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NASA NTRS1990

A dipole moment of the microwave background as a cosmological effect

A spherically symmetrical Tolman-Bondi cosmological model is presented in which the curvature of space and the entropy variety with distance from the center. The dipole and quadrupole moments in the distribution of the microwave background radiation are calculated as a function of cosmic time and position of an observer, assuming that the distance to the horizon is much smaller than any characteristic scale in the model. The quadrupole moment is found to be affected mostly by the gradient in the curvature of space while the dipole moment is dominated by the gradient of entropy. The results indicate that the observed dipole in the microwave background may be cosmological in origin. Observational tests of this argument are suggested.

Paczynski, Bohdan↗

NASA NTRS1990

Application of reversal electron attachment for ultrasensitive detection of thermal electron-attaching molecules - CCl4 and C6H5O2

A standard gas-dilution method was used to determine the selective response of the reversal electron attachment detector to carbon tetrachloride concentrations in nitrogen. Data are provided that determine the lowest concentration of sample detectable with the present instrumental configuration as being below 1.0 part per trillion by volume. The incorporation of a 90-deg electrostatic deflector with the quadrupole mass spectrometer is shown to be vital, and with it, negative-ion quadrupole mass spectrometry is used to characterize the ionization process. Observations are also made of the reversal electron attachment response to nitrobenzene. The analytical potential of reversal electron capture negative-ion mass spectrometry is examined, and areas for future development are discussed.

Bernius, Mark T.↗

NASA NTRS1991

Oscillations of rotating neutron stars

A perturbation technique is used to compute the rotational corrections to the nonradial oscillation spectrum of a realistic neutron star model. The l = l(0) oscillations are coupled to l = l(0) + or - 1 oscillations by the Coriolis force. To calculate the rotational corrections to the quadrupole, l(0) = 2, oscillation modes, previous calculations of the nonradial oscillation spectrum of this neutron star model are extended to include l(0) = 1 and l(0) = 3 modes, as well as many higher overtones at each value of l(o). As an example of this technique, the rotational corrections to two quadrupole toroidal modes are computed. For these modes the coupling to the spheroidal class of oscillations produced by the Coriolis force introduces a nonzero radial component to the velocity field, as well as a nonvanishing Lagrangian density perturbation. This result is used to compute the neutrino damping rates for these toroidal modes of a rotating neutron star. The neutrino damping time can approach the gravitational radiation damping time in rotating neutron stars if the central temperature is high enough. The rotationally induced coupling of spheroidal oscillations to toroidal modes can also produce significant displacements at the stellar surface in some of the toroidal modes. The damping rates due to this process for the rotationally corrected toroidal modes are estimated. The coupling of surface motions to the toroidal modes also have interesting implications for channeling energy, e.g., that associated with a glitch in the crust, to the surface of the star. Perhaps this might produce observable effects in the pulsar emission process or a gamma-ray burst event.

Strohmayer, Tod E.↗

NASA NTRS1991

Critical problems of computational aeroacoustics

The aeroacoustics of rigid boundaries is discussed. Lighthill gave a formulation of this problem in which he showed that the sources of the acoustic field were quadrupole in nature. We have preferred a different formulation of the problem, in which the quadrupoles are sources for a nonlinear wave equation, as opposed to the linear one used by Lighthill. This is given here in a figure which also gives further details of a solution procedure for the Euler equations appropriate for the aeroelastic problem and motivated by the analysis of Crow. In accordance with our formulation, we contend that an algorithm for accurate solutions of an inhomogeneous nonlinear wave equation is of prime importance.

Rogers, Joel C. W.↗

NASA NTRS1991

On the Galactic origin of gamma-ray bursts

Statistical properties of the distribution of gamma-ray bursts (GRBs) are analyzed assuming that bursters are located in the Galactic disk or in the Galactic halo. It is shown that, in almost all models, angular anisotropy as measured with either dipole or quadrupole moments is much stronger and should be much easier to detect than the radial nonuniformity of the source distribution as measured with V/V sub max test. Recent reports that V/V sub max is about 0.4 demonstrate that the 'edge' of GRBs distribution has been reached. Therefore, if the bursters are in the Galaxy, then their distribution in the sky should be very anisotropic, with a large dipole or quadrupole moment for halo or disk origin, respectively. Absence of strong anisotropy would indicate cosmological origin. Another possibility could be a very extended halo origin, with the core radius Rc greater than 17 kpc, the range of observations Dmax greater than 50 kpc, and a spherical density distribution, the set of conditions that would be very difficult to understand.

Paczynski, Bohdan↗

NASA NTRS1992

Structure in the COBE differential microwave radiometer first-year maps

Results of the first year of data from the differential microwave radiometers on the Cosmic Background Explorer are presented. Statistically significant structure that is well described as scale-invariant fluctuations with a Gaussian distribution is shown. The rms sky variation, smoothed to a total 10-deg FWHM Gaussian, is 30 +/-5 micro-K for Galactic latitude greater than 20-deg data with the dipole anisotropy removed. The rms cosmic quadrupole amplitude is 13 +/-4 micro-K. The angular autocorrelation of the signal in each radiometer channel and cross-correlation between channels are consistent and give a primordial fluctuation power-law spectrum with index of 1.1 +/-0.5, and an rms-quadrupole-normalized amplitude of 16 +/-4 micro-K. These features are in accord with the Harrison-Zel'dovich spectrum predicted by models of inflationary cosmology.

Smoot, G. F.↗

NASA NTRS1993

Propagation of high frequency jet noise using geometric acoustics

Spherical directivity of noise radiated from a convecting quadrupole source embedded in an arbitrary spreading jet is obtained by ray-tracing methods of geometrical acoustics. The six propagation equations are solved in their general form in a rectangular coordinate system. The noise directivity in the far field is calculated by applying an iteration scheme that finds the required radiation angles at the source resulting in propagation through a given observer point. Factors influencing the zone of silence are investigated. The caustics of geometrical acoustics and the exact locations where it forms is demonstrated by studying the variation in ray tube area obtained from transport equation. For a ring source convecting along the center-axis of an axisymmetric jet, the polar directivity of the radiated noise is obtained by an integration with respect to azimuthal directivity of compact quadrupole sources distributed on the ring. The Doppler factor is shown to vary slightly from point to point on the ring. Finally the scaling of the directivity pattern with power -3 of Doppler factor is investigated and compared with experimental data.

Khavaran, A.↗

NASA NTRS1993

Omega from the anisotropy of the redshift correlation function

Peculiar velocities distort the correlation function of galaxies observed in redshift space. In the large scale, linear regime, the distortion takes a characteristic quadrupole plus hexadecapole form, with the amplitude of the distortion depending on the cosmological density parameter omega. Preliminary measurements are reported here of the harmonics of the correlation function in the CfA, SSRS, and IRAS 2 Jansky redshift surveys. The observed behavior of the harmonics agrees qualitatively with the predictions of linear theory on large scales in every survey. However, real anisotropy in the galaxy distribution induces large fluctuations in samples which do not yet probe a sufficiently fair volume of the Universe. In the CfA 14.5 sample in particular, the Great Wall induces a large negative quadrupole, which taken at face value implies an unrealistically large omega 20. The IRAS 2 Jy survey, which covers a substantially larger volume than the optical surveys and is less affected by fingers-of-god, yields a more reliable and believable value, omega = 0.5 sup +.5 sub -.25.

Hamilton, A. J. S.↗

NASA NTRS1993

Propagation of high frequency jet noise using geometric acoustics

Khavaran, A.↗

NASA NTRS1991

High-speed helicopter rotor noise - Shock waves as a potent source of sound

In this paper we discuss the problem of high speed rotor noise prediction. In particular, we propose that from the point of view of the acoustic analogy, shocks around rotating blades are sources of sound. We show that, although for a wing at uniform steady rectilinear motion with shocks the volume quadrupole and shock sources cancel in the far field to the order of 1/r, this cannot happen for rotating blades. In this case, some cancellation between volume quadrupoles and shock sources occurs, yet the remaining shock noise contribution is still potent. A formula for shock noise prediction is presented based on mapping the deformable shock surface to a time independent region. The resulting equation is similar to Formulation 1A of Langley. Shock noise prediction for a hovering model rotor for which experimental noise data exist is presented. The comparison of measured and predicted acoustic data shows good agreement.

Farassat, F.↗

NASA NTRS1992

A two-dimensional MHD global coronal model - Steady-state streamers

A 2D, time-dependent, numerical, MHD model for the simulation of coronal streamers from the solar surface to 15 solar is presented. Three examples are given; for dipole, quadrupole and hexapole (Legendre polynomials P1, P2, and P3) initial field topologies. The computed properties are density, temperature, velocity, and magnetic field. The calculation is set up as an initial-boundary value problem wherein a relaxation in time produces the steady state solution. In addition to the properties of the solutions, their accuracy is discussed. Besides solutions for dipole, quadrupole, and hexapole geometries, the model use of realistic values for the density and Alfven speed while still meeting the requirement that the flow speed be super-Alfvenic at the outer boundary by extending the outer boundary to 15 solar radii.

Wang, A.-H.↗

NASA NTRS1992

Line-width temperature dependence of selected R-branch transitions in the nu-3 fundamental of (N-14)2O-16 between 135 and 295 K

Tunable diode laser spectroscopy has been used to measure the temperature dependence of N2 foreign gas broadening coefficients for eight R-branch transitions in the nu-3 fundamental of (N-14)2O-16 at 135, 176, 210, and 295 K. The exponent n of the relation for quadrupole-quadrupole collisional interactions is found to range from 0.66 to 0.71, in approximate agreement with the theoretically predicted value of 0.75.

