Showing papers on "Radius published in 2003"

The inner structure of ΛCDM haloes – I. A numerical convergence study

Abstract: We present a comprehensive set of convergence tests which explore the role of various numerical parameters on the equilibrium structure of a simulated dark matter halo. We report on results obtained with two independent, state-of-the-art, multi-stepping, parallel N-body codes: pkdgrav and gadget. We find that convergent mass profiles can be obtained for suitable choices of the gravitational softening, time-step, force accuracy, initial redshift, and particle number. For softenings chosen so that particle discreteness effects are negligible, convergence in the circular velocity is obtained at radii where the following conditions are satisfied: (i) the time-step is much shorter than the local orbital time-scale; (ii) accelerations do not exceed a characteristic acceleration imprinted by the gravitational softening; and (iii) enough particles are enclosed so that the collisional relaxation time-scale is longer than the age of the Universe. Convergence also requires sufficiently high initial redshift and accurate force computations. Poor spatial, time, or force resolution leads generally to systems with artificially low central density, but may also result in the formation of artificially dense central cusps. We have explored several adaptive time-stepping choices and we have obtained the best results when individual time-steps are chosen according to the local acceleration and the gravitational softening (Δti (e/ai)1/2), although further experimentation may yield better and more efficient criteria. The most stringent requirement for convergence is typically that imposed on the particle number by the collisional relaxation criterion. This implies that, in order to estimate accurate circular velocities at radii where the density contrast may reach 106, the region must enclose of the order of 3000 particles (or more than a few times 106 within the virial radius). Applying these criteria to a galaxy-sized ΛCDM halo, we find that the spherically averaged density profile becomes progressively shallower from the virial radius inwards, reaching a logarithmic slope shallower than −1.2 at the innermost resolved point, 0.005 r200, with little evidence for convergence to a power-law behaviour in the inner regions.

2-D Radiative Transfer in Protostellar Envelopes: I. Effects of Geometry on Class I Sources

Abstract: We present 2-D radiation transfer models of Class I Protostars and show the effect of including more realistic geometries on the resulting spectral energy distributions and images. We begin with a rotationally flattened infalling envelope as our comparison model, and add a flared disk and bipolar cavity. The disk affects the spectral energy distribution most strongly at edge-on inclinations, causing a broad dip at about 10 um (independent of the silicate feature) due to high extinction and low scattering albedo in this wavelength region. The bipolar cavities allow more direct stellar+disk radiation to emerge into polar directions, and more scattering radiation to emerge into all directions. The wavelength-integrated flux, often interpreted as luminosity, varies with viewing angle, with pole-on viewing angles seeing 2-4 times as much flux as edge-on, depending on geometry. Thus, observational estimates of luminosity should take into account the inclination of a source. The envelopes with cavities are significantly bluer in near-IR and mid-IR color-color plots than those without cavities. Using 1-D models to interpret Class I sources with bipolar cavities would lead to an underestimate of envelope mass and an overestimate of the implied evolutionary state. We compute images at near-, mid-, and far-IR wavelengths. We find that the mid-IR colors and images are sensitive to scattering albedo, and that the flared disk shadows the midplane on large size scales at all wavelengths plotted. Finally, our models produce polarization spectra which can be used to diagnose dust properties, such as albedo variations due to grain growth. Our results of polarization across the 3.1 um ice feature agree well with observations for ice mantles covering 5% of the radius of the grains.

A high velocity ionised outflow and XUV photosphere in the narrow emission line quasar PG1211+143

Abstract: We report on the analysis of a ~60 ksec XMM observation of the bright, narrow emission line quasar PG 1211+143. Absorption lines are seen in both EPIC and RGS spectra corresponding to H- and He-like ions of Fe, S, Mg, Ne, O, N and C. The observed line energies indicate an ionised outflow velocity of ~24000 km s^-1. The highest energy lines require a column density of N_H ~ 5 x 10^23 cm^-2, at an ionisation parameter of log(xi) ~ 3.4. If the origin of this high velocity outflow lies in matter being driven from the inner disc, then the flow is likely to be optically thick within a radius ~130 Schwarzschild radii, providing a natural explanation for the Big Blue Bump (and strong soft X-ray) emission in PG 1211+143.

