arXiv subjects

William R. Forman

Publications and source records attributed to William R. Forman.

At least 37 records · Page 2Linked to original sources

arXiv2022

Exploring Gravitationally-Lensed $z\gtrsim6$ X-ray AGN Behind the RELICS clusters

Although observations of high-redshift quasars demonstrate that many supermassive black holes (BHs) reached large masses within one billion years after the Big Bang, the origin of the first BHs is still a mystery. A promising way to constrain the origin of the first BHs is to explore the average properties of $z\gtrsim6$ BHs. However, typical BHs remain hidden from X-ray surveys, which is due to their relatively faint nature and the limited sensitivity of X-ray telescopes. Gravitational lensing provides an attractive way to study this unique galaxy population as it magnifies the faint light from these high-redshift galaxies. Here, we study the X-ray emission originating from 155 gravitationally-lensed $z\gtrsim6$ galaxies that were detected in the RELICS survey. We utilize Chandra X-ray observations to search for AGN in the individual galaxies and in the stacked galaxy samples. We did not identify an individual X-ray source that was undoubtedly associated with a high-redshift galaxy. We stack the signal from all galaxies and do not find a statistically significant detection. We split our sample based on stellar mass, star-formation rate, and lensing magnification and stack these sub-samples. We obtain a $2.2σ$ detection for massive galaxies with an X-ray luminosity of $(3.7\pm1.6)\times10^{42} \ \rm{erg \ s^{-1}}$, which corresponds to a $(3.0\pm1.3)\times10^5 \ \rm{M_{\odot}}$ BH accreting at its Eddington rate. Other stacks remain undetected and we place upper limits on the AGN emission. These limits imply that the bulk of BHs at $z\gtrsim6$ either accrete at a few percent of their Eddington rate and/or are $1-2$ orders of magnitude less massive than expected based on the stellar mass of their host galaxy.

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arXiv2021

Predictions for the X-ray circumgalactic medium of edge-on discs and spheroids

We investigate how the X-ray circumgalactic medium (CGM) of present-day galaxies depends on galaxy morphology and azimuthal angle using mock observations generated from the EAGLE cosmological hydrodynamic simulation. By creating mock stacks of {\it eROSITA}-observed galaxies oriented to be edge-on, we make several observationally-testable predictions for galaxies in the stellar mass range $M_\star=10^{10.7-11.2}\;$M$_{\odot}$. The soft X-ray CGM of disc galaxies is between 60 and 100\% brighter along the semi-major axis compared to the semi-minor axis, between 10-30 kpc. This azimuthal dependence is a consequence of the hot ($T>10^6$ K) CGM being non-spherical: specifically it is flattened along the minor axis such that denser and more luminous gas resides in the disc plane and co-rotates with the galaxy. Outflows enrich and heat the CGM preferentially perpendicular to the disc, but we do not find an observationally-detectable signature along the semi-minor axis. Spheroidal galaxies have hotter CGMs than disc galaxies related to spheroids residing at higher halos masses, which may be measurable through hardness ratios spanning the $0.2-1.5$ keV band. While spheroids appear to have brighter CGMs than discs for the selected fixed $M_\star$ bin, this owes to spheroids having higher stellar and halo masses within that $M_\star$ bin, and obscures the fact that both simulated populations have similar total CGM luminosities at the exact same $M_\star$. Discs have brighter emission inside 20 kpc and more steeply declining profiles with radius than spheroids. We predict that the {\it eROSITA} 4-year all-sky survey should detect many of the signatures we predict here, although targeted follow-up observations of highly inclined nearby discs after the survey may be necessary to observe some of our azimuthally-dependent predictions.

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arXiv2021

Exemplary Merging Clusters: Weak-lensing and X-ray Analysis of the Double Radio Relic Merging Galaxy Clusters MACS 1752.0+4440 and ZWCL 1856.8+6616