Loewenstein, Max↗

NASA NTRS1993

The millimeter-wave spectrum of AlOH

The pure rotational spectrum of the AlOH and AlOD molecules in their X 1Sigma(+) (v = 0) ground electric states has been measured in the laboratory using direct absorption millimeter/submillimeter spectroscopy. The species were produced by the reaction of aluminum vapor, created in a Broida-type oven, with hydrogen peroxide or D2O2. Eight rotational transitions of AlOH and five transitions for AlOD were measured in the frequency range of 157-378 GHz to an accuracy better than +/- 75 kHz. Electric quadrupole interactions, arising from the aluminum nuclear spin of 5/2, were observed in the J = 4 - 5 and the J = 5 - 6 transitions of AlOH. The rotational constants of these molecules have been determined from a nonlinear least-squares fit to the data. The electric quadrupole coupling constant, eqQ, has been measured as well, and was found to have a value of -42.4 +/- 4.3 MHz. The spectra are consistent with quasi-linear ground states for AlOH and AlOD, as predicted by theory. AlOH is of astrophysical interest because of the relatively high cosmic abundance of aluminum.

Apponi, A. J.↗

NASA NTRS1994

Non-dipolar magnetic field models and patterns of radio emission: Uranus and Neptune compared

The magnetic field geometries of Uranus and Neptune are superficially similar, and are similarly unlike those of other planets: the field strengths are similar, and they contain extraordinarily large non-dipolar components. As a corollary, the best dipolar field models of each of the two planets comprises a dipole that is considerably offset from the planetary center and tilted away from the rotational axis. However, in other respects the best field models of the two planets are quite different. Uranus has a quadrupole model in which all the terms are well determined and in which none of the higher order terms is determined. To represent the magnetometer data acquired during Voyager's Neptune encounter requires a model of order 8 (instead of Uranus' order 2), yet many of the coefficients are poorly determined. A second model, an octupole model comprising the terms up to order three of the order 8 model, has been suggested by the magnetometer team as being useful; its use, however, is limited only to the region outside of about 2R(exp N), whereas planetary radio emissions have their sources well inside this surface. Computer code has been written that permits an analysis of the detailed motion of low energy charged particles moving in general planetary magnetic fields. At Uranus, this code reveals the existence of an isolated region of the inner magnetosphere above the day side in which particles may be trapped, separate from the more general magnetospheric trapping. An examination of the so-call ordinary mode uranian radio emissions leads us to believe that these emissions are in fact extraordinary mode emissions coming from particles trapped in this isolated region. A similar attempt to discover trapping regions at Neptune has proved, unfortunately, to be impossible. This arises from three factors: (1) the computation needed to track particles in an eighth order field is more than an order of magnitude greater than that needed to perform a similar calculation in a quadrupole field, and is beyond the capacity of workstation-class computers; (2) the octupole field model is known to be in error by too large an ammount for it, or any similarly truncated version of the eighth order model, to produce trustworthy results; (3) the eighth order model can, in effect, be infinitely varied without affecting the field strength along the spacecraft trajectory.

Evans, D. R.↗

NASA NTRS1994

Comments on the statistical analysis of excess variance in the COBE differential microwave radiometer maps

Cosmic anisotrophy produces an excess variance sq sigma(sub sky) in the Delta maps produced by the Differential Microwave Radiometer (DMR) on cosmic background explorer (COBE) that is over and above the instrument noise. After smoothing to an effective resolution of 10 deg, this excess sigma(sub sky)(10 deg), provides an estimate for the amplitude of the primordial density perturbation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal root mean square (rms) quadrupole amplitude, (Q sq/RMS)(exp 0.5). The effects of monopole and dipole subtraction and the non-Gaussian shape of the DMR beam cause the derived (Q sq/RMS)(exp 0.5) to be 5%-10% larger than would be derived using simplified analytic approximations. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the sigma(sub sky)(10 deg) statistic and the Boughn-Cottingham statistic are consistent with the (Q sq/RMS)(exp 0.5) = 17 +/- 5 micro K reported by Smoot et al. (1992) and Wright et al. (1992).

