. The contribution of turbulent heating has to be $\lesssim 10\%$ in order for turbulence velocities to match Hitomi observations. If the dominant source of multiphase gas is not cooling from the ICM (but say uplift from the central galaxy), the importance of turbulent heating cannot be excluded.

Substructures associated with the sloshing cold front in the Perseus cluster

X-ray substructures in clusters of galaxies provide indirect clues about the microphysical properties of the intracluster medium (ICM), which are still not very well known. In order to investigate X-ray substructures in detail, we studied archival $\sim$1~Msec Chandra data of the core of the Perseus cluster, focusing on the substructures associated with the sloshing cold front. In the east half of the cold front, we found a Kelvin-Helmholtz instability (KHI) layer candidate. The measured width-to-azimuthal extension ratio and the thermodynamic properties are all consistent with it being a KHI layer currently developing along the sloshing cold front. We found a thermal pressure deficit of the order of 10$^{-2}~\mathrm{keV~cm^{-3}}$ at the KHI layer. Assuming that turbulent pressure fully supports the pressure deficit, we estimated the turbulent strength at several hundred km~s$^{-1}$, which translates into the turbulent heating rate of $Q_\mathrm{turb}\sim 10^{-26}~\mathrm{erg~cm^{-3}~s^{-1}}$. This value agrees within an order of magnitude with the previous estimation derived from the surface brightness fluctuations, and can balance the radiative cooling at this radius. In the west half of the cold front, we found feather-like structures which are similar to the structures observed in recent numerical simulations of the gas sloshing of magnetized plasma. Their thermodynamic properties are consistent with one of the feathers being a projected gas depletion layer induced by the amplified magnetic field whose strength is $B\sim$30$~\mathrm{\mu G}$.

The Dragonfly Nearby Galaxies Survey. V. HST/ACS Observations of 23 Low Surface Brightness Objects in the Fields of NGC 1052, NGC 1084, M96, and NGC 4258

Abstract We present Hubble Space Telescope/Advanced Camera for Surveys (ACS) imaging of 23 very low surface brightness (μ e,V ∼ 25–27.5) galaxies detected in the fields of four nearby galaxy groups. These objects were selected from deep optical imaging obtained with the Dragonfly Telephoto Array. Seven are newly identified, while most of the others had been seen previously in visual surveys of deep photographic plates and more recent surveys. Few have previously been studied in detail. From the ACS images, we measure distances to the galaxies using both the tip of the red giant branch method and the surface brightness fluctuations method. We demonstrate that the two methods are consistent with each other in the regime where both can be applied. The distances to 15 out of 20 galaxies with stable measurements are consistent with that of the targeted group within errors. This suggests that assuming group membership based solely on projected proximity is ∼75% successful in this regime. The galaxies are nearly round, with a median axis ratio of 0.85, and visually resemble dwarf spheroidal galaxies. The objects have a range of sizes, from R e = 0.4 kpc to R e = 1.8 kpc, with a median . They range in luminosity from M V = −11.4 to M V = −15.6, with a median . Galaxies with R e ∼ 1 kpc and M V ∼ −12 are fairly rare in the Local Group, but we find many of them in this relatively small sample. Four of the objects fall in the class of ultra-diffuse galaxies, with R e > 1.5 kpc and μ 0,V > 24 mag arcsec−2, including the recently identified dark matter deficient galaxy NGC 1052-DF2.

