Total Gravitational Mass Research Articles

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed---the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically symmetric spacetime: it decays in time according to an inverse power law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.

Galaxy Cluster Gas Mass Fractions from Sunyaev‐Zeldovich Effect Measurements: Constraints on \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $\Omega _{M}$ \end{document}

Using sensitive centimeter-wave receivers mounted on the Owens Valley Radio Observatory and Berkeley-Illinois-Maryland-Association millimeter arrays, we have obtained interferometric measurements of the Sunyaev-Zel'dovich (SZ) effect toward massive galaxy clusters. We use the SZ data to determine the pressure distribution of the cluster gas and, in combination with published X-ray temperatures, to infer the gas mass and total gravitational mass of 18 clusters. The gas mass fraction, f_g, is calculated for each cluster, and is extrapolated to the fiducial radius r_{500} using the results of numerical simulations. The mean f_g within r_{500} is 0.081+0.009 -0.011/(h_{100} (statistical uncertainty at 68% confidence level, assuming OmegaM=0.3, OmegaL=0.7). We discuss possible sources of systematic errors in the mean f_g measurement. We derive an upper limit for OmegaM from this sample under the assumption that the mass composition of clusters within r_{500} reflects the universal mass composition: Omega_M h < Omega_B/f_g. The gas mass fractions depend on cosmology through the angular diameter distance and the r_{500} correction factors. For a flat universe (OmegaL = 1 - OmegaM) and h=0.7, we find the measured gas mass fractions are consistent with Omegam less than 0.40, at 68% confidence. Including estimates of the baryons contained in galaxies and the baryons which failed to become bound during the cluster formation process, we find OmegaM \~0.25.

The Bar‐Mode Instability in Differentially Rotating Neutron Stars: Simulations in Full General Relativity

We study the dynamical stability against bar-mode deformation of rapidly spinning neutron stars with diUerential rotation. We perform fully relativistic three-dimensional simulations of compact stars with M/R 0.1, where M is the total gravitational mass and R the equatorial circumferential radius. We adopt an adiabatic equation of state with adiabatic index ! 2. As in Newtonian theory, we —nd that stars above a critical value of b 4 T /W (where T is the rotational kinetic energy and W the gravita- tional binding energy) are dynamically unstable to bar formation. For our adopted choices of stellar compaction and rotation pro—le, the critical value of is D0.24¨0.25, only slightly smaller than b b dGR the well-known Newtonian value D0.27 for incompressible Maclaurin spheroids. The critical value depends only very weakly on the degree of diUerential rotation for the moderate range we surveyed. All unstable stars form bars on a dynamical timescale. Models with sufficiently large b subsequently form spiral arms and eject mass, driving the remnant to a dynamically stable state. Models with moderately large do not develop spiral arms or eject mass but adjust to form dynamically stable b Z b dGR ellipsoidal-like con—gurations. If the bar-mode instability is triggered in supernova collapse or binary neutron star mergers, it could be a strong and observable source of gravitational waves. We determine characteristic wave amplitudes and frequencies. Subject headings: dense matterrelativitystars: neutronstars: rotation

Boson stars: alternatives to primordial black holes?

The present surge for the astrophysical relevance of boson stars stems from the speculative possibility that these compact objects could provide a considerable fraction of the non-baryonic part of dark matter within the halo of galaxies. For a very light `universal' axion of effective string models, their total gravitational mass will be in the most likely range of ∼0.5 M ⊙ of MACHOs. According to this framework, gravitational microlensing is indirectly “weighing” the axion mass, resulting in ∼10 −10 eV/ c 2. This conclusion is not changing much, if we use a dilaton type self-interaction for the bosons. Moreover, we review their formation, rotation and stability as likely candidates of astrophysical importance.

