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NASA NTRS1991

The physical properties of double degenerate common proper motion binaries

Spectral types and spectrophotometry are presented for 21 double degenerate (DD) common proper motion binaries, along with estimates of their colors, absolute visual and bolometric magnitudes, and cooling ages. The oldest pairs in the sample are 9 x 10 to the 9th yr; the differential cooling ages range from 0.01 to 0.84. The median and mean separations of the DD pairs are 426 and 407 Au, respectively, both apparently smaller than the WD+MS values. The average UVW motions and velocity dispersions are significantly larger than the average velocities and dispersions associated with selected samples of single white dwarfs and MS+WD binaries when the latter are restricted to the same color/Mv range as the DD systems. This may be a result of the dynamical inflation of the velocity dispersion of DD systems due to their extremely ancient total stellar ages.

Sion, Edward M.↗
NASA NTRS1993

Spectral decomposition of AVIRIS data

A set of techniques is presented that uses only information contained within a raw Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) scene to estimate and to remove additive components such as multiple scattering and instrument dark current. Multiplicative components (instrument gain, topographic modulation of brightness, atmospheric transmission) can then be normalized, permitting enhancement, extraction, and identification of relative reflectance information related to surface composition and mineralogy. The technique for derivation of additive-component spectra from a raw AVIRIS scene is an adaption of the 'regression intersection method' of Crippen. This method uses two surface units that are spatially extensive, and located in rugged terrain. For a given wavelength pair, subtraction of the derived additive component from individual band values will remove topography in both regions in a band/band ratio image. Normalization of all spectra in the scene to the average scene spectrum then results in cancellation of multiplicative components and production of a relative-reflectance scene. The resulting AVIRIS product contains relative-reflectance features due to mineral absorption that depart from the average spectrum. These features commonly are extremely weak and difficult to recognize, but they can be enhanced by using two simple 3-D image-processing tools. The validity of these techniques will be demonstrated by comparisons between relative-reflectance AVIRIS spectra and those derived by using JPL standard calibrations. The AVIRIS data used in this analysis were acquired over the Kelso Dunes area (34 deg 55' N, 115 deg 43' W) of the eastern Mojave Desert, CA (in 1987) and the Upheaval Dome area (38 deg 27' N, 109 deg 55' W) of the Canyonlands National Park, UT (in 1991).

Gaddis, Lisa↗
NASA NTRS1994

The DQ Herculis stars

We review the properties of the DQ Herculis stars: cataclysmic variables containing an accreting, magnetic, rapidly rotating white dwarf. These stars are characterized by strong X-ray emission, high-excitation spectra, and very stable optical and X-ray pulsations in their light curves. There is considerable resemblance to their more famous cousins, the AM Herculis stars, but the latter class is additionally characterized by spin-orbit synchronism and the presence of strong circular polarization. We list eighteen stars passing muster as certain or very likely DQ Her stars. The rotational periods range from 33 s to 2.0 hr. Additional periods can result when the rotating searchlight illuminates other structures in the binary. A single hypothesis explains most of the observed properties: magnetically channeled accretion within a truncated disk. Some accretion flow still seems to proceed directly to the magnetosphere, however. The white dwarfs' magnetic moments are in the range 10(sup 32) - 10(sup 34) G cc, slightly weaker than in AM Her stars but with some probable overlap. The more important reason why DQ Hers have broken synchronism is probably their greater accretion rate and orbital separation. The observed L(sub x)/L(sub V) values are surprisingly low for a radially accreting white dwarf, suggesting that most of the accretion energy is not radiated in a strong shock above the magnetic pole. The fluxes can be more satisfactorily explained if most of the radial infall energy manages to bypass the shock and deposit itse lf directly in the white dwarf photosphere, where it should emerge as extreme ultraviolet (EUV) radiation. This also provides an adequate source of ionizing photons to power the high-excitation optical and UV emission lines. This is probably the DQ Her analog to the famous 'soft X-ray excess' in AM Her stars. However, unlike the AM Her case, this radiation has not been directly observed, so the analogy must not (yet) be embraced too firmly. There is some conventional wisdom today which segregates the short-period from the long-period DQ Her stars. But the observational grounds for this distinction are slim, except in one respect: X-ray emission from short-period systems appears to be weaker and softer. This must be due to the shallower depth of the potential well, and/or the greater difficulty the fast rotators have in enforcing radial accretion flow.

