Quantifying the Morphologies and Dynamical Evolution of Galaxy Clusters. I. The Method

We describe and test a method to quantitatively classify clusters of galaxies according to their projected morphologies. This method will be subsequently used to place constraints on cosmological parameters ($\Omega$ and the power spectrum of primordial fluctuations on scales at or slightly smaller than that of clusters) and to test theories of cluster formation. We specifically address structure that is easily discernible in projection and dynamically important to the cluster. The method is derived from the two-dimensional multipole expansion of the projected gravitational potential and yields dimensionless {\it power ratios} as morphological statistics. If the projected mass profile is used to characterize the cluster morphology, the power ratios are directly related to the cluster potential. However, since detailed mass profiles currently exist for only a few clusters, we use the X-ray--emitting gas as an alternative tracer of cluster morphology. In this case, the relation of the power ratios to the potential is qualitatively preserved. We demonstrate the feasibility of the method by analyzing simulated observations of simple models of X-ray clusters using the instrument parameters of the ROSAT PSPC. For illustrative purposes, we apply the method to ROSAT PSPC images of A85, A514, A1750, and A2029. These clusters, which differ substantially in their X-ray morphologies, are easily distinguished by their respective power ratios. We discuss the suitability of this method to address the connection between cluster morphology and cosmology and to assess whether an individual cluster is sufficiently relaxed for analysis of its intrinsic shape using hydrostatic methods. Approximately 50 X-ray observations of Abell clusters with the PSPC will be amenable to morphological analysis using the method of this paper.Comment: To appear in ApJ October 20, 1995. 29 pages (7 figures missing), PostScrip

Facet modulation selective epitaxy–a technique for quantum-well wire doublet fabrication

The technique of facet modulation selective epitaxy and its application to quantum-well wire doublet fabrication are described. Successful fabrication of wire doublets in the AlxGa1–xAs material system is achieved. The smallest wire fabricated has a crescent cross section less than 140 Å thick and less than 1400 Å wide. Backscattered electron images, transmission electron micrographs, cathodoluminescence spectra, and spectrally resolved cathodoluminescence images of the wire doublets are presented

Quantifying the Morphologies and Dynamical Evolution of Galaxy Clusters. II. Application to a Sample of ROSAT Clusters

We quantify the morphologies and dynamical states of 59 galaxy clusters using the power-ratio technique of Buote & Tsai applied to ROSAT PSPC X-ray images. The clusters exhibit a particularly strong $P_2/P_0 - P_4/P_0$ correlation in the $1h^{-1}_{80}$ Mpc aperture which may be interpreted as an evolutionary track; the location of a cluster on the correlation line indicates the dynamical state of the cluster and the distribution of clusters along this track measures the rate of formation and evolution of clusters in our sample. The power ratios anti-correlate with the cooling-flow rate indicating a reasonable dependence of the flow rate on cluster morphology. The relationship of the power ratios to the optical Bautz-Morgan (BM) Type is more complex. This is because the power ratios are sensitive to unrelaxed regions of clusters within a specified scale, whereas BM types are sensitive to unrelaxed regions over many scales. We discuss further astrophysical applications exploiting the relationship between the power ratios and the evolutionary states of clusters.Comment: 31 pages (8 figures), PostScript, to appear in ApJ on February 10, 1996. In this version we added four more clusters to our sample and revised the error estimates for the power ratios (and the corresponding figures

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material

Designing Visible Light-Cured Thiol-Acrylate Hydrogels for Studying the HIPPO Pathway Activation in Hepatocellular Carcinoma Cells

Various polymerization mechanisms have been developed to prepare peptide-immobilized poly(ethylene glycol) (PEG) hydrogels, a class of biomaterials suitable for studying cell biology in vitro. Here, a visible light mediated thiol-acrylate photopolymerization scheme is reported to synthesize dually degradable PEG-peptide hydrogels with controllable crosslinking and degradability. The influence of immobilized monothiol pendant peptide is systematically evaluated on the crosslinking of these hydrogels. Further, methods are proposed to modulate hydrogel crosslinking, including adjusting concentration of comonomer or altering the design of multifunctional peptide crosslinker. Due to the formation of thioether ester bonds, these hydrogels are hydrolytically degradable. If the dithiol peptide linkers used are susceptible to protease cleavage, these thiol-acrylate hydrogels can be designed to undergo partial proteolysis. The differences between linear and multiarm PEG-acrylate (i.e., PEGDA vs PEG4A) are also evaluated. Finally, the use of the mixed-mode thiol-acrylate PEG4A-peptide hydrogels is explored for in situ encapsulation of hepatocellular carcinoma cells (Huh7). The effects of matrix stiffness and integrin binding motif (e.g., RGDS) on Huh7 cell growth and HIPPO pathway activation are studied using PEG4A-peptide hydrogels. This visible light poly-merized thiol-acrylate hydrogel system represents an alternative to existing light-cured hydrogel platforms and shall be useful in many biomedical applications

Time Scale for Rapid Draining of a Surficial Lake Into the Greenland Ice Sheet

A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial lake, of approximately 44×10^6 m^3, into the Greenland ice sheet over a time scale moderately longer than 1 hr. The lake had been instrumented to record the time-dependent fall of water level and the uplift of the ice nearby. Liquid water, denser than ice, was presumed to have descended through the sheet along a crevasse system and spread along the bed as a hydraulic facture. The event led two of the present authors to initiate modeling studies on such natural hydraulic fractures. Building on results of those studies, we attempt to better explain the time evolution of such a drainage event. We find that the estimated time has a strong dependence on how much a pre-existing crack/crevasse system, acting as a feeder channel to the bed, has opened by slow creep prior to the time at which a basal hydraulic fracture nucleates. We quantify the process and identify appropriate parameter ranges, particularly of the average temperature of the ice beneath the lake (important for the slow creep opening of the crevasse). We show that average ice temperatures 5–7  °C below melting allow such rapid drainage on a time scale which agrees well with the 2006 observations