Photospheric radius expansion X-ray bursts as standard candles

Abstract: We examined the maximum bolometric peak luminosities during type I X-ray bursts from the persistent or transient luminous X-ray sources in globular clusters. We show that for about two thirds of the sources the maximum peak luminosities during photospheric radius expansion X-ray bursts extend to a critical value of 3:790:1510 38 erg s 1 , assuming the total X-ray burst emission is entirely due to black-body radiation and the recorded maximum luminosity is the actual peak luminosity. This empirical critical luminosity is consistent with the Eddington luminosity limit for hydrogen poor material. Since the critical luminosity is more or less always reached during photospheric radius expansion X-ray bursts (except for one source), such bursts may be regarded as empirical standard candles. However, because significant deviations do occur, our standard candle is only accurate to within 15%. We re-evaluated the distances to the twelve globular clusters in which the X-ray bursters reside.

Compression properties of syntactic foams: effect of cenosphere radius ratio and specimen aspect ratio

Abstract: The present work is aimed at characterizing syntactic foams for flatwise (specimen aspect ratio of 0.5) properties and investigating the effect of change in the internal radius of cenospheres. The density and mechanical properties of the syntactic foam can be changed while keeping cenosphere volume fraction and particle–matrix interfacial area the same by using cenospheres of same outer radius but different inner radius. Five types of cenospheres, with the same mean outer radius but a different internal radius, have been selected for the fabrication of syntactic foams. ASTM C 365-94, a standard for the flatwise compressive properties of sandwich cores, is followed in the present work. The results obtained in the study are compared with the results of edgewise (specimen aspect ratio of 2) compressive properties evaluated in earlier work. Results show an increase in compressive strength and modulus with decrease in internal radius of cenospheres. The peak compressive strength and modulus were measured to be higher for the specimens tested in flatwise orientation compared to that in edgewise orientation. Varying only one parameter, the internal radius of cenospheres, helped in understanding the role of cenospheres and matrix resin in deformation and fracture process of syntactic foams.

Dust in the Early Universe: Dust Formation in the Ejecta of Population III Supernovae

Abstract: We investigate the formation of dust grains in the ejecta of population III supernovae including pair--instability supernovae, applying a theory of non-- steady state nucleation and grain growth. In the calculations, the time evolution of gas temperature in theejecta, which strongly affects the number density and size of newly formed grains, is calculated by solving the radiative transfer equation taking account of the energy deposition of radio active elements. Two extreme cases are considered for the mixing of elements in the ejecta; unmixed and uniformly mixed cases within the He--core. The results of calculations are summarized as the followings; in the unmixed ejecta, a variety of grain species condense, reflecting the difference of the elemental composition at the formation site in the ejecta, otherwise only oxide grains condense in the uniformly mixed ejecta. The average size of newly formed grains spans the range of three orders of magnitude, depending on the grain species and the formation condition, and the maximum radius is limited to less than 1 $\mu$m, which does not depend on the progenitor mass. The size distribution function summed up over all grain species is approximated by a power--law formula whose index is -3.5 for the larger radius and -2.5 for the smaller one; the radius at the crossover point ranges from 0.004 to 0.1 $\mu$m, depending on the model of supernovae. The fraction of mass locked into dust grains increases with increasing the progenitor mass; 2--5 % of the progenitor mass for core collapse supernovae and 15--30 % for pair--instability supernovae whose progenitor mass ranges from 140 to 260 $M_{\odot}$. Thus, if the very massive stars populate the first generation stars, a large amount of dust grains would be produced in the early universe.

Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass-anisotropy degeneracy

Abstract: We study velocity moments of elliptical galaxies in the Coma cluster using Jeans equations. The dark matter distribution in the cluster is modelled by a generalised formula based upon the results of cosmological N-body simulations. Its inner slope (cuspy or flat), concentration, and mass within the virial radius are kept as free parameters, as well as the velocity anisotropy, assumed independent of position. We show that the study of line-of-sight velocity dispersion alone does not allow to constrain the parameters. By a joint analysis of the observed profiles of velocity dispersion and kurtosis we are able to break the degeneracy between the mass distribution and velocity anisotropy. We determine the dark matter distribution at radial distances larger than 3% of the virial radius and we find that the galaxy orbits are close to isotropic. Due to limited resolution, different inner slopes are found to be consistent with the data and we observe a strong degeneracy between the inner slope $\alpha$ and concentration $c$: the best-fitting profiles have the two parameters related with $c=19 - 9.6 \alpha$. Our best-fitting NFW profile has concentration $c=9$, which is 50% higher than standard values found in cosmological simulations for objects of similar mass. The total mass within the virial radius of $2.9 h_{70}^{-1}$ Mpc is $1.4 \times 10^{15} h_{70}^{-1} M_{\sun}$ (with 30% accuracy), 85% of which is dark. At this distance from the cluster centre, the mass-to-light ratio in the blue band is $351 h_{70}$ solar units. The total mass within the virial radius leads to estimates of the density parameter of the Universe, assuming that clusters trace the mass-to-light ratio and baryonic fraction of the Universe, with $\Omega_0=0.29 \pm 0.1$.

Unveiling the Inner Disk Structure of T Tauri Stars

Abstract: We present near-infrared spectra of the excess continuum emission from the innermost regions of classical T Tauri disks. In almost all cases, the shape of the excess is consistent with that of a single-temperature blackbody with T ~ 1400 K, similar to the expected dust sublimation temperature for typical dust compositions. The amount of excess flux roughly correlates with the accretion luminosity in objects with similar stellar properties. We compare our observations with the predictions of simple disk models having an inner rim located at the dust sublimation radius, including irradiation heating of the dust from both the stellar and accretion luminosities. The models yield inner rim radii in the range 0.07-0.54 AU, increasing with higher stellar and accretion luminosities. Using typical parameters that fit our observed sample, we predict a rim radius ~0.2 AU for the T Tauri star DG Tau, which agrees with recent Keck near-infrared interferometric measurements. For large mass accretion rates, the inner rim lies beyond the corotation radius at (or within) which magnetospheric accretion flows are launched, which implies that pure gaseous disks must extend inside the dust rim. Thus, for a significant fraction of young stars, dust cannot exist in the innermost disk, calling into question theories in which solid particles are ejected by a wind originating at the magnetospheric radius.

Three-Dimensional Distribution of the ISM in the Milky Way Galaxy: I. The H I Disk

Abstract: We derived the three-dimensional distribution of H I gas in the Milky Way Galaxy using the latest H I survey data cubes and rotation curves. The distance of the H I gas was determined by the kinematic distance using a rotation curve. We solved the near–far problem in the inner Galaxy by a fitting method which involves introducing a model of vertical H I distribution. In our resultant maps we could trace three prominent arms: the Sagittarius–Carina arm, the Perseus arm, and the Outer arm. These three arms were found to be logarithmic spiral arms. The pitch angles of the Sagittarius–Carina, Perseus, and Outer arms were estimated to be about 11 ◦ ,1 8 ◦ ,a nd 7 ◦ , respectively. The Sun is located in a region rich in H I gas between the Sagittarius–Carina arm and the Perseus arm. The H I disk shows large and asymmetric warping in the outer disk: the H I disk goes up to about 1.5kpc above the Galactic plane in the northern hemisphere, and down to about 1kpc in the southern hemisphere, which means asymmetric warping. The inner H I disk is also found to be tilting. The radius of the HI disk is about 17kpc and the H I mass within this radius is estimated to be 2.5×10 9 M� , which corresponds to 1.5% of the dynamical mass predicted from the rotation curve. We also found that the H I outskirt is largely swelling in the fourth quadrant, and hence the Galaxy is significantly lopsided. The scale-height of the H I layer increases with the radius, and is correlated with the H I volume density at the centroid of the H I layer.