The investigation of merging galaxy clusters that exhibit radio relics is strengthening our understanding of the formation and evolution of galaxy clusters, the nature of dark matter, the intracluster medium, and astrophysical particle acceleration. Each merging cluster provides only a single view of the cluster formation process and the variety of merging clusters is vast. Clusters hosting double radio relics are rare and extremely important because they allow tight constraints on the merger scenario. We present a weak-lensing and X-ray analysis of MACSJ1752.0+4440 ($z$=0.365) and ZWCL1856.8+6616 ($z$=0.304), two double radio relic clusters. Our weak-lensing mass estimates show that each cluster is a major merger with approximately 1:1 mass ratio. The total mass of MACSJ1752.0+4440 (ZWCL1856.8+6616) is $M_{200}=14.7^{+3.8}_{-3.3}\times10^{14}\ $M$_\odot$ ($M_{200}=2.4^{+0.9}_{-0.7}\times10^{14}\ $M$_\odot$). We find that these two clusters have comparable features in their weak-lensing and gas distributions, even though the systems have vastly different total masses. From the likeness of the X-ray morphologies and the remarkable symmetry of the radio relics, we propose that both systems underwent nearly head-on collisions. However, revelations from the hot-gas features and our multiwavelength data analysis suggest that ZWCL1856.8+6618 is likely at a later merger phase than MACSJ1752.0+4440. We postulate that the SW radio relic in MACSJ1752.0+4440 is a result of particle re-acceleration.

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arXiv2021

Interaction of the massive cluster system Abell 3016/3017 embedded in a cosmic filament

The galaxy cluster system RXCJ0225.9-4154 with the two sub-clusters A3016 and A3017 is embedded in a large-scale structure filament with signatures of filamentary accretion. A Chandra observation of this system shows the two clusters as well as a filament of X-ray emission connecting them and a galaxy group therein. The main cluster, A3017, shows indications of shocks most probably from a recent interaction with cluster components along the filament axis as well as a cold front. The filament between the two clusters is likely to be heated by the accretion shocks of the clusters and we discuss two scenarios for the origin of this X-ray filament. The paper describes many properties of the components of the cluster merger system that are used to assist the interpretation of the observed configuration.

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arXiv2021

Chandra Observations of the Planck ESZ Sample: A Re-Examination of Masses and Mass Proxies

Using Chandra observations, we derive the $Y_{\rm X}$ proxy and associated total mass measurement, $M_{500}^{\rm Y_X}$, for 147 clusters with $z \leq 0.35$ from the Planck Early Sunyaev-Zel'dovich catalog, and for 80 clusters with $z \leq 0.30$ from an X-ray flux-limited sample. We re-extract the Planck $Y_{\rm SZ}$ measurements and obtain the corresponding mass proxy, $M_{500}^{\rm SZ}$, from the full Planck mission maps, minimizing the Malmquist bias due to observational scatter. The masses re-extracted using the more precise X-ray position and characteristic size agree with the published PSZ2 values, but yield a significant reduction in the scatter (by a factor of two) in the $M_{500}^{\rm SZ}$-$M_{500}^{\rm X}$ relation. The slope is $0.93\pm0.03$, and the median ratio, $M_{500}^{\rm SZ}/M_{500}^{\rm X}= 0.91\pm0.01$, is within the expectations from known X-ray calibration systematics. The $Y_{\rm SZ}/Y_{\rm X}$ ratio is $0.88\pm0.02$, in good agreement with predictions from cluster structure, and implying a low level of clumpiness. In agreement with the findings of the Planck Collaboration, the slope of the $Y_{\rm SZ}$-$D_{\rm A}^{-2} Y_{X}$ flux relation is significantly less than unity ($0.89\pm0.01$). Using extensive simulations, we show that this result is not due to selection effects, intrinsic scatter, or covariance between quantities. We demonstrate analytically that changing the $Y_{\rm SZ}$-$Y_{X}$ relation from apparent flux to intrinsic properties results in a best-fit slope that is closer to unity and increases the dispersion about the relation. The redistribution resulting from this transformation implies that the best fit parameters of the $M_{500}^{\rm SZ}$-$M_{500}^{\rm X}$ relation will be sample-dependent.

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arXiv2020

Collision of Merger and Accretion Shocks: Formation of Mpc-scale Contact Discontinuity in the Perseus Cluster

Two Mpc-size contact discontinuities have recently been identified in the XMM-Newton and Suzaku X-ray observations of the outskirts of the Perseus cluster (Walker et al. 2020). These structures have been tentatively interpreted as "sloshing cold fronts", which are customarily associated with differential motions of the cluster gas, perturbed by a merger. In this study we consider an alternative scenario, namely, that the most prominent discontinuity near the cluster virial radius is the result of the collision between the accretion shock and the "runaway" merger shock. We also discuss the possible origin of the second discontinuity at ~1.2 Mpc.