Gas Perturbations in the Cool Cores of Galaxy Clusters: Effective Equation of State, Velocity Power Spectra, and Turbulent Heating

Abstract We present the statistical analysis of X-ray surface brightness and gas density fluctuations in the cool cores of 10 nearby, X-ray-bright galaxy clusters that have deep Chandra observations and show observational indications of radio-mechanical active galactic nucleus (AGN) feedback. Within the central parts of the cool cores, the total variance of fluctuations is dominated by isobaric and/or isothermal fluctuations on spatial scales ∼10–60 kpc, which are likely associated with slow gas motions and bubbles of relativistic plasma. Adiabatic fluctuations, associated with weak shocks and/or sonic turbulence, constitute less than 10% of the total variance in all clusters. The typical amplitude of density fluctuations is small, ∼10% or less on scales of ∼10–15 kpc. The observed subdominant contribution of adiabatic fluctuations and the small amplitude of density fluctuations support a model of gentle AGN feedback. The measured one-component velocities of gas motions are typically below 100–150 km s−1 on scales <50 kpc and can be up to ∼300 km s−1 on ∼100 kpc scales. The nonthermal energy is <12% of the thermal energy. Regardless of the source that drives these motions, the dissipation of the energy in such motions provides heat that is sufficient to balance radiative cooling on average, albeit with significant uncertainties. The results presented here support previous conclusions based on the analysis of the Virgo and Perseus Clusters and agree with the Hitomi measurements. With next-generation observatories like Athena and Lynx, these techniques will be yet more powerful.

The Distance of the Dark Matter Deficient Galaxy NGC 1052–DF2

Abstract We recently inferred that the galaxy NGC 1052–DF2 has little or no dark matter and a rich system of unusual globular clusters. We assumed that the galaxy is a satellite of the luminous elliptical galaxy NGC 1052 at ≈20 Mpc, on the basis of its surface brightness fluctuations (SBFs) distance of 19.0 ± 1.7 Mpc, its radial velocity of ≈1800 km s−1, and its projected position. Here we analyze the color–magnitude diagram (CMD) of NGC 1052–DF2, following the suggestion by Trujillo et al. that the tip of the red giant branch (TRGB) can be detected in currently available Hubble Space Telescope (HST) data and the galaxy is at ∼13 Mpc. Using fully populated galaxy models we show that the CMD is strongly influenced by blends. These blends produce a “phantom” TRGB ∼2 times brighter than the true TRGB, which can lead to erroneous distance estimates ∼1.4 times smaller than the actual distance. We compare NGC 1052–DF2 to model images as well as other galaxies in our HST sample, and show that the large population of unblended RGB stars expected for distances of ∼13 Mpc is not detected. We also provide a new distance measurement to NGC 1052–DF2 that is free of calibration uncertainties, by anchoring it to a satellite of the megamaser host galaxy NGC 4258. From a megamaser-TRGB-SBF distance ladder we obtain D = 18.7 ± 1.7 Mpc, consistent with our previous measurement and with the distance to the elliptical galaxy NGC 1052.

Mid-IR colors and surface brightness fluctuations as tracers of stellar mass-loss in the TP-AGB

AbstractI present integrated colors and surface brightness fluctuation magnitudes in the mid-IR, derived from stellar population synthesis models that include the effects of the dusty envelopes around TP-AGB stars. The models are based on the Bruzual & Charlot CB* isochrones; they are single-burst, range in age from a few Myr to 14 Gyr, and comprise metallicities between Z = 0.0001 and Z = 0.04. I compare these models to mid-IR data of AGB stars and star clusters in the Magellanic Clouds, and study the effects of varying self-consistently the mass-loss rate, the stellar parameters, and the output spectra of the stars plus their dusty envelopes.

Surface brightness fluctuation spectrum: a new probe of evolved stars in unresolved stellar populations

Surface brightness fluctuation spectrum: a new probe of evolved stars in unresolved stellar populations

Tracers of Stellar Mass-loss. II. Mid-IR Colors and Surface Brightness Fluctuations

Abstract I present integrated colors and surface brightness fluctuation magnitudes in the mid-infrared (IR), derived from stellar population synthesis models that include the effects of the dusty envelopes around thermally pulsing asymptotic giant branch (TP-AGB) stars. The models are based on the Bruzual & Charlot CB* isochrones; they are single-burst, range in age from a few Myr to 14 Gyr, and comprise metallicities between Z = 0.0001 and Z = 0.04. I compare these models to mid-IR data of AGB stars and star clusters in the Magellanic Clouds, and study the effects of varying self-consistently the mass-loss rate, the stellar parameters, and the output spectra of the stars plus their dusty envelopes. I find that models with a higher than fiducial mass-loss rate are needed to fit the mid-IR colors of “extreme” single AGB stars in the Large Magellanic Cloud. Surface brightness fluctuation magnitudes are quite sensitive to metallicity for 4.5 μm and longer wavelengths at all stellar population ages, and powerful diagnostics of mass-loss rate in the TP-AGB for intermediate-age populations, between 100 Myr and 2–3 Gyr.