Optimal sizes of dielectric microspheres for cavity QED with strong coupling

Abstract: The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED) Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number n0 and critical atom number N0 cannot be minimized simultaneously, so that an "optimal" sphere size is taken to be the radius for which the geometric mean sqrt(n[sub 0]N[sub 0]), is minimized While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2 transition in atomic cesium at lambda0 = 852 nm using fused-silica microspheres, for which the maximum coupling coefficient ga/(2pi)[approximate]750 MHz occurs for a sphere radius a = 363 µm corresponding to the minimum for n0[approximate]606×10^–6 By contrast, the minimum for N0[approximate]900×10^–6 occurs for a sphere radius of a = 812 µm, while the optimal sphere size for which sqrt(n[sub 0]N[sub 0]) is minimized occurs at a = 783 µm On an experimental front, we have fabricated fused-silica microspheres with radii a~10 µm and consistently observed quality factors Q>=08×10^7 These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling

A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

Abstract: It is shown that if A is a bounded linear operator on a complex Hilbert space, then w(A) ≤ 2 (‖A‖+ ‖A2‖1/2), where w(A) and ‖A‖ are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.

Spatially resolved X-ray spectroscopy of cooling clusters of galaxies

Abstract: We present spatially resolved X-ray spectra taken with the EPIC cameras of XMM-Newton of a sample of 17 cooling clusters and three non-cooling clusters for comparison. The deprojected spectra are analyzed with a multi-temperature model, independent of any a priori assumptions about the physics behind the cooling and heating mechanisms. All cooling clusters show a central decrement of the average temperature, most of them of a factor of ~2. At each radius within the cooling region the gas is non-isothermal. The differential emission measure distribution peaks near the maximum (ambient) temperature, and steeply declines towards lower temperatures, proportional to T^3, or alternatively a cut-off at about a quarter to half of the maximum temperature. In general, we find a poor correlation between radio flux of the central galaxy and the temperature decrement of the cooling flow. This is interpreted as evidence that except for a few cases heating by a central AGN is not the most common cause of weak cooling flows. We investigate the role of heat conduction by electrons and find that the theoretically predicted conductivity rates are not high enough to balance radiation losses. The differential emission measure distribution has remarkable similarities with the predictions from coronal magnetic loop models. Also the physical processes involved (radiative cooling, thermal conduction along the loops, gravity) are similar for clusters loops and coronal loops. If coronal loop models apply to clusters, we find that a few hundred loops per scale height should be present. The typical loop sizes deduced from the observed emission measure distribution are consistent with the characteristic magnetic field sizes deduced from Faraday rotation measurements.

First radius measurements of very low mass stars with the VLTI

Abstract: We present 4 very low mass stars radii measured with the VLTI using the 2.2m VINCI test instrument. The observations were carried out during the commissioning of the 104-meter-baseline with two 8-meter-telescopes. We measure angular diameters of 0.7-1.5 mas with accuracies of 0.04-0.11 mas, and for spectral type ranging from M0V to M5.5V. We determine an empirical mass-radius relation for M dwarfs based on all available radius measurements. The observed relation agrees well with theoretical models at the present accuracy level, with possible discrepancy around 0.5-0.8 M that needs to be confirmed. In the near future, dozens of M dwarfs radii will be measured with 0.1-1% accuracy, with the VLTI, thanks to the improvements expected from the near infrared instrument AMBER. This will bring strong observational constraints on both atmosphere and interior physics.

Chandra Observations of A2029: The Dark Matter Profile Down to below 0.01rvir in an Unusually Relaxed Cluster

