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Results for “Density Laws”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Cold dissipationless collapse of spherical systems - Sensitivity to the initial density law

The collapse of cold, initially spherical systems with varying degrees of central condensation is investigated. The way in which the final shape of a collapsing system depends on the initial density law is examined. For an initial stellar number density rho varies as r exp -n, where n is in the range 0-2.5, the final, nearly prolate shape is given by a/c is approximately equal to 1.28(1 + 0.16 n), where a/c is the ratio of long to short axes of the inertia ellipsoid computed from the moment of inertia tensor of the most tightly bound 80 percent of the mass. The properties associated with the final states in the present computations are also studied. The collapsing systems develop an anisotropic halo dominated by radial orbits surrounding an isotropic core as predicted by Burkert (1990).

Cannizzo, John K.↗
NASA NTRS1994

Thin shell formation in radiative shocks. 1: Supernova remnants in low-density media

This paper explores the onset of thin-shell formation in interstellar shocks associated with supernova explosions. We outline a simple but useful scheme that indicates the time at which thin shell formation begins for supernova remnants (SNRs) evolving in a range of interstellar environments, extending the previous analytical models to arbitrary power-law density media. The result depends on the gas cooling properties and the shock velocity and radius. This is then applied to the specific case of SNRs in low-density media. The procedure for defining the time for the onset of shell formation, t(sub sf), equates the value of the adiabat, kappa = p/rho(exp gamma), to zero using the known time dependence of the shock radius and velocity. For the case of a power-law density ambient medium of the form rho(r) = Br(exp -omega), it is found that shell formation can be prevented when the ambient density drops faster than a critical rate. For a cooling function of the form Lambda = Lambda(sub 0) tau(exp beta), with beta = -0.5 (appropriate for line cooling), shell formation never occurs for omega greater than or equal to 9/5. The shell formation time is then computed for spherical shocks in a power-law density medium. For omega = 0, the onset of shell formation is found to be at t(sub sf) approx. equal to 2.87 x 10(exp 4) E51(exp 3/14) n(sub 0 exp -4.7) yr, which agrees well with previous estimates derived by other means. We compare the analytical shell formation time with the results of detailed numerical models for omega = 0 and three different ambient densities and find good agreement. The extension of the criterion for the onset of thin shell formation using the ratio of cooling to swept-up column density is also described. This method provides a useful approximation for cases when the exact solution is not known.

Franco, Jose↗
NASA NTRS1992

Hydrodynamic instabilities in supernova remnants - Self-similar driven waves

An initial study aimed at elucidating the multidimensional aspects of the hydrodynamic instabilities in supernova remnants is presented. Self-similar solutions are found to exist for the interaction of a steep power-law density profile expanding into a relatively flat stationary power-law density profile. Consideration of the pressure and entropy profiles in the shocked 1D flows shows that the flows are subject to convective instability, by a local criterion. The growth rate for the instability becomes very large near the contact discontinuity between the two shocked regions. A linear analysis of the complete self-similar solutions shows that the solutions are unstable above a critical wavenumber and that the growth rate is greatest at the position of the contact discontinuity. The X-ray image of the remnant of SN 1572 (Tycho) shows emission from clumps of supernova ejecta, which is good evidence for instabilities in this remnant.

Chevalier, Roger A.↗
NASA NTRS1986

Near-infrared observations of IRAS sources in and near dense cores

We report 0.4 to 20 micron photometry of 27 Infrared Astronomy Satellite (IRAS) point sources associated with dense cores in nearby dark clouds. It is found that these objects have a bimodal distribution of spectral slopes. The objects in the group with steep spectral slopes are typically within one half power radius of the core peak and are not visible on the POSS. The remainder of the objects are typically further from their cores, are optically visible and have shallow spectral slopes (s is approximately 0.6). Most of the sources in this group which have been previously identified are T Tauri stars. Both the groups of objects have essentially the same luminosity function with median luminosity of 1 to 2 L(solar), which is similiar to the luminosity function for T Tauri stars. The near-infrared (J,H,K,L) colors of the objects have been used to estimate the visual extinction to the stars. This indicates that the typical steep spectrum source has extinction A(upsilon) of approximately 30 magnitudes, which is larger by a factor of 3 to 4 than a uniform core can provide, thus the density must rise steeply in the vicinity of the star. For those objects where optical estimates of the extinction are available the optical estimates are typically smaller than our IR estimates by a factor of 1.6. For multiple scattering by grains that scatter primarily in the forward direction, this implies a grain albedo of 0.4 at V, consistent with theoretical predictions for bare grains. Using this derived extinction, the FIR emission from a spherical shell with an inverse power law density which contributes the correct amount of extinction has been modelled. It is shown that to be consistent with both the observations of the density of the core at a scale of 1.5 x 10(17) cm and the extinction derived from the near-IR colors there must be a circumstellar hole of radius 10-100 A.U. for all density laws with exponents greater than 1.2. It is also shown that a component in addition to the star and circumstellar shell is necessary to match the observed spectrum of steep spectrum sources.

Fuller, G. A.↗
NASA NTRS1972

Evidence for a continuous, power law, electron density irregularity spectrum

The spectral form of the irregularities in electron density that cause interplanetary scintillation (IPS) of small angular diameter radio sources is discussed. The intensity scintillation technique always yields an irregularity scale size, which is of the order of the first Fresnel zone for the wavelength at which the observations are taken. This includes not only the radio wavelength measurements of the structure of the interplanetary medium, but also radio wavelength measurements of the irregularity structure of the ionosphere and interstellar medium, and optical wavelength measurements of the irregularity structure of the atmosphere.

Cronyn, W. M.↗
NASA NTRS1978

Discovery of polarized light scattered by dust around Alpha Orionis

Following the suggestion by Jura and Jacoby (1976), linearly polarized blue continuum starlight scattered by the dust shell around the M2 Iab star Alpha Orionis (Betelgeuse) has been discovered. The polarization has been traced in the NE, NW, SE, and SW directions and has positive (tangential) orientation. Some asymmetry of the optical depth in the shell exists 15 and 30 arcsec from the star. In the NE direction the polarization was measured as far as 90 arcsec (17,000 AU) from the star. The dependence of the average intensity of the scattered light from the nebula on angular distance from the star is more consistent with an inverse-square density law than with inverse 1.5 or inverse-cube laws. Assuming that the density is proportional to the inverse square of distance from the star, the scattering optical depth in blue light along a radius of 0.03 arcsec is no more than 0.15 + or - 0.05. Future observations of the wavelength dependence of polarization will allow a determination of grain size.

Mcmillan, R. S.↗
NASA NTRS1990

On the formation and expansion of H II regions

The evolution of H II regions in spherical clouds with small, constant-density cores and power-law density distributions r exp -w outside the core is described analytically. It is found that there is a critical exponent above which the cloud becomes completely ionized. Its value in the formation phase depends on the initial conditions, but it has a well-defined value w(crit) = 3/2 during the expansion phase. For w less than w(crit), the radius of the H II region grows at a given rate, while neutral mass accumulates in the interphase between the ionization and shock fronts. For w = w(crit), the fronts move together without mass accumulation. Cases with w greater than w(crit) lead to the champagne phase: once the cloud is fully ionized, the expansion becomes supersonic. For self-gravitating disks without magnetic fields, the main features include a new 'variable-size' stage. The initial shape of the H II region has a critical point beyond which the disk becomes completely ionized.

Franco, Jose↗
NASA NTRS2022

Quantifying Feedback from Narrow Line Region Outflows in Nearby Active Galaxies. IV. The Effects of Different Density Estimates on the Ionized Gas Masses and Outflow Rates

Active galactic nuclei (AGN) can launch outflows of ionized gas that may influence galaxy evolution, and quantifying their full impact requires spatially resolved measurements of the gas masses, velocities, and radial extents. We previously reported these quantities for the ionized narrow-line region outflows in six low-redshift AGN, where the gas velocities and extents were determined from Hubble Space Telescope long-slit spectroscopy. However, calculating the gas masses required multicomponent photoionization models to account for radial variations in the gas densities, which span ∼6 orders of magnitude. To simplify this method for larger samples with less spectral coverage, we compare these gas masses with those calculated from techniques in the literature. First, we use a recombination equation with three different estimates for the radial density profiles. These include constant densities, those derived from [S ii], and power-law profiles based on constant values of the ionization parameter (U). Second, we use single-component photoionization models with power-law density profiles based on constant U, and allow U to vary with radius based on the [O iii]/Hβ ratios. We find that assuming a constant density of nH = 10(^2) cm(^−3) overestimates the gas masses for all six outflows, particularly at small radii where the outflow rates peak. The use of [S ii] marginally matches the total gas masses, but also overestimates at small radii. Overall, single-component photoionization models where U varies with radius are able to best match the gas mass and outflow rate profiles when there are insufficient emission lines to construct detailed models.

Mitchell Revalski↗
NASA NTRS1995

Models of far-IR sources at W3-IRS4 and W3-IRS5

Far-IR continuum maps made with the KAO of W3 at 47 and 95 micrometers show peaks identified with the mid-IR sources IRS4 and IRS5 and extended emission identified with the radio source W3A. We have taken the steepest radial scan profiles from the peaks at IRS4 and IRS5 to represent the objects as spherical clouds. Spherically symmetric models were created in an attempt to match the observed profiles. Radiative transfer dust cloud models heated by central protostars or stars do not match extended emission in the 47 micrometers scan profile for any assumed density distribution for either source. However, both sources can be approximately fit by power law density profiles and ad hoc temperature profiles which are much less steep than those by the single source radiative transfer models. One possible physical explanation for the shallow temperature gradients suggested by the data is heating by a distribution of luminosity sources.

Campbell, M. F.↗
NASA NTRS1994

A family of models for spherical stellar systems

We describe a one-parameter family of models of stable sperical stellar systems in which the phase-space distribution function depends only on energy. The models have similar density profiles in their outer parts (rho propotional to r(exp -4)) and central power-law density cusps, rho proportional to r(exp 3-eta), 0 less than eta less than or = 3. The family contains the Jaffe (1983) and Hernquist (1990) models as special cases. We evaluate the surface brightness profile, the line-of-sight velocity dispersion profile, and the distribution function, and discuss analogs of King's core-fitting formula for determining mass-to-light ratio. We also generalize the models to a two-parameter family, in which the galaxy contains a central black hole; the second parameter is the mass of the black hole. Our models can be used to estimate the detectability of central black holes and the velocity-dispersion profiles of galaxies that contain central cusps, with or without a central black hole.

Tremaine, Scott↗
NASA NTRS1975

Direct observations of higher frequency density fluctuations in the interplanetary plasma

Direct observations from the plasma spectrometers on Pioneer 6 at 1 AU in December, 1965, have been used to obtain the power associated with fluctuations in the number density of solar-wind protons in the frequency range from .001 to .01 Hz. A power-law spectrum is obtained in this frequency range. The extension of the power-law density spectrum based on direct observations to these higher frequencies is consistent with previous extrapolations of both spacecraft and interplanetary scintillation observations and with the dominance of large-scale turbulence in the solar wind. This result is also consistent with direct observations of the solar-wind proton speed and the interplanetary magnetic field.

Intriligator, D. S.↗
NASA NTRS1993

The first detection of a collapsed core globular cluster in M31

We report on the observations of a globular cluster (designated G105 = Bo 343) in the nearby spiral galaxy M31, using the Hubble Space Telescope (HST). Image deconvolutions using three different methods indicate that this cluster has a density profile with the morphology characteristic of stellar systems which have undergone core collapse, i.e., a power-law density cusp near the center. This is the first such detection in a galaxy as distant as M31. This discovery may lead to extensive future statistical studies of the globular cluster system of M31, and thus a better understanding of its evolution.

Bendinelli, O.↗
NASA NTRS1978

Scaling relationships for mercury and gaseous propellant ion thrusters

A model describing the doubly charged ion densities in argon and xenon ion thrusters is presented. Doubly charged ions are shown to be produced in significant numbers from both the neutral and singly ionized states. Doubly-to-singly charged ion density ratios calculated using this model are compared to experimental values of this ratio measured in the 15 cm multipole thruster using both propellants. Agreement between theory and experiment is shown to be good. Using this doubly charged ion model, and a similar one obtained previously for mercury, together with the constant neutral loss rate theory, Child's current density law and accelerator grid fabrication limitations, a set of scaling relationships are developed. These relationships show the propellant utilizations, thrust densities and discharge power levels that can be expected as thruster diameter and/or specific impulse are increased and doubly charged ion densities are held at acceptably low values.