The Next Generation Virgo Cluster Survey (NGVS). XVIII. Measurement and Calibration of Surface Brightness Fluctuation Distances for Bright Galaxies in Virgo (and Beyond)

Abstract We describe a program to measure surface brightness fluctuation (SBF) distances to galaxies observed in the Next Generation Virgo Cluster Survey (NGVS), a photometric imaging survey covering 104 deg2 of the Virgo cluster in the u*, g, i, and z bandpasses with the Canada–France–Hawaii Telescope. We describe the selection of the sample galaxies, the procedures for measuring the apparent i-band SBF magnitude , and the calibration of the absolute as a function of observed stellar population properties. The multiband NGVS data set provides multiple options for calibrating the SBF distances, and we explore various calibrations involving individual color indices as well as combinations of two different colors. Within the color range of the present sample, the two-color calibrations do not significantly improve the scatter with respect to wide-baseline, single-color calibrations involving u*. We adopt the calibration as a reference for the present galaxy sample, with an observed scatter of 0.11 mag. For a few cases that lack good u* photometry, we use an alternative relation based on a combination of and colors, with only a slightly larger observed scatter of 0.12 mag. The agreement of our measurements with the best existing distance estimates provides confidence that our measurements are accurate. We present a preliminary catalog of distances for 89 galaxies brighter than B T ≈ 13.0 mag within the survey footprint, including members of the background M and W Clouds at roughly twice the distance of the main body of the Virgo cluster. The extension of the present work to fainter and bluer galaxies is in progress.

A Precise Distance to the Host Galaxy of the Binary Neutron Star Merger GW170817 Using Surface Brightness Fluctuations∗

Abstract The joint detection of gravitational waves (GWs) and electromagnetic radiation from the binary neutron star (BNS) merger GW170817 has provided unprecedented insight into a wide range of physical processes: heavy element synthesis via the r-process; the production of relativistic ejecta; the equation of state of neutron stars and the nature of the merger remnant; the binary coalescence timescale; and a measurement of the Hubble constant via the “standard siren” technique. In detail, all of these results depend on the distance to the host galaxy of the merger event, NGC 4993. In this Letter we measure the surface brightness fluctuation (SBF) distance to NGC 4993 in the F110W and F160W passbands of the Wide Field Camera 3 Infrared Channel (WFC3/IR) on the Hubble Space Telescope (HST). For the preferred F110W passband we derive a distance modulus of ( m − M ) = 33.05 ± 0.08 ± 0.10 mag, or a linear distance d = 40.7 ± 1.4 ± 1.9 Mpc (random and systematic errors, respectively); a virtually identical result is obtained from the F160W data. This is the most precise distance to NGC 4993 available to date. Combining our distance measurement with the corrected recession velocity of NGC 4993 implies a Hubble constant H 0 = 71.9 ± 7.1 km s−1 Mpc−1. A comparison of our result to the GW-inferred value of H 0 indicates a binary orbital inclination of i ≳ 137°. The SBF technique can be applied to early-type host galaxies of BNS mergers to ∼100 Mpc with HST and possibly as far as ∼300 Mpc with the James Webb Space Telescope, thereby helping to break the inherent distance-inclination degeneracy of the GW data at distances where many future BNS mergers are likely to be detected.