NON-OCCURRENCE OF TRAPPED SURFACES AND BLACK HOLES IN SPHERICAL GRAVITATIONAL COLLAPSE

By using the most general form of Einstein equations for General Relativistic (GTR) spherical collapse of an isolated fluid having arbitrary equation of state and radiation transport properties, we show that they obey a Global Constraint, 2GM(r, t)/R(r, t)c2≤1, where R is the “invariant circumference radius”, t is the comoving time, and M(r, t) is the gravitational mass enclosed within a comoving shell r. This inequality specifically shows that, contrary to the traditional intuitive Newtonian idea, which equates the total gravitational mass (Mb) with the fixed baryonic mass (M0), the trapped surfaces are not allowed in general theory of relativity (GTR), and therefore, for continued collapse, the final gravitational mass Mf→0 as R→0. This result should be valid for all spherical collapse scenarios including that of collapse of a spherical homogeneous dust as enunciated by Oppenheimer and Snyder (OS). Since the argument of a logarithmic function cannot be negative, the Eq. (36) of the O–S paper (T∼In\(T \sim \ln \tfrac{{y_b + 1}}{{y_b - 1}}\)) categorically demands that yb=Rb/Rgb≥1, or 2GMb/Rbc2≤1, where Rb referes to the invariant radius at the outer boundary. Unfortunately, OS worked with an approximate form of Eq. (36) [Eq. 37], where this fundamentalconstraint got obfuscated. And although OS noted that for a finite value of M(r, t) the spatial metric coefficient for an internal point fails to blow up even when the collapse is complete\(e^{\lambda (r < r_b )} \) ≠ ∞ for R→0, they, nevertheless, ignored it, and, failed to realize that such a problem was occurring because they were assuming a finite value ofMf, where Mf is the value of the finite gravitational mass, in violation of their Eq. (36).

Evolution of Thin-wall Configurations ofTexture Matter

We consider the matter of global textures withinthe frameworks of a perfect fluid model in generalrelativity. We examine thermodynamical properties oftexture matter in comparison with radiation fluid and bubble matter. Then we study dynamics ofthin-wall selfgravitating texture objects, and show thatclassical motion can be elliptical (finite), parabolicalor hyperbolical. It is shown that total gravitational mass of neutral textures in equilibrium equalszero, as was expected. Finally, we carry out theWheeler-DeWitt minisuperspace quantization of thetheory, obtain exact wave functions and discrete spectra of bound states with provision for spatialtopology.

ASCA Observations of the Sculptor Supercluster

We present ASCA results of the Sculptor supercluster, a rich supercluster with a redshift of 0.11, near to the south galactic pole. We searched for excess emission associated with the supercluster, and obtained the 3 σ upper limit as 16% of the brightness of the cosmic X-ray background in the 0.8–10 keV band. The X-ray properties of member clusters were analyzed and compared with other clusters. As for temperature-luminosity relation, no difference between the clusters in this supercluster and other clusters could be found. Applying the β model, we estimated the gas mass and the total gravitational mass associated with individual clusters, as well as those of the overall supercluster.

A comparison of x-ray and lensing mass estimates in Abell 1689 and Abell 2218

Estimates of the total gravitational mass in the clusters Abell 1689 and Abell 2218 are derived from the density and temperature distributions of the x-ray emitting intracluster gas under the assumption of hydrostatic equilibrium. The x-ray values are found to be significantly less than recent estimates derived from weak gravitational lensing of background sources. Possible explanations for this discrepancy are discussed.

A model of the universe with decaying vacuum energy

The consequences of taking the total active gravitational mass of the universe phasewise constant together with a decaying vacuum energy in the background of Robertson-Walker space-time are investigated. The model so determined admits a contracted Ricci-collineation along the fluid flow vectorν i. It is geometrically closed but ever-expanding and does not possess the initial singularity, horizon, entropy, monopole or cosmological constant problems of the standard big bang cosmology. Estimates of the present matter; radiation and vacuum energy densities, the age of the universe and the present values of the deceleration parameter and the scale factor are also obtained.

Mapping the Total Gravitating Mass in Three Groups of Galaxies

We report on the detection and analysis of hot ionized gas in three groups of galaxies (MKW 4s, AWM5, NGC 6329 group) at distances above 100 Mpc (recession velocities above 8000 km s−1). In all three cases their emission is centered on the dominant member of the group (NGC 4104, NGC 6269, NGC 6329, respectively). The central electron densities of the gas ne,0 are about 0.02 cm−3, decreasing to the outside as: ne = ne,0 [1 + (r/rc)2]-3β/2, with an exponent β=0.40 ‥ 0.77, (see Tab. 1). In each case, the spectra are well-represented by thermal Raymond-Smith spectra with kT ≃ 1.0 to 1.3 keV in the center and a weak increase by ca. 0.5 keV to the outside, indicating a slight cooling flow. The fits suggest that none of the central galaxies hosts an AGN that contributes significantly to the emission in the ROSAT band (0.1 to 2.4 keV). Using the radial temperature and density distributions, the total gravitating mass within a radius r can be derived. This value is 1.7±0.4 1013 M⊙ within 300 kpc for all three cases, as opposed to to 1014‥15 M⊙ for rich clusters.

The X-ray emission of E and S0 Galaxies

It is well known by now that E and S0 galaxies are associated with hot, X-ray emitting gaseous halos, subject to central cooling flows, but otherwise homogeneous, which can be used to trace the galaxy potential and thus measure the total gravitational mass. Recent ASCA observations suggest that these halos have a surprisingly low metal abundance.

Gravitational energy in asymptotically anti-de Sitter spacetimes.

The prescription proposed by Komar in order to calculate the total gravitational mass acting on a test particle in a given stationary asymptotically flat spacetime is generalized to stationary asymptotically anti\char21{}de Sitter spacetimes. It is shown that this generalized Komar mass is different from the total gravitational energy calculated by Henneaux and Teitelboim for the Kerr\char21{}anti-de Sitter spacetime. This last total energy agrees, however, with the total charge-energy calculated using the Brown-York action formalism.

Spatially Resolved X-Ray Spectroscopy of the Merging Galaxy Cluster A2256

view Abstract Citations (30) References (37) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Spatially Resolved X-Ray Spectroscopy of the Merging Galaxy Cluster A2256 Miyaji, T. ; Mushotzky, R. F. ; Loewenstein, M. ; Serlemitsos, P. J. ; Marshall, F. E. ; Petre, R. ; Jahoda, K. M. ; Boldt, E. A. ; Holt, S. S. ; Swank, J. ; Szymkowiak, A. E. ; Kelley, R. Abstract The cluster of galaxies A2256 was observed with BBXRT (Broad Band X-ray Telescope) during the Astro 1 mission with a total exposure of ∼4000 s. Moderate resolution spectra of parts of this cluster of galaxies give information complementary to the high spatial resolution observation of the same cluster by ROSAT. ROSAT spectral images (Briel et al.) have shown evidence of a merger with the northwest clump being cooler than the main cluster body. The BBXRT spectra also show an indication of a lower temperature [kT = 4.6(+0.9, -0.7) keV, 90% confidence errors] in the same general area. The BBXRT data from other regions within 10' from the center show temperatures (T ∼ 7 keV) consistent with the Ginga overall average and constrain the temperature gradient by limiting the polytropic index to γ = 1.10±0.35 (90% confidence errors). We have detected absorption in excess of the galactic value in several regions of the cluster, similar to that seen in other clusters with the Einstein SSS. One of the observed regions shows an apparent oxygen edge absorption feature at 0.54 ≲ Eedge ≲ 0.62 keV with an edge optical depth of the order of unity. This range of edge energy corresponds to absorption by oxygen with ionization stage between O2+ and O4+. This suggests the existence of about 1012-1013 Msun of warm (T ∼ 0.5-5 × 105 K) absorbing gas. It is unlikely that this component has its origin in the hot intracluster gas, compressed by the shock waves generated in the cluster merging and subsequently cooled, because the cooling timescale of the postshock gas is too large. It may have originated from the cold gas in the subcluster cooling flow heated up by shock waves or ionized by radiation sources. Using spatially resolved temperature information and absolute fluxes from the BBXRT data, along with core radius and the β-parameter of the modified King profile from the ROSAT PSPC data, we have obtained radial mass profiles of the X-ray emitting gas and the total gravitational mass. At r ∼0.8 h50-1 Mpc, the binding mass range is ∼2.8-3.7 × 1014 Msun for a range of models consistent with the BBXRT spectral data. This gives a total mass within ∼0.8 Mpc of about 5 times the mass of X-ray emitting gas. The total mass and gas fraction of the inner 1 Mpc of the cluster are very similar to those of the Coma Cluster. Publication: The Astrophysical Journal Pub Date: December 1993 DOI: 10.1086/173459 Bibcode: 1993ApJ...419...66M Keywords: X-RAYS: GALAXIES full text sources ADS | data products SIMBAD (2) NED (1)

ROSAT observations of galaxy clusters and cosmological implications

Clusters of galaxies are filled with a hot teneous plasma which is emitting soft X-rays over very extended regions. The ROSAT observatory with its high resolution and high sensitivity X-ray telescope allows to image nearby clusters in great detail and is therefore ideally suited to study the structure and morphology of galaxy clusters. In particular the distribution of the intracluster gas can be mapped, some information on the temperature structure of the gas can be obtained, the gravitational mass can be infered, and the dynamical state of the clusters can be investigated. Results of such studies for some nearby clusters as Virgo, Perseus and Coma are presented. Gas mass fractions of the total gravitational mass of the cluster in excess of 10 to 15% are infered from X-ray observations where the cluster emission can be traced out to an Abell radius (3 Mpc). If these values are taken to be representative for the matter composition in the Universe it has interesting consequences for cosmology as for example for the nucleosythesis models and the mean density of the Universe.