Abstract: We have used a high spatial resolution Chandra observation to examine the core mass distribution of the unusually regular cD cluster A2029. This bright, nearby system is especially well suited for analysis of its mass distribution under the assumption of hydrostatic equilibrium; it exhibits an undisturbed, symmetric X-ray morphology and a single-phase intracluster medium (ICM). From the deprojected temperature and density profiles, we estimate the total mass and the contributions of the gas and dark matter (DM) components from less than 3'' to ~3' (<4.4-260 h kpc, 0.001-0.1rvir). The gas density profile is not adequately described by a single-β model fit because of an increase in the density at the center (r < 17 h kpc, <12''), but it is well fitted by either a double-β model, or a "cusped" β model. The temperature data increase as a function of radius and are well fitted by a Bertschinger & Meiksin profile and may be approximated by a power-law T(r) ∝ r, with αT = 0.27 ± 0.01. Using the fitted profiles to obtain smooth functions of density and temperature, we employed the equation of hydrostatic equilibrium to compute the total enclosed mass as a function of radius. We report a total mass of 9.15 ± 0.25 × 1013 h M☉ within 260 h kpc, using the chosen parameterization of gas density and temperature. The mass profile is remarkably well described down to 0.002rvir by the Navarro, Frenk, & White (NFW) profile, or a Hernquist profile, over two decades of radius and three decades of mass. For the NFW model, we measure a scale radius rs = 540 ± 90 h kpc (≈0.2rvir) and concentration parameter c = 4.4 ± 0.9. The mass profile is also well approximated by a simple power-law fit [M(< r) ∝ r], with αm = 1.81 ± 0.04 (corresponding to a logarithmic density profile slope of -1.19 ± 0.04). The density profile is too shallow to be fitted with the profile described by Moore et al. The consistency with NFW down to less than 0.01rvir is incompatible with the flattened core DM profiles predicted for self-interacting DM (e.g., Spergel & Steinhardt) and thus contrasts with the strong deviations from cold dark matter (CDM) predictions observed in the rotation curves of low surface brightness galaxies and dwarf galaxies. This suggests that while CDM simulations may adequately describe objects of cluster mass, they do not currently properly account for the formation and evolution of smaller halos. Assuming that the cD dominates the optical cluster light within its effective radius (Re = 52'',76 h kpc), we observe a total mass-to-light ratio M/LV ≈ 12 M☉/L☉ at r < 20 h kpc, rising rapidly to greater than 100 M☉/L☉ beyond 200 h kpc. The consistency with a single NFW mass component and the large M/L suggests the cluster is DM-dominated down to very small radii (0.005rvir). We observe the ICM gas mass to rise from 3% ± 1% of the total mass in the center to 13.9% ± 0.4% at the limit of our observations. This provides an upper limit to the current matter density of the universe, Ωm ≤ 0.29 ± 0.03 h.

The influence of surface tension on the circular hydraulic jump

Abstract: We present the results of a combined theoretical and experimental investigation of the influence of surface tension the acceleration due to gravity. The theory of viscous hydraulic jumps (Watson 1964) is extended through inclusion of the curvature force, and yields a new prediction for the radius of circular hydraulic jumps. Our experimental investigation demonstrates that the surface tension correction is generally small in laboratory settings, but appreciable for jumps of small radius and height.

A Theory for the Radius of the Transiting Giant Planet HD 209458B

Abstract: Using a full frequency-dependent atmosphere code that can incorporate irradiation by a central primary star, we calculate self-consistent boundary conditions for the evolution of the radius of the transiting planet HD 209458b. Using a well-tested extrasolar giant planet evolutionary code, we then calculate the behavior of this planet's radius with age. The measured radius is in fact a transit radius that resides high in HD 209458b's inflated atmosphere. Using our derived atmospheric and interior structures, we find that irradiation plus the proper interpretation of the transit radius can yield a theoretical radius that is within the measured error bars. We conclude that if HD 209458b's true transit radius is at the lower end of the measured range, an extra source of core heating power is not necessary to explain the transit observations.

Two Dimensional Adiabatic Flows onto a Black Hole: I. Fluid Accretion

Abstract: When gas accretes onto a black hole, at a rate either much less than or much greater than the Eddington rate, it is likely to do so in an "adiabatic" or radiatively inefficient manner. Under fluid (as opposed to MHD) conditions, the disk should become convective and evolve toward a state of marginal instability. The resulting disk structure is "gyrentropic," with convection proceeding along common surfaces of constant angular momentum, Bernoulli function and entropy, called "gyrentropes." We present a family of two-dimensional, self-similar models which describes the time-averaged disk structure. We then suppose that there is a self-similar, Newtonian torque and that the Prandtl number is large. This torque drives inflow and meridional circulation and the resulting flow is computed. Convective transport will become ineffectual near the disk surface. It is conjectured that this will lead to a large increase of entropy across a "thermal front" which we identify as the effective disk surface and the base of an outflow. The conservation of mass, momentum and energy across this thermal front permits a matching of the disk models to self-similar outflow solutions. We then demonstrate that self-similar disk solutions can be matched smoothly onto relativistic flows at small radius and thin disks at large radius. This model of adiabatic accretion is contrasted with some alternative models that have been discussed recently. The disk models developed in this paper should be useful for interpreting numerical, fluid dynamical simulations. Related principles to those described here may govern the behaviour of astrophysically relevant, magnetohydrodynamic disk models.