Patterson, Joseph↗
NASA NTRS1994

Solar coronal temperature diagnostics using emission line from multiple stages of ionization of iron

We obtained spatially resolved extreme-ultraviolet (EUV) spectra of AR 6615 on 1991 May 7 with NASA/ Goddard Space Flight Center's Solar EUV Rocket Telescope and Spectrograph (SERTS). Included are emission lines from four different stages of ionization of iron: Fe(+15) lambda 335 A, Fe(+14) lambda 327 A, Fe(+13) lambda 334 A, and Fe(+12) lambda 348 A. Using intensity ratios from among these lines, we have calculated the active region coronal temperature along the Solar Extreme Ultraviolet Telescope and Spectrograph (SERTS) slit. Temperatures derived from line ratios which incorporate adjacent stages of ionization are most sensitive to measurement uncertainties and yield the largest scatter. Temperatures derived from line ratios which incorporate nonadjacent stages of ionization are less sensitive to measurement uncertainties and yield little scatter. The active region temperature derived from these latter ratios has an average value of 2.54 x 10(exp 6) K, with a standard deviation approximately 0.12 x 10(exp 6) K, and shows no significant variation with position along the slit.

Brosius, Jeffrey W.↗
NASA NTRS1994

On the derivation of empirical limits on the helium abundance in coronal holes below 1.5 solar radius

We present a simple technique describing how limits on the helium abundance, alpha, defined as the ratio of helium to proton number density, can be inferred from measurements of the electron density and temperature below 1.5 solar radius. As an illustration, we apply this technique to two different data sets: emission-line intensities in the extreme ultraviolet (EUV) and white-light observations, both measured in polar coronal holes. For the EUV data, the temperature gradient is derived from line intensity ratios, and the density gradient is replaced by the gradient of the line intensity. The lower limit on alpha derived from these data is 0.2-0.3 at 1 solar radius and drops very sharply to interplanetary values of a few percent below 1.06 solar radius. The white-light observations yield density gradients in the inner corona beyond 1.25 solar radius but do not have corresponding temperature gradients. In this case we consider an isothermal atmosphere, and derive an upper limit of 0.2 for alpha. These examples are used to illustrate how this technique could be applicable to the more extensive data to be obtained with the upcoming SOHO mission. Although only ranges on alpha can be derived, the application of the technique to data currently available merely points to the fact that alpha can be significantly large in the inner corona.

Habbal, Shadia Rifai↗
NASA NTRS2000

Creep Properties of NiAl-1Hf Single Crystals Re-Investigated

NiAl-1Hf single crystals have been shown to be quite strong at 1027 C, with strength levels approaching those of advanced Ni-based superalloys. Initial testing, however, indicated that the properties might not be reproducible. Study of the 1027 C creep behavior of four different NiAl-1Hf single-crystal ingots subjected to several different heat treatments indicated that strength lies in a narrow band. Thus, we concluded that the mechanical properties are reproducible. Recent investigations of the intermetallic NiAl have confirmed that minor alloying additions combined with single-crystal growth technology can produce elevated temperature strength levels approaching those of Ni-based superalloys. For example, General Electric alloy AFN 12 {Ni-48.5(at.%) Al-0.5Hf-1Ti-0.05Ga} has a creep rupture strength equivalent to Rene 80 combined with a approximately 30-percent lower density, a fourfold improvement in thermal conductivity, and the ability to form a self-protective alumina scale in aggressive environments. Although the compositions of strong NiAl single crystals are relatively simple, the microstructures are complex and vary with the heat treatment and with small ingot-toingot variations in the alloy chemistry. In addition, initial testing suggested a strong dependence between microstructure and creep strength. If these observations were true, the ability to utilize NiAl single-crystal rotating components in turbine machinery could be severely limited. To investigate the possible limitations in the creep response of high-strength NiAl single crystals, the NASA Glenn Research Center at Lewis Field initiated an in depth investigation of the effect of heat treatment on the microstructure and subsequent 1027 C creep behavior of [001]-oriented NiAl-1Hf with a nominal chemistry of Ni-47.5Al-1Hf-0.5Si. This alloy was selected since four ingots, grown over a number of years and possessing slightly different compositions, were available for study. Specimens taken from the ingots were subjected to several heat treatment schedules, examined by transmission electron microscopy, and tested in both compression and tension. An example of the microstructure found in a [001]-oriented NiAl-1Hf specimen after a solution treatment at 1317 C for 50 hr followed by air cooling is illustrated in the image on the left, where the NiAl matrix contains a uniform distribution of nanometer-scale Gphase (Ni16Hf6Si7) precipitates. Other heat treating schedules produced microstructures with nanometