A binding-energy criterion for the dynamical stability of spherical stellar systems in general relativity

1980 ◽  
Vol 238 ◽  
pp. 1101 ◽  
Author(s):  
J. R. Ipser
Keyword(s):  
General Relativity ◽  
Binding Energy ◽  
Energy Criterion ◽  
Dynamical Stability ◽  
Stellar Systems

scholarly journals Relative stability of planar clusters B11, B12, and B13 in neutral- and charged-states

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Levan Chkhartishvili
Keyword(s):  
Binding Energy ◽  
Relative Stability ◽  
Energy Criterion ◽  
Nanostructured Coating ◽  
Neutron Absorption ◽  
Coating Materials ◽  
Boron Cluster ◽  
Boron Clusters ◽  
Planar Structures ◽  
Electromagnetic Radiations

Theoretically, within the diatomic model, there is studied the relative stability of most abundant boron clusters B11, B12, and B13 with planar structures in neutral, positively and negatively charge-states. According to the specific (pet atom) binding energy criterion, B12+ (6.49 eV) is found to be the most stable boron cluster, while B11– + B13+ (5.83 eV) neutral pair is expected to present the preferable ablation channel for boron-rich solids. Obtained results would be applicable in production of boron-clusters-based nanostructured coating materials with super-properties such as lightness, hardness, conductivity, chemically inertness, neutron-absorption, etc. making them especially effective for protection against cracking, wear, corrosion, neutron- and electromagnetic-radiations, etc.

scholarly journals Binary Evolution in Stellar Systems

1975 ◽  
Vol 69 ◽  
pp. 95-97
Author(s):  
R. H. Miller
Keyword(s):  
Binding Energy ◽  
Massive Star ◽  
Massive Stars ◽  
Large Fraction ◽  
Stellar Systems ◽  
Total Binding Energy ◽  
Physical Systems ◽  
Total Binding ◽  
Binary Evolution ◽  
Favor Exchange

Aarseth has shown by means of n-body calculations that, in star systems with a range of particle masses, the most massive stars quickly form a binary which soon takes up a large fraction of the total binding energy of the cluster. Similar effects appear in other kinds of physical systems as well; mesic atoms behave in much the same way. The phase volumes of two otherwise equivalent stellar systems, each dominated by a tightly bound binary, favor exchange to incorporate the more massive star in the binary by a factor equal to the cube of the ratio of masses.

scholarly journals Relative stability of planar clusters B11, B12, and B13 in neutral- and charged-states

2018 ◽  
Author(s):  
Levan Chkhartishvili
Keyword(s):  
Binding Energy ◽  
Relative Stability ◽  
Energy Criterion ◽  
Nanostructured Coating ◽  
Neutron Absorption ◽  
Coating Materials ◽  
Boron Cluster ◽  
Boron Clusters ◽  
Planar Structures ◽  
Electromagnetic Radiations

Theoretically, within the diatomic model, there is studied the relative stability of most abundant boron clusters B11, B12, and B13 with planar structures in neutral, positively and negatively charge-states. According to the specific (pet atom) binding energy criterion, B12+ (6.49 eV) is found to be the most stable boron cluster, while B11– + B13+ (5.83 eV) neutral pair is expected to present the preferable ablation channel for boron-rich solids. Obtained results would be applicable in production of boron-clusters-based nanostructured coating materials with super-properties such as lightness, hardness, conductivity, chemically inertness, neutron-absorption, etc. making them especially effective for protection against cracking, wear, corrosion, neutron- and electromagnetic-radiations, etc.