Quantitative Noncontact Electrostatic Force Imaging of Nanocrystal Polarizability

Abstract: A simple analytical model describing tip-surface interactions in an electrostatic force microscopy (EFM) experiment is proposed. Tip-surface capacitance is modeled as a sum of capacitances of cone, sphere, and plate with the substrate. Individual tips are calibrated according to this model by the choice of tip radius. Differences in EFM signal amplitude between probes are explained by differences in the sphere radii. Three tips with different sphere radii were used to detect EFM force gradients on an array of samples of dispersed Au nanoparticles with diameters ranging from 6 to 18 nm. The spatial distribution of the electric field created by an Au nanoparticle polarized by the inhomogeneous field of the tip is calculated analytically. The particle diameter and tip-surface separation dependence of the measured force gradient due to metal sphere polarization is compared to that predicted by the model. A statistically significant z-offset factor is introduced into the model to correct for the curvature mismatch between the model system and the actual tip.

Low-Mass Neutron Stars and the Equation of State of Dense Matter

Abstract: Neutron star radii provide useful information about the equation of state of neutron-rich matter. Particularly interesting is the density dependence of the equation of state (EOS). For example, the softening of the EOS at high density, where the pressure rises slower than anticipated, could signal a transition to an exotic phase. However, extracting the density dependence of the EOS requires measuring the radii of neutron stars for a broad range of masses. A "normal" 1.4 M☉ (M☉ = solar mass) neutron star has a central density of a few times the nuclear-matter saturation density (ρ0). In contrast, low-mass (0.5 M☉) neutron stars have central densities near ρ0, so their radii provide information about the EOS at low density. Unfortunately, low-mass neutron stars are rare because they may be hard to form. Instead, a precision measurement of nuclear radii of atomic nuclei may contain similar information. Indeed, we find a strong correlation between the neutron radius of 208Pb and the radius of a 0.5 M☉ neutron star. Thus, the radius of a 0.5 M☉ neutron star can be inferred from a measurement of the neutron radius of 208Pb. Comparing this value to the measured radius of a 1.4 M☉ neutron star should provide the strongest constraint to date on the density dependence of the EOS.

Robust normal mode constraints on inner-core anisotropy from model space search.

Abstract: A technique for searching full model space that was applied to measurements of anomalously split normal modes showed a robust pattern of P-wave and S-wave anisotropy in the inner core. The parameter describing P-wave anisotropy changes sign around a radius of 400 kilometers, whereas S-wave anisotropy is small in the upper two-thirds of the inner core and becomes negative at greater depths. Our results agree with observed travel-time anomalies of rays traveling at epicentral distances varying from 150° to 180°. The models may be explained by progressively tilted hexagonal close-packed iron in the upper half of the inner core and could suggest a different iron phase in the center.