Wilbur, P. J.↗
NASA NTRS1994

CS multitransitional study of density distribution in star-forming regions. 2: The S140 region

The S140 molecular cloud was observed in five transitions of CS with resolutions of 11 to 45 arcsec. The data were analyzed with both the LVG and microturbulent models of radiative transfer to derive the density structure. It was found that the CS emission comes from three components of gas: a spherical component centered on the infrared cluster, an arc component along the ionization front between the S140 H II region and the dense molecular cloud core, and a high-velocity component from the dense part of a molecular outflow. The spherical component contributes most to the CS emission and was analyzed in more detail than the other components. Using a temperature distribution derived from an analysis of the dust emission from S140, we fit a power-law density distribution of n(r) = n(sub i)(r/r(sub i))(exp -alpha) to the spherical component. The best fit was for n(sub i) = 1.4 x 10(exp 6) (density at r(sub i) = 0.026 pc) and alpha = 0.8. The density (n(sub i)) was found to be greater than or equal to the density required to account for the dust emission, depending on the dust opacity laws adopted. The presence of optical emission (Dinerstein, Lester, & Rank 1979) suggests a clumpy structure for the dense gas. Considerations of the virial mass and the lowest amount of column density required to produce dust emission put the volume filling factor (f(sub nu)) of the dense gas at approximately 0.14-0.5. We compared S140 with other regions of star formation where the density structure has been derived from excitation analysis. Source-source variations in density gradients and clumpiness clearly exist, ranging from alpha = 2 and f(sub nu) approximately 1 in B335 to alpha approximately 0, f(sub nu) approximately 0.1 in M17. There is a tendency for more massive star-forming regions to have a flatter density distribution, a more clumpy structure, and a large number of young stars. The implications of this tendency are discussed.

Zhou, Shudong↗
NASA NTRS2019

Dust Formation in AGN Winds

Infrared observations of active galactic nuclei (AGNs) reveal emission from the putative dusty circumnuclear "torus" invoked by AGN unification, which is heated up by radiation from the central accreting black hole (BH).The strong 9.7 and 18 m silicate features observed in the AGN spectra, in both emission and absorption, further indicate the presence of such dusty environments. We present detailed calculations of the chemistry of silicate dust formation in AGN accretion disk winds. The winds considered herein are magnetohydrodynamic winds driven off the entire accretion disk domain that extends from the BH vicinity to the radius of BH influence, of order ~1-100 pc depending on the mass of the resident BH. Our results indicate that these winds provide conditions conducive to the formation of significant amounts of dust, especially for objects accreting close to their Eddington limit, making AGNs a significant source of dust in the universe, especially for luminous quasars. Our models justify the importance of an r1 density law in the winds for efficient formation and survival of dust grains. The dust production rate scales linearly with the mass of the central BH and varies as a power law of index between 2 and 2.5 with the dimensionless mass accretion rate. The resultant distribution of the dense dusty gas resembles atoroidal shape, with high column density and optical depths along the equatorial viewing angles, in agreement with the AGN unification picture

Arkaprabha Sarangi↗
NASA NTRS1986

A new method for reconstructing type III trajectories

A local density approximation (LDA) method is developed for reconstructing the trajectories of type III radio bursts through the interplanetary medium. The method uses the measured source directions and the measured frequency drift rates of the type III burst to determine the locations of the radio source in the interplanetary medium at consecutive frequency levels. The technique is used to reconstruct the trajectory of an actual type III burst and the results are compared to the trajectory obtained from the global density law method. The LDA method represents an improvement in that it utilizes more observed data on the type III burst and that it takes full account of the local density variations at the source locations.

Reiner, M. J.↗
NASA NTRS1974

The power associated with density fluctuations and velocity fluctuations in the solar wind

Direct observations from Pioneer 6 of solar-wind-proton fluctuations have been used to obtain the power spectra associated with solar-wind-proton number density and velocity fluctuations in the frequency range of 0.001 to 0.01 Hz, extending previous analyses by an order of magnitude at the higher frequencies. The slopes of the power spectra associated with the density fluctuations and the velocity fluctuations are similar and are in agreement with the shape of the power spectra found at the lower frequencies. The power spectra indicate that the power-law density spectrum observed at lower frequencies extends to at least 0.01 Hz. This smooth variation in the spectrum at these frequencies is consistent with previous extrapolations of both spacecraft and interplanetary scintillation observations.

Intriligator, D. S.↗