ON EINSTEIN CLUSTERS

2012 ◽  
Vol 12 ◽  
pp. 146-173 ◽  
Author(s):  
ANDREA GERALICO ◽  
FRANCESCA POMPI ◽  
REMO RUFFINI
Keyword(s):  
Binding Energy ◽  
Energy Density ◽  
Energy Criterion ◽  
Galactic Halos ◽  
Density Profiles ◽  
Constant Energy ◽  
White Type ◽  
Constant Energy Density ◽  
The Stability

The classification of Einstein clusters based on the analysis of the stability of circular orbits according to the effective potential theory is compared with that resulting from the application of the maximum binding energy criterion. The stability properties are investigated for different choices of the energy density profile. The cases of clusters with constant energy density, those characterized by arbitrarily large values of the central gravitational redshift and clusters with Burkert-type and Navarro-Frenk-White-type energy density profiles used in the literature to model galactic halos are discussed.

scholarly journals Dynamics of Relativistic Stellar Systems

1975 ◽  
Vol 69 ◽  
pp. 420-431
Author(s):  
J. R. Ipser
Keyword(s):  
General Relativity ◽  
Dynamical Systems ◽  
Gravitational Collapse ◽  
Star Clusters ◽  
Stellar Systems ◽  
Equilibrium Models ◽  
The Stability

Relativistic stellar-dynamical systems and their possible occurrence in nature are discussed. Features of the equilibrium models that have been constructed for spherical star clusters in general relativity are delineated. The results of studies of the stability of relativistic spherical clusters are reviewed. It is noted that the results, while not conclusive, indicate that realistic spherical clusters are stable against gravitational collapse if their central redshifts zc ≲ 0.55 and unstable if zc ≳ 0.55. More work is needed on this and other problems.

scholarly journals NECESSARY AND SUFFICIENT CONDITION FOR HYDROSTATIC EQUILIBRIUM IN GENERAL RELATIVITY

2007 ◽  
Vol 16 (01) ◽  
pp. 35-52 ◽  
Author(s):  
P. S. NEGI
Keyword(s):  
General Relativity ◽  
Variational Method ◽  
Upper Bound ◽  
Trial Function ◽  
Hydrostatic Equilibrium ◽  
Dynamical Stability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Equilibrium Configurations ◽  
Necessary And Sufficient

We present explicit examples to show that the "compatibility criterion" (recently obtained by us toward providing equilibrium configurations compatible with the structure of general relativity) which states that for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), where M is the total mass and R is the radius of the configuration] of any static configuration cannot exceed the compactness ratio, uh, of the homogeneous density sphere (i.e., u ≤ uh) is capable of providing a necessary and sufficient condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the M–R relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion such that each member of this sequence satisfies the extreme case of causality condition v = c = 1 at the center. The maximum stable value of u ≃ 0.3389 (which occurs for the model corresponding to the maximum value of mass in the mass–radius relation) and the corresponding central value of the local adiabatic index, (Γ1)0 ≃ 2.5911, of this model are found fully consistent with those of the corresponding absolute values, u max ≤ 0.3406 and (Γ1)0 ≤ 2.5946, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the "trial function," ξ = reν/4, as well as the mass–central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favor of the statement regarding compatibility criterion mentioned above. Together with other results, this study also confirms the previous claim that just the choice of the "trial function," ξ = reν/4, is capable of providing the necessary and sufficient condition for dynamical stability of a mass on the basis of variational method. Obviously, the upper bound on the compactness ratio of neutron stars, u ≅ 0.3389, which belongs to two-density model studied here, turns out to be much stronger than the corresponding "absolute" upper bound mentioned in the literature.

scholarly journals Collisionless Equilibria in General Relativity: Stable Configurations beyond the First Binding Energy Maximum

2021 ◽  
Vol 918 (2) ◽  
pp. 48
Author(s):  
Sebastian Günther ◽  
Christopher Straub ◽  
Gerhard Rein
Keyword(s):  
General Relativity ◽  
Binding Energy ◽  
Energy Maximum

Desiderata in connection by the calibration of the MK-system

1966 ◽  
Vol 24 ◽  
pp. 348-349
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Absolute Magnitude ◽  
Review Article ◽  
Stellar Systems ◽  
Astronomical Data ◽  
Intrinsic Colour

This is only an informal remark about some difficulties I am worrying about.I have tried to recalibrate the MK system in terms of intrinsic colour (B–V)0and absolute magnitudeMv. The procedures used have been described in a review article by Voigt (Mitt. Astr. Ges.1963, p. 25–35), and the results for stars of the luminosity classes Ia-O,I and II have been given also in Blaauw's article on the calibration of luminosity criteria in vol. III (Basic Astronomical Data, p. 401) ofStars and Stellar Systems.

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