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arXiv2020

Encounters of Merger and Accretion Shocks in Galaxy Clusters and their Effects on Intracluster Medium

Several types/classes of shocks naturally arise during formation and evolution of galaxy clusters. One such class is represented by accretion shocks, associated with deceleration of infalling baryons. Such shocks, characterized by a very high Mach number, are present even in 1D models of cluster evolution. Another class is composed of "runaway merger shocks", which appear when a merger shock, driven by a sufficiently massive infalling subcluster, propagates away from the main-cluster center. We argue that, when the merger shock overtakes the accretion shock, a new long-living shock is formed that propagates to large distances from the main cluster (well beyond its virial radius) affecting the cold gas around the cluster. We refer to these structures as Merger-accelerated Accretion shocks (MA-shocks) in this paper. We show examples of such MA-shocks in 1D and 3D simulations and discuss their characteristic properties. In particular, (1) MA-shocks shape the boundary separating the hot intracluster medium (ICM) from the unshocked gas, giving this boundary a "flower-like" morphology. In 3D, MA-shocks occupy space between the dense accreting filaments. (2) Evolution of MA-shocks highly depends on the Mach number of the runaway merger shock and the mass accretion rate parameter of the cluster. (3) MA-shocks may lead to the misalignment of the ICM boundary and the splashback radius.

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arXiv2020

EAGLE and Illustris-TNG predictions for resolved eROSITA X-ray observations of the circumgalactic medium around normal galaxies

We simulate stacked observations of nearby hot X-ray coronae associated with galaxies in the EAGLE and Illustris-TNG hydrodynamic simulations. A forward modeling pipeline is developed to predict 4-year eROSITA observations and stacked image analysis, including the effects of instrumental and astrophysical backgrounds. We propose an experiment to stack z~0.01 galaxies separated by specific star-formation rate (sSFR) to examine how the hot (T>=10^6 K) circumgalactic medium (CGM) differs for high- and low-sSFR galaxies. The simulations indicate that the hot CGM of low-mass (M_*~10^{10.5} Msol), high-sSFR (defined as the top one-third ranked by sSFR) central galaxies will be detectable to a galactocentric radius r~30-50 kpc. Both simulations predict lower luminosities at fixed stellar mass for the low-sSFR galaxies (the lower third of sSFR) with Illustris-TNG predicting 3x brighter coronae around high-sSFR galaxies than EAGLE. Both simulations predict detectable emission out to r~150-200 kpc for stacks centered on high-mass (M_*~10^{11.0} Msol) galaxies, with EAGLE predicting brighter X-ray halos. The extended soft X-ray luminosity correlates strongly and positively with the mass of circumgalactic gas within the virial radius (f_{CGM}). Prior analyses of both simulations have established that f_{CGM} is reduced by expulsive feedback driven mainly by black hole growth, which quenches galaxy growth by inhibiting replenishment of the ISM. Both simulations predict that eROSITA stacks should not only conclusively detect and resolve the hot CGM around L^* galaxies for the first time, but provide a powerful probe of how the baryon cycle operates, for which there remains an absence of consensus between state-of-the-art simulations.

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arXiv2020

X-ray scaling relations for a representative sample of Planck selected clusters observed with XMM-Newton

We report the scaling relations derived by fitting the X-ray parameters determined from analyzing the XMM-Newton observations of 120 galaxy clusters in the Planck Early Sunyaev-Zel'dovich sample spanning the redshift range of 0.059$<$$z$$<$0.546. We find that the slopes of all the investigated scaling relations significantly deviate from the self-similar predictions, if self-similar redshift evolution is assumed. When the redshift evolution is left free to vary, the derived slopes are more in agreement with the self-similar predictions. Relaxed clusters have on average $\sim$30$\%$ higher X-ray luminosity than disturbed clusters at a given mass, a difference that, depending on the relative fraction of relaxed and disturbed clusters in the samples (e.g. SZ vs X-ray selected), have a strong impact in the normalization obtained in different studies. Using the core-excised cluster luminosities reduces the scatter and brings into better agreement the $L$-$M_{tot}$ and $L$-$T$ relations determined for different samples. $M_{tot}$-$T$, $M_{tot}$-$Y_X$, and $M_{tot}$-$M_{gas}$ relations show little dependence on the dynamical state of the clusters, but the normalizations of these relations may depend on the mass range investigated. Although most of the clusters investigated in this work reside at relatively low redshift, the fits prefer values of $γ$, the parameter accounting for the redshift evolution, different from the self-similar predictions. This suggests an evolution ($<$2$σ$ level, with the exception of the $M_{tot}$-$T$ relation) of the scaling relations. For the first time, we find significant evolution ($>$3$σ$) of the $M_{tot}$-$T$ relation, pointing to an increase of the kinetic-to-thermal energy ratio with redshift. This is consistent with a scenario in which higher redshift clusters are on average more disturbed than their lower redshift counterparts.

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arXiv2020

AGN feedback in the FR II galaxy 3C 220.1

We present results from a deep (174 ks) Chandra observation of the FR-II radio galaxy 3C 220.1, the central brightest cluster galaxy (BCG) of a $kT \sim$ 4 keV cluster at $z=0.61$. The temperature of the hot cluster medium drops from $\sim5.9$ keV to $\sim3.9$ keV at $\sim$ 35 kpc radius, while the temperature at smaller radii may be substantially lower. The central active galactic nucleus (AGN) outshines the whole cluster in X-rays, with a bolometric luminosity of $2.0\times10^{46}$ erg s$^{-1}$ ($\sim10$% of the Eddington rate). The system shows a pair of potential X-ray cavities $\sim35$ kpc east and west of the nucleus. The cavity power is estimated within the range of $1.0\times10^{44}$ erg s$^{-1}$ and $1.7\times10^{45}$ erg s$^{-1}$, from different methods. The X-ray enhancements in the radio lobes could be due to inverse Compton emission, with a total 2-10 keV luminosity of $\sim8.0\times10^{42}$ erg s$^{-1}$. We compare 3C 220.1 with other cluster BCGs, including Cygnus A, as there are few BCGs in rich clusters hosting an FR-II galaxy. We also summarize the jet power of FR-II galaxies from different methods. The comparison suggests that the cavity power of FR-II galaxies likely under-estimates the jet power. The properties of 3C 220.1 suggest that it is at the transition stage from quasar-mode feedback to radio-mode feedback.

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arXiv2019

Chandra Observations of the Spectacular A3411-12 Merger Event

We present deep Chandra observations of A3411-12, a remarkable merging cluster that hosts the most compelling evidence for electron re-acceleration at cluster shocks to date. Using the $Y_X-M$ scaling relation, we find $r_{500} \sim 1.3$ Mpc, $M_{500} = (7.1 \pm 0.7) \times 10^{14} \ M_{\rm{\odot}}$, $kT=6.5\pm 0.1$ keV, and a gas mass of $M_{\rm g,500} = (9.7 \pm 0.1) \times 10^{13} M_\odot$. The gas mass fraction within $r_{500}$ is $f_{\rm g} = 0.14 \pm 0.01$. We compute the shock strength using density jumps to conclude that the Mach number of the merging subcluster is small ($M \leq 1.15_{-0.09}^{+0.14}$). We also present pseudo-density, projected temperature, pseudo-pressure, and pseudo-entropy maps. Based on the pseudo-entropy map we conclude that the cluster is undergoing a mild merger, consistent with the small Mach number. On the other hand, radio relics extend over Mpc scale in the A3411-12 system, which strongly suggests that a population of energetic electrons already existed over extended regions of the cluster.

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arXiv2019

Runaway Merger Shocks in Galaxy Cluster Outskirts and Radio Relics

Moderately strong shocks arise naturally when two subclusters merge. For instance, when a smaller subcluster falls into the gravitational potential of a more massive cluster, a bow shock is formed and moves together with the subcluster. After pericenter passage, however, the subcluster is decelerated by the gravity of the main cluster, while the shock continues moving away from the cluster center. These shocks are considered as promising candidates for powering radio relics found in many clusters. The aim of this paper is to explore the fate of such shocks when they travel to the cluster outskirts, far from the place where the shocks were initiated. In a uniform medium, such a "runaway" shock should weaken with distance. However, as shocks move to large radii in galaxy clusters, the shock is moving down a steep density gradient that helps the shock to maintain its strength over a large distance. Observations and numerical simulations show that, beyond $R_{500}$, gas density profiles are as steep as, or steeper than, $\sim r^{-3}$, suggesting that there exists a "Habitable zone" for moderately strong shocks in cluster outskirts where the shock strength can be maintained or even amplified. A characteristic feature of runaway shocks is that the strong compression, relative to the initial state, is confined to a narrow region just behind the shock. Therefore, if such a shock runs over a region with a pre-existing population of relativistic particles, then the boost in radio emissivity, due to pure adiabatic compression, will also be confined to a narrow radial shell.

