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Results for “VIRIAL THEOREM”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions

The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.

Iwamoto, N.↗
NASA NTRS1990

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud.

Zweibel, Ellen G.↗
NASA NTRS1990

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud.

Zweibel, Ellen G.↗
NASA NTRS1992

On the virial theorem for turbulent molecular clouds

An Eulerian, rather than Lagrangian, form of the virial theorem is derived for a turbulent, magnetized cloud embedded in a steady, turbulent, low-density intercloud medium. The role of turbulent pressure in cloud confinement is clarified, and it is shown that, in the absence of a magnetic field, a cloud can be at a somewhat lower pressure than the intercloud medium. Simple forms for the magnetic term in the virial equation are obtained. Radiation pressure is considered; its effects are relatively small under average conditions in the interstellar medium. Under typical conditions, external pressure and magnetic fields are shown to have a relatively small effect on virial estimates of the mass of self-gravitating clouds.

Mckee, Christopher F.↗
NASA NTRS1986

Acoustic radiation stress in solids

It is shown that the radiation-induced static strains associated with acoustic waves propagating in solids are obtained directly from the virial theorem for an elastic continuum and that the radiation stresses result from combining the virial theorem with the Boltzmann-Ehrenfest principle of adiabatic invariance. The experimental confirmation of critical theoretical predictions in solids is reported. The implications of the results for the fundamental thermal properties of crystals are addressed.

Cantrell, John H.↗
NASA NTRS1983

X-ray emission from clusters of galaxies

Some X-ray spectral observations of approximately 30 clusters of galaxies from HEAO-1 are summarized. There exists strong correlations between X-ray luminosity, L(x), and temperature kT in the form L(x)alphaT to the 2.3 power. This result combined with the L(x) central galaxy density relation and the virial theorem indicates that the core dadius of the gas should be roughly independent of L(x) or KT and that more luminous clusters have a greater fraction of their virial mass in gas. The poor correlation of KT and optical velocity dispersion seems to indicate that clusters have a variety of equations of state. There is poor agreement between X-ray imaging observations and optical and X-ray spectral measures of the polytropic index. Most clusters show Fe emission lines with a strong indication that they all have roughly 1/2 solar abundance. The evidence for cooling in the cores of several clusters is discussed based on spectral observations with the Einstein solid state spectrometer.

Mushotzky, R. F.↗
NASA NTRS1984

X-ray emission from clusters of galaxies

Some X-ray spectral observations of approximately 30 clusters of galaxies from HEAO-1 are summarized. There exists strong correlation betwen X-ray luminosity, L(x), and temperature kT in the form L(x)alphaT to the 2.3 power. This result combined with the L(x) central galaxy density relation and the virial theorem indicates that the core dadius of the gas should be roughly independent of L(x) or Kt and that more luminous clusters have a greater fraction of their virial mass in gas. The poor correlation of KT and optical velocity dispersion seems to indicate that clusters have a variety of equations of state. There is poor agreement between X-ray imaging observations and optical and X-ray spectral measures of the polytropic index. Most clusters show Fe emission lines with a strong indication that they all have roughly 1/2 solar abundance. The evidence for cooling in the cores several clusters is discussed based on spectral observations with the Einstein solid state spectrometer.

Mushotzky, R. F.↗
NASA NTRS1961

NEUTRINO EMISSION PROCESSES, STELLAR EVOLUTION AND SUPERNOVA. PART II.

When the internal temperature of a star exceeds 1 BK (109 °K) the evolution is very rapid. The time scale is around 3000 years. Energy dissipated by emission of neutrinos is several orders of magnitude higher than that by optical radiation. Neutrinos have exceedingly long mean free path (∼10(exp 20) gram/cm(exp 2)) and they will escape as soon as they are produced. The star will contract to release gravitational energy to make up the energy lost to neutrinos and the internal temperature will rise to comply with the virial theorem. It is possible in this fast evolutionary phase, to neglect optical radiations all together as compared with the neutrino radiation. A set of structural equations is thus obtained. The envelope is replaced by boundary conditions. A simple model is constructed to illustrate our approach.

Star↗
NASA NTRS1971

Velocity dispersions in galaxies: 1: The SO galaxy NGC 7332

A Coude spectrum of the SO galaxy NGC 7332 with 0.9 A resolution from 4186 to 4364 A was obtained with the SEC vidicon television camera and the Hale telescope. Comparisons with spectra of G and K giant stars, numerically broadened for various Maxwellian velocity distributions, give a dispersion velocity in the line of sight of 160 + or - 20 km/sec with the best fit at G8III. The dispersion appears to be constant within + or - 35 km/sec out to 1.4 kpc (H = 100 km/sec/mpc). After correction for projection, the rotation curve has a slope of 0.16 km/sec/pc at the center and a velocity of 130 km/sec at 1.4 kpc where it is still increasing. For an estimated effective radius of 3.5 kpc enclosing half the light, the virial theorem gives a mass of 1.4 x 10 to the 11th power solar masses if the mass-to-light ratio is constant throughout the galaxy. The photographic luminosity is 8.3 x 10 to the 9th power solar luminosities so that the M/L ratio is 17.

Morton, D. C.↗