The role of magnetic fields in cluster cooling flows

Radial inflow and shear of the intracluster magnetic field will produce a dramatic increase in the strength of the field and will cause the field to become more radial within cooling flows. The magnetic pressure becomes comparable to the thermal pressure within a radius of typically 10 kpc. Within this region, reconnection of the magnetic field is efficient, and maintains the field in equipartition with the gas pressure. Buoyancy is ineffective in transporting the magnetic field out of the cooling flow. Reconnection releases the magnetic energy at a rate of 10^42^-10^43^ ergs s^-1^. Part of this energy may accelerate nonthermal, relativistic particles, resulting in diffuse radio emission from the central regions of cooling flows. The largest portion of the reconnection energy is likely to be dissipated in heating the cooling flow gas and may provide a major source of ionization and heating to the emission-line filaments in cooling flows. One dimensional, steady state, numerical models for cooling flows with magnetic fields show that the field has no dramatic effect on the structure of the cooling flow. The primary effect in the inner regions of cooling flows is to effectively increase the heat capacity of the gas by a factor of ~ 2. Also affected by a similar factor are the total gravitational mass derived by applying the hydrostatic equation to the gas pressure, and the accretion rates derived from the gas density and temperature profiles. The most important directly observable effect of the magnetic field in cooling flows is likely to be very strong Faraday rotation of the polarization of radio sources occurring within or behind the cooling flow. The rotation measure should increase rapidly towards the center of the cooling flow (roughly as r^-2^) and should reach values of RM ~ 10^3-4^ rad m^-2^ at projected radii within the equipartition radius. Comparison to several recent observations of the polarization of radio sources associated with the central galaxies in cooling flow clusters suggests that such large rotation measures may be common in cooling flows.

Does the electron contain negative mass?

Recent experimental evidence that the diameter of the electron is no larger than 10 -16 cm has important implications for its internal structure. Modelling it as a charged sphere obeying Einstein-Maxwell theory, we find that it must contain some negative rest mass. Moreover, the total active gravitational mass within this sphere is negative, which calls into question one of the assumptions made in singularity theorems of general relativity.

Electromagnetic mass model of a static charged perfect fluid sphere

Using the results, which they have been already published in two earlier papers (Dionysiou, 1982; Dionysiou and Kostakis, 1983; these papers will hereafter be referred to as Papers I, II, respectively), one can easily see that the total gravitational mass, the density and pressure of a static charged perfect fluid sphere are of electromagnetic origin.

The total effective mass of the Kerr–Newman metric

We find the total effective gravitational mass which acts on a particle moving in the Kerr–Newman metric. We also identify the contribution to that mass by the electric field energy which is stored in any given portion of the space surrounding the metric source.

Minimum size of charged particles in general relativity

Spherical charged matter distributions are examined in a coordinate-free manner within the framework of general relativity. Irrespective of models chosen to describe the interior structure of a charged particle, it is found that the latter's total gravitational mass is positive definite, being finite only when there exists a lower bound for its invariant extension. For a simple choice of matter and charge distributions it is then shown that there is a minimum invariant size for the particle, below which no solution of the field equations exists, the matter density becoming negative and the spacetime developing an intrinsic singularity in the exterior of the particle for radii less than this minimum. A mass renormalization is derived, valid at the moment of time symmetry, which relates the particle's total mass to its charge, bare mass and invariant extension. Our results are compared with those obtained previously by Arnowitt, Deser and Misner, who consider the simpler distribution of a charged spherical shell. Qualitatively, the two situations share the same features. However, in the more realistic spherical distributions the formulae are correspondingly more complicated, and the minimum extension is found to be greater than that of the shell, as one might expect on physical grounds. Moreover, the correspondence between negative valued matter distributions and intrinsic singularities was not evident in the shell case.

On the stability of homogeneous, spherically symmetric, charged fluids in relativity

A normal mode, stability analysis is applied to a spherically symmetric fluid system which contains a constant surface charge. The stability of the system is analyzed for the situation in which the electromagnetic mass is only a small fraction of the total mass and also for the situation in which the electromagnetic mass is the total gravitational mass. This latter situation corresponds to that of a Poincaré-Lorentz fluid electron.