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arXiv2019

Detection of Superluminal Motion in the X-Ray Jet of M87

Chandra HRC observations are investigated for evidence of proper motion and brightness changes in the X-ray jet of the nearby radio galaxy M87. Using images spanning 5 yr, proper motion is measured in the X-ray knot HST-1, with a superluminal apparent speed of $6.3 \pm 0.4 c$, or $24.1 \pm 1.6\rm\ mas\ yr^{-1}$, and in Knot D, with a speed of $2.4\pm 0.6c$. Upper limits are placed on the speeds of the remaining jet features. The X-ray knot speeds are in excellent agreement with existing measurements in the radio, optical, and ultraviolet. Comparing the X-ray results with images from the Hubble Space Telescope indicates that the X-ray and optical/UV emitting regions co-move. The X-ray knots also vary by up to 73% in brightness, whereas there is no evidence of brightness changes in the optical/UV. Using the synchrotron cooling models, we determine lower limits on magnetic field strengths of $\sim 420~μ\rm G$ and $\sim 230~μ\rm G$ for HST-1 and Knot A, respectively, consistent with estimates of the equipartition fields. Together, these results lend strong support to the synchrotron cooling model for Knot HST-1, which requires that its superluminal motion reflects the speed of the relativistic bulk flow in the jet.

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arXiv2019

A 1D fluid model of the Centaurus A jet

We implement a steady, one-dimensional flow model for the X-ray jet of Centaurus A in which entrainment of stellar mass loss is the primary cause of dissipation. Using over 260 ks of new and archival Chandra/ACIS data, we have constrained the temperature, density and pressure distributions of gas in the central regions of the host galaxy of Centaurus A, and so the pressure throughout the length of its jet. The model is constrained by the observed profiles of pressure and jet width, and conserves matter and energy, enabling us to estimate jet velocities, and hence all the other flow properties. Invoking realistic stellar populations within the jet, we find that the increase in its momentum flux exceeds the net pressure force on the jet unless only about one half of the total stellar mass loss is entrained. For self-consistent models, the bulk speed only falls modestly, from ~0.67c to ~0.52c over the range of 0.25-5.94 kpc from the nucleus. The sonic Mach number varies between ~5.3 and 3.6 over this range.

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arXiv2019

Variability and Proper Motion of X-ray Knots in the Jet of Centaurus A

We report results from Chandra observations analyzed for evidence of variability and proper motion in the X-ray jet of Centaurus A. Using data spanning 15 years, collective proper motion of $11.3\pm3.3$ mas yr$^{-1}$, or $0.68\pm0.20c$, is detected for the fainter X-ray knots and other substructure present within the jet. The three brightest knots (AX1A, AX1C, and BX2) are found to be stationary to an upper limit of $0.10c$. Brightness variations up to 27% are detected for several X-ray knots in the jet. For the fading knots, BX2 and AX1C, the changes in spectral slope expected to accompany synchrotron cooling are not found, ruling it out and placing upper limits of $\simeq 80\rm\ μG$ for each of their magnetic field strengths. Adiabatic expansion can account for the observed decreases in brightness. Constraints on models for the origin of the knots are established. Jet plasma overrunning an obstacle is favored as the generator of stationary knots, while moving knots are likely produced either by internal differences in jet speed or the late stages of jet interaction with nebular or cloud material.