Studying the ICM in clusters of galaxies via surface brightness fluctuations of the cosmic X-ray background

We study the surface brightness fluctuations of the cosmic X-ray background (CXB) using Chandra data of XBOOTES. After masking out resolved sources we compute the power spectrum of fluctuations of the unresolved CXB for angular scales from ~2 arcsec to ~3 deg. The non-trivial large-scale structure (LSS) signal dominates over the shot-noise of unresolved point sources at all scales above ~1 arcmin and is produced mainly by the intracluster medium (ICM) of unresolved clusters and groups of galaxies, as shown in our previous publication. The shot-noise-subtracted power spectrum of CXB fluctuations has a power-law shape with the slope of $\Gamma = 0.96 \pm 0.06$. Its energy spectrum is well described by the redshifted emission spectrum of optically-thin plasma with the best-fit temperature of $T \approx 1.3$ keV and the best-fit redshift of $z \approx 0.40$. They are in good agreement with theoretical expectations based on the X-ray luminosity function and scaling relations of clusters. From these values we estimate the typical mass and luminosity of the objects responsible for CXB fluctuations, $M_{500} \sim 10^{13.6}\,{\rm M}_{\odot}/h$ and $L_{0.5-2.0\,{\rm keV}} \sim 10^{42.5}$ erg/s. On the other hand, the flux-weighted mean temperature and redshift of resolved clusters are $T \approx 2.4$ keV and $z \approx 0.23$, confirming that fluctuations of unresolved CXB are caused by cooler (i.e. less massive) and more distant clusters, as expected. We show that the power spectrum shape is sensitive to the ICM structure all the way to the outskirts, out to $\sim{\rm few}\times R_{500}$. We also look for possible contribution of the warm-hot intergalactic medium (WHIM) to the observed CXB fluctuations. Our results underline the significant diagnostics potential of the CXB fluctuation analysis in studying the ICM structure in clusters.

Probing Large-scale Coherence between Spitzer IR and Chandra X-Ray Source-subtracted Cosmic Backgrounds

Abstract We present new measurements of the large-scale clustering component of the cross-power spectra of the source-subtracted Spitzer-IRAC cosmic infrared background and Chandra-ACIS cosmic X-ray background surface brightness fluctuations Our investigation uses data from the Chandra Deep Field South, Hubble Deep Field North, Extended Groth Strip/AEGIS field, and UDS/SXDF surveys, comprising 1160 Spitzer hours and ∼12 Ms of Chandra data collected over a total area of 0.3 deg2. We report the first (>5σ) detection of a cross-power signal on large angular scales >20″ between [0.5–2] keV and the 3.6 and 4.5 μm bands, at ∼5σ and 6.3σ significance, respectively. The correlation with harder X-ray bands is marginally significant. Comparing the new observations with existing models for the contribution of the known unmasked source population at z < 7, we find an excess of about an order of magnitude at 5σ confidence. We discuss possible interpretations for the origin of this excess in terms of the contribution from accreting early black holes (BHs), including both direct collapse BHs and primordial BHs, as well as from scattering in the interstellar medium and intra-halo light.

DeepChandraobservations of the stripped galaxy group falling into Abell 2142

In the local Universe, the growth of massive galaxy clusters mainly operates through the continuous accretion of group-scale systems. The infalling group in Abell 2142 is the poster child of such an accreting group, and as such, it is an ideal target to study the astrophysical processes induced by structure formation. We present the results of a deep (200 ks) observation of this structure with Chandra, which highlights the complexity of this system in exquisite detail. In the core of the group, the spatial resolution of Chandra reveals the presence of a leading edge and a complex AGN-induced activity. The morphology of the stripped gas tail appears straight in the innermost 250 kpc, suggesting that magnetic draping efficiently shields the gas from its surroundings. However, beyond $\sim300$ kpc from the core, the tail flares and the morphology becomes strongly irregular, which could be explained by a breaking of the drape, e.g. because of turbulent motions. The power spectrum of surface-brightness fluctuations is relatively flat ($P_{2D}\propto k^{-2.3}$), which indicates that thermal conduction is strongly inhibited even beyond the region where magnetic draping is effective. The amplitude of density fluctuations in the tail is consistent with a mild level of turbulence with a Mach number $M_{3D}\sim0.1-0.25$. Overall, our results show that the processes leading to the thermalization and mixing of the infalling gas are slow and relatively inefficient.