The mass profile of galaxy clusters out to ~2 r200

Abstract: We analyze the internal dynamics of 43 non-interacting clusters which are selected from the 2dF Galaxy Redshift Survey 100k public release. We join together the 43 clusters into an ensemble cluster by appropriately scaling their galaxy velocities and clustercentric distances. We solve the Jeans equation for the hydrostatic equilibrium for the member galaxies within the virial radius of the ensemble cluster, assuming isotropic orbits. We constrain the cluster mass profile within the virial radius by exploring parameterized models for the cluster mass-density profile. We find that both cuspy profiles and profiles with a core are acceptable. In particular, the concentration parameter of the best fit NFW model is as predicted from numerical simulations in a LambdaCDM cosmology. Density profiles with very large core-radii are ruled out. Beyond the virial radius, dynamical equilibrium cannot be taken for granted, and the Jeans equation may not be applicable. In order to extend our dynamical analysis out to ~2 virial radii, we rely upon the method which uses the amplitude of caustics in the space of galaxy clustercentric distances and velocities. We find very good agreement between the mass profile determined with the caustic method and the extrapolation to ~2 virial radii of the best-fit mass profile determined by the Jeans analysis in the virialized inner region. We determine the mass-to-number density profile, and find it is fully consistent with a constant within the virial radius. The mass-to-number density profile is however inconsistent with a constant when the full radial range from 0 to ~2 virial radii is considered, unless the sample used to determine the number density profile is restricted to the early-type galaxies.

The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations

Abstract: A systematic study of failure initiation in small-scale specimens has been performed to assess the effect of size scale on “failure properties” by drawing on the classical analysis of elliptically perforated specimens. Limitations imposed by photolithography restricted the minimum radii of curvature of the specimen perforations to one micron. By varying the radius of curvature and the size of the ellipses, the effects of domain size and stress concentration amplitude could be assessed separately to the point where the size of individual grains (∼0.3 μm ) becomes important. The measurements demonstrate a strong influence of the domain size under elevated stress on the “failure strength” of MEMS scale specimens, while the amplitude, or the variation, of the stress concentration factor is less significant. In agreement with probabilistic considerations of failure, the “local failure strength” at the root of a notch clearly increases as the radius of curvature becomes smaller. Accordingly, the statistical scatter also increases with decreasing size of the (super)stressed domain. When the notch radius becomes as small as 1 μm the failure stress increases on average by a factor of two relative to the tension values derived from unnotched specimens. This effect becomes moderate for larger radii of curvature, up to a radius of 8 μm (25 times the grain size), for which the failure stress at the notch tip closely approaches the value of the tensile strength for un-notched tensile configurations. We deduce that standard tests, performed on micron-sized, non-perforated, tension specimens, provide conservative strength values for design purposes. In addition, a Weibull analysis shows for surface-micromachined specimens a dependence of the strength on the specimen length, rather than the surface area or volume, which implies that the sidewall geometry, dimensions and surface conditions can dominate the failure process.

The Mass Profile of Galaxy Clusters out to ~2r200

Abstract: We use the public release of 100,000 galaxies from the Two Degree Field Galaxy Redshift Survey (2dFGRS) to analyze the internal dynamics of galaxy clusters. We select 43 noninteracting clusters that are adequately sampled in the 2dFGRS public release. Members of these clusters are selected out to ~2 virial radii. We build an ensemble cluster by stacking together the 43 clusters, after appropriate scaling of their galaxy velocities and clustercentric distances. We solve the Jeans equation for the hydrostatic equilibrium for the member galaxies within the virial radius of the ensemble cluster, assuming isotropic orbits. We constrain the cluster mass profile within the virial radius by exploring parameterized models for the cluster mass density profile. We find that both cuspy profiles and profiles with a core are acceptable. In particular, the concentration parameter of the best-fit Navarro-Frenk-White model is as predicted from numerical simulations in a Λ cold dark matter cosmology. Density profiles with very large core radii are ruled out. Beyond the virial radius, dynamical equilibrium cannot be taken for granted, and the Jeans equation may not be applicable. In order to extend our dynamical analysis out to ~2 virial radii, we rely on the method that uses the amplitude of the caustics in the space of galaxy clustercentric distances and velocities. We find very good agreement between the mass profile determined with the caustic method and the extrapolation to ~2 virial radii of the best-fit mass profile determined by the Jeans analysis in the virialized inner region. We determine the mass-to-number density profile and find that it is fully consistent with a constant within the virial radius. The mass-to-number density profile is, however, inconsistent with a constant when the full radial range from 0 to ~2 virial radii is considered, unless the sample used to determine the number density profile is restricted to the early-type galaxies.