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arXiv2018

Detection of the Missing Baryons toward the Sightline of H1821+643

Based on constraints from Big Bang nucleosynthesis and the cosmic microwave background, the baryon content of the high-redshift Universe can be precisely determined. However, at low redshift, about one-third of the baryons remain unaccounted for, which poses the long-standing missing baryon problem. The missing baryons are believed to reside in large-scale filaments in the form of warm-hot intergalactic medium (WHIM). In this work, we employ a novel stacking approach to explore the hot phases of the WHIM. Specifically, we utilize the 470 ks Chandra LETG data of the luminous quasar, H1821+643, along with previous measurements of UV absorption line systems and spectroscopic redshift measurements of galaxies toward the quasar's sightline. We repeatedly blueshift and stack the X-ray spectrum of the quasar corresponding to the redshifts of the 17 absorption line systems. Thus, we obtain a stacked spectrum with $8.0$ Ms total exposure, which allows us to probe X-ray absorption lines with unparalleled sensitivity. Based on the stacked data, we detect an OVII absorption line that exhibits a Gaussian line profile and is statistically significant at the $3.3 σ$ level. Since the redshifts of the UV absorption line systems were known a priori, this is the first definitive detection of an X-ray absorption line originating from the WHIM. The equivalent width of the OVII line is $(4.1\pm1.3) \ \mathrm{mÅ}$, which corresponds to an OVII column density of $(1.4\pm0.4)\times10^{15} \ \mathrm{cm^{-2}}$. We constrain the absorbing gas to have a density of $n_{\rm H} = (1-2)\times10^{-6} \ \rm{cm^{-3}}$ for a single WHIM filament. We derive $Ω_{\rm b} \rm(O\,VII) = (0.0023 \pm 0.0007) \, \left[ f_{O\,VII} \, {Z/Z_{\odot}} \right]^{-1}$ for the cosmological mass density of OVII, assuming that all 17 systems contribute equally.

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arXiv2018

Detection of a Star Forming Galaxy in the Center of a Low-Mass Galaxy Cluster

Brightest Cluster Galaxies (BCGs) residing in the centers of galaxy clusters are typically quenched giant ellipticals. A recent study hinted that star-forming galaxies with large disks, so-called superluminous spirals and lenticulars, are the BCGs of a subset of galaxy clusters. Based on the existing optical data it was not possible to constrain whether the superluminous disk galaxies reside at the center of galaxy clusters. In this work, we utilize XMM-Newton X-ray observations of five galaxy clusters to map the morphology of the intracluster medium (ICM), characterize the galaxy clusters, determine the position of the cluster center, and measure the offset between the cluster center and the superluminous disk galaxies. We demonstrate that one superluminous lenticular galaxy, 2MASX J10405643-0103584, resides at the center of a low-mass ($M_{\rm 500} = 10^{14} \ \rm{M_{\odot}}$) galaxy cluster. This represents the first conclusive evidence that a superluminous disk galaxy is the central BCG of a galaxy cluster. We speculate that the progenitor of 2MASX J10405643-0103584 was an elliptical galaxy, whose extended disk was re-formed due to the merger of galaxies. We exclude the possibility that the other four superluminous disk galaxies reside at the center of galaxy clusters, as their projected distance from the cluster center is $150-1070$ kpc, which corresponds to $(0.27-1.18)R_{\rm 500}$. We conclude that these clusters host quiescent massive elliptical galaxies at their center.

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arXiv2018

Standoff Distance of Bow Shocks in Galaxy Clusters as Proxy for Mach Number

X-ray observations of merging clusters provide many examples of bow shocks leading merging subclusters. While the Mach number of a shock can be estimated from the observed density jump using Rankine-Hugoniot condition, it reflects only the velocity of the shock itself and is generally not equal to the velocity of the infalling subcluster dark matter halo or to the velocity of the contact discontinuity separating gaseous atmospheres of the two subclusters. Here we systematically analyze additional information that can be obtained by measuring the standoff distance, i.e. the distance between the leading edge of the shock and the contact discontinuity that drives this shock. The standoff distance is influenced by a number of additional effects, e.g. (1) the gravitational pull of the main cluster (causing acceleration/deceleration of the infalling subcluster), (2) the density and pressure gradients of the atmosphere in the main cluster, (3) the non-spherical shape of the subcluster, and (4) projection effects. The first two effects tend to bias the standoff distance in the same direction, pushing the bow shock closer to (farther away from) the subcluster during the pre- (post-)merger stages. Particularly, in the post-merger stage, the shock could be much farther away from the subcluster than predicted by a model of a body moving at a constant speed in a uniform medium. This implies that a combination of the standoff distance with measurements of the Mach number from density/temperature jumps can provide important information on the merger, e.g. differentiating between the pre- and post-merger stages.

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