Accurate Distances to Important Spiral Galaxies: M63, M74, NGC 1291, NGC 4559, NGC 4625, and NGC 5398*

Abstract Accurate distances are fundamental for interpreting various measured properties of galaxies. Surprisingly, many of the best-studied spiral galaxies in the Local Volume have distance uncertainties that are much larger than can be achieved with modern observation techniques. Using Hubble Space Telescopeoptical imaging, we use the tip of the red giant branch method to measure the distances to six galaxies that are included in the Spitzer Infrared Nearby Galaxies Survey program and its offspring surveys. The sample includes M63, M74, NGC 1291, NGC 4559, NGC 4625, and NGC 5398. We compare our results with distances reported to these galaxies based on a variety of methods. Depending on the technique, there can be a wide range in published distances, particularly from the Tully–Fisher relation. In addition, differences between the planetary nebular luminosity function and surface brightness fluctuation techniques can vary between galaxies, suggesting inaccuracies that cannot be explained by systematics in the calibrations. Our distances improve upon previous results, as we use a well-calibrated, stable distance indicator, precision photometry in an optimally selected field of view, and a Bayesian maximum likelihood technique that reduces measurement uncertainties.

The halo of M 49 and its environment as traced by planetary nebulae populations

The galaxy M49 (NGC 4472) is the brightest early-type galaxy in the Virgo Cluster. It is located in Subcluster B and has an unusually blue, metal-poor outer halo. Planetary nebulae (PNe) are excellent tracers of diffuse galaxy and intragroup light. We present a photometric survey of PNe in the galaxy's extended halo to characterise its PN population, as well as the surrounding intragroup light (IGL) of the Subcluster B. PNe were identified based on their bright [OIII]5007 \AA\ emission and absence of a broad-band continuum. We identify 738 PNe out to a radius of 155 kpc from M49's centre from which we define a complete sample of 624 PNe within a limiting magnitude of m_5007=28.8. Comparing the PN number density to the broad-band stellar surface brightness profile, we find a variation of the PN-specific frequency (alpha-parameter) with radius. The outer halo beyond 60 kpc has a 3.2 times higher alpha-parameter compared to the main galaxy halo, which is likely due to contribution from the surrounding blue IGL. We use the Planetary Nebulae Luminosity Function (PNLF) as an indicator of distance and stellar population. Its slope, which correlates empirically with galaxy type, varies within the inner halo. In the eastern quadrant of M49, the PNLF slope is shallower, indicating an additional localised, bright PN population following an accretion event, likely that of the dwarf irregular galaxy VCC1249. We also determined a distance modulus of mu = 31.29+/-0.08 for M49, corresponding to a physical distance of 18.1+/-0.6 Mpc, which agrees with a recent surface-brightness fluctuations distance. The PN populations in the outer halo of M49 are consistent with the presence of a main Sersic galaxy halo with a slight (B-V) colour gradient of 10${}^{-4}$ mag/arcsec surrounded by intragroup light with a very blue colour of (B-V)=0.25 and a constant surface brightness mu_V=28.0 mag/arcsec${}^2$.