Wright, E. L.↗

NASA NTRS1995

Magnetic field evolution in white dwarfs: The hall effect and complexity of the field

We calculate the evolution of the magnetic fields in white dwarfs, taking into account the Hall effect. Because this effect depends nonlinearly upon the magnetic field strength B, the time dependences of the various multipole field components are coupled. The evolution of the field is thus significantly more complicated than has been indicated by previous investigations. Our calculations employ recent white dwarf evolutionary sequences computed for stars with masses 0.4, 0.6, 0.8, and 1.0 solar mass. We show that in the presence of a strong (up to approximately 10(exp 9) G) internal toroidal magnetic field; the evolution of even the lowest order poloidal modes can be substantially changed by the Hall effect. As an example, we compute the evolution of an initially weak quadrupole component, which we take arbitrarily to be approximately 0.1%-1% of the strength of a dominant dipole field. We find that coupling provided by the Hall effect can produce growth of the ratio of the quadrupole to the dipole component of the surface value of the magnetic field strength by more than a factor of 10 over the 10(exp 9) to 10(exp 10) year cooling lifetime of the white dwarf. Some consequences of these results for the process of magnetic-field evolution in white dwarfs are briefly discussed.

Muslimov, A. G.↗

NASA NTRS1995

The COBE normalization for standard cold dark matter

The Cosmic Background Explorer Satellite (COBE) detection of microwave anisotropies provides the best way of fixing the amplitude of cosmological fluctuations on the largest scales. This normalization is usually given for an n = 1 spectrum, including only the anisotropy caused by the Sachs-Wolfe effect. This is certainly not a good approximation for a model containing any reasonable amount of baryonic matter. In fact, even tilted Sachs-Wolfe spectra are not a good fit to models like cold dark matter (CDM). Here, we normalize standard CDM (sCDM) to the two-year COBE data and quote the best amplitude in terms of the conventionally used measures of power. We also give normalizations for some specific variants of this standard model, and we indicate how the normalization depends on the assumed values on n, Omega(sub B) and H(sub 0). For sCDM we find the mean value of Q = 19.9 +/- 1.5 micro-K, corresponding to sigma(sub 8) = 1.34 +/- 0.10, with the normalization at large scales being B = (8.16 +/- 1.04) x 10(exp 5)(Mpc/h)(exp 4), and other numbers given in the table. The measured rms temperature fluctuation smoothed on 10 deg is a little low relative to this normalization. This is mainly due to the low quadrupole in the data: when the quadrupole is removed, the measured value of sigma(10 deg) is quite consistent with the best-fitting the mean value of Q. The use of the mean value of Q should be preferred over sigma(10 deg), when its value can be determined for a particular theory, since it makes full use of the data.

Bunn, Emory F.↗

NASA NTRS1995

Aerodynamic sound of flow past an airfoil

The long term objective of this project is to develop a computational method for predicting the noise of turbulence-airfoil interactions, particularly at the trailing edge. We seek to obtain the energy-containing features of the turbulent boundary layers and the near-wake using Navier-Stokes Simulation (LES or DNS), and then to calculate the far-field acoustic characteristics by means of acoustic analogy theories, using the simulation data as acoustic source functions. Two distinct types of noise can be emitted from airfoil trailing edges. The first, a tonal or narrowband sound caused by vortex shedding, is normally associated with blunt trailing edges, high angles of attack, or laminar flow airfoils. The second source is of broadband nature arising from the aeroacoustic scattering of turbulent eddies by the trailing edge. Due to its importance to airframe noise, rotor and propeller noise, etc., trailing edge noise has been the subject of extensive theoretical (e.g. Crighton & Leppington 1971; Howe 1978) as well as experimental investigations (e.g. Brooks & Hodgson 1981; Blake & Gershfeld 1988). A number of challenges exist concerning acoustic analogy based noise computations. These include the elimination of spurious sound caused by vortices crossing permeable computational boundaries in the wake, the treatment of noncompact source regions, and the accurate description of wave reflection by the solid surface and scattering near the edge. In addition, accurate turbulence statistics in the flow field are required for the evaluation of acoustic source functions. Major efforts to date have been focused on the first two challenges. To this end, a paradigm problem of laminar vortex shedding, generated by a two dimensional, uniform stream past a NACA0012 airfoil, is used to address the relevant numerical issues. Under the low Mach number approximation, the near-field flow quantities are obtained by solving the incompressible Navier-Stokes equations numerically at chord Reynolds number of 104. The far-field noise is computed using Curle's extension to the Lighthill analogy (Curle 1955). An effective method for separating the physical noise source from spurious boundary contributions is developed. This allows an accurate evaluation of the Reynolds stress volume quadrupoles, in addition to the more readily computable surface dipoles due to the unsteady lift and drag. The effect of noncompact source distribution on the far-field sound is assessed using an efficient integration scheme for the Curle integral, with full account of retarded-time variations. The numerical results confirm in quantitative terms that the far-field sound is dominated by the surface pressure dipoles at low Mach number. The techniques developed are applicable to a wide range of flows, including jets and mixing layers, where the Reynolds stress quadrupoles play a prominent or even dominant role in the overall sound generation.

Wang, Meng↗