Spectral energy distributions of marginally self-gravitating quasi-stellar object discs

Abstract: We calculate spectral energy distributions (SEDs) of steady accretion discs at high accretion rates, as appropriate for bright quasi-stellar objects (QSOs), under the assumption that the outer pans are heated sufficientlyto maintain marginal gravitational stability, presumably by massive stars formed within the disc. The SED is independent of the nature of these auxiliary sources if their inputs are completely thermalized. Standard assumptions are made for angular momentum transport, with an alpha parameter less than unity. With these prescriptions, the luminosity of the disc is sensitive to its opacity, in contrast to standard discs powered by the release of orbital energy alone. Compared with the latter, our discs have a broader SED, with a second peak in the near-infrared that is energetically comparable with the blue bump. The energy in the second peak increases with the outer radius of the disc, provided that the accretion rate is constant with radius. By comparing our computed SEDs with observed ones, we limit the outer radius of the disc to be less than 10 5 Schwarzschild radii (Rs), or about 1 pc, in a typical QSO. We also discuss some properties of our minimum-Q discs in the regions where auxiliary heating is dominant (10 3 -10 5 R S ).

Galaxy flow in the Canes Venatici I cloud

Abstract: We present an analysis of Hubble Space Telescope/WFPC2 images of eighteen galaxies in the Canes Venatici I cloud. We derive their distances from the luminosity of the tip of the red giant branch stars with a typical accuracy of ∼ 12%. The resulting distances are 3.9 Mpc (UGC 6541), 4.9 Mpc (NGC 3738), 3.0 Mpc (NGC 3741), 4.5 Mpc (KK 109), >6.3 Mpc (NGC 4150), 4.2 Mpc (UGC 7298), 4.5 Mpc (NGC 4244), 4.6 Mpc (NGC 4395), 4.9 Mpc (UGC 7559), 4.2 Mpc (NGC 4449), 4.4 Mpc (UGC 7605), 4.6 Mpc (IC 3687), 4.7 Mpc (KK 166), 4.7 Mpc (NGC 4736), 4.2 Mpc (UGC 8308), 4.3 Mpc (UGC 8320), 4.6 Mpc (NGC 5204), and 3.2 Mpc (UGC 8833). The CVnI cloud has a mean radial velocity of 286 ′ 9 km s - 1 , a mean distance of 4.1 ′ 0.2 Mpc, a radial velocity dispersion of 50 km s - 1 , a mean projected radius of 760 kpc, and a total blue luminosity of 2.2 × 10 1 0 L O .. Assuming virial or closed orbital motions for the galaxies, we estimated their virial and their orbital mass-to-luminosity ratio to be 176 and 88 M O . /L O ., respectively. However, the CVnI cloud is characterized by a crossing time of 15 Gyr, and is thus far from a state of dynamical equilibrium. The large crossing time for the cloud, its low content of dSph galaxies (<6%), and the almost "primordial" shape of its luminosity function show that the CVnI complex is in a transient dynamical state, driven rather by the free Hubble expansion than by galaxy interactions.

Models for Interstellar Extinction in the Galaxy.

Abstract: We present two models for the interstellar extinction in the Galaxy that are based on the hypothesis that the interstellar dust is well mixed with the gas, with a constant ratio (except for a small dependence of metallicity on the Galactic radius), and therefore that the extinction is proportional to the column density of the gas. In the first model we assume that the Galaxy is axisymmetric; the gas density in the disk is a function of the Galactic radius and of the distance perpendicular to the Galactic plane, and the extinction is proportional to the column density of the gas. In the second model we take into account the spiral structure of the Galaxy. In this case, instead of increasing almost linearly with distance, the extinction increases by steps each time a spiral arm is crossed, but only increases slowly in the interarm regions. The gas density distribution is obtained from the Berkeley and Parkes H I surveys and from the Columbia University CO survey. The IRAS 100 μm brightness distribution is also used as a tracer of the interstellar dust column density. The predictions of the models are compared with data taken from a number of catalogs that present color excess and distances for large samples of stars. Our models are useful for estimating distances of objects and color corrections for objects for which the distance can be estimated by some other method, and also for star counts and brightness models of the Galaxy, among other applications.