Resolving the Discrepancy of Distance to M60, a Giant Elliptical Galaxy in Virgo

Abstract There is a well-known discrepancy in the distance estimation of M60, a giant elliptical galaxy in Virgo; the planetary nebula luminosity function (PNLF) distance moduli for this galaxy are, on average, 0.4 mag smaller than the values based on the surface brightness fluctuation (SBF) in the literature. We present photometry of the resolved stars in an outer field of M60 based on deep F775W and F850LP images in the Hubble Space Telescope obtained as part of the Pure Parallel Program in the archive. Detected stars are mostly old red giants in the halo of M60. With this photometry, we determine a distance to M60 using the tip of the red giant branch (TRGB). A TRGB is detected at F850LP mag, in the luminosity function of the red giants. This value corresponds to F814W mag and mag, where QT is a color-corrected F814W magnitude. From this we derive a distance modulus, ( Mpc). This value is 0.3 mag larger than the PNLF distances and 0.1 mag smaller than the SBF distances in the previous studies, which indicates that the PNLF distances to M60 reported in the literature have larger uncertainties than the suggested values.

Can AGN and galaxy clusters explain the surface brightness fluctuations of the cosmic X-ray background?

Fluctuations of the surface brightness of cosmic X-ray background (CXB) carry unique information about faint and low luminosity source populations, which is inaccessible for conventional large-scale structure (LSS) studies based on resolved sources. We used Chandra data of the XBOOTES field ($\sim9\,\mathrm{deg^2}$) to conduct the most accurate measurement to date of the power spectrum of fluctuations of the unresolved CXB on the angular scales of $\sim3\,$arcsec $-$ $\sim17\,$arcmin. We find that at sub-arcmin angular scales, the power spectrum is consistent with the AGN shot noise, without much need for any significant contribution from their one-halo term. This is consistent with the theoretical expectation that low-luminosity AGN reside alone in their dark matter halos. However, at larger angular scales we detect a significant LSS signal above the AGN shot noise. Its power spectrum, obtained after subtracting the AGN shot noise, follows a power law with the slope of $-0.8\pm0.1$ and its amplitude is much larger than what can be plausibly explained by the two-halo term of AGN. We demonstrate that the detected LSS signal is produced by unresolved clusters and groups of galaxies. For the flux limit of the XBOOTES survey, their flux-weighted mean redshift equals $\left<z\right>\sim0.3$, and the mean temperature of their intracluster medium (ICM), $\left<T\right>\approx 1.4$ keV, corresponds to the mass of $M_{500} \sim 10^{13.5}\,\mathrm{M}_\odot$. The power spectrum of CXB fluctuations carries information about the redshift distribution of these objects and the spatial structure of their ICM on the linear scales of up to $\sim$Mpc, i.e. of the order of the virial radius.

The Planetary Nebulae Luminosity Function (PNLF): current perspectives

AbstractThis paper starts with a brief historical review about the PNLF and its use as a distance indicator. Then the PNLF distances are compared with Surface Brightness Fluctuations (SBF) distances and Tip of the Red Giant Branch (TRGB) distances. A Monte Carlo method to generate simulated PNLFs is described, leading to the last subject: recent progress in reproducing the expected maximum final mass in old stellar populations, a stellar astrophysics enigma that has been challenging us for quite some time.

Arithmetic with X-ray images of galaxy clusters: effective equation of state for small-scale perturbations in the ICM

We discuss a novel technique of manipulating X-ray images of galaxy clusters to reveal the nature of small-scale density/temperature perturbations in the intra cluster medium (ICM). As we show, this technique can be used to differentiate between sound waves and isobaric perturbations in Chandra images of the Perseus and M87/Virgo clusters. The comparison of the manipulated images with the radio data and with the results of detailed spectral analysis shows that this approach successfully classifies the types of perturbations and helps to reveal their nature. For the central regions (5-100 kpc) of the M87 and Perseus clusters this analysis suggests that observed images are dominated by isobaric perturbations, followed by perturbations caused by bubbles of relativistic plasma and weak shocks. Such a hierarchy is best explained in a "slow" AGN feedback scenario, when much of the mechanical energy output of a central black hole is captured by the bubble enthalpy that is gradually released during buoyant rise of the bubbles. The "image arithmetic" works best for prominent structure and for datasets with excellent statistics, visualizing the perturbations with a given effective equation of state. The same approach can be extended to faint perturbations via cross-spectrum analysis of surface brightness fluctuations in X-ray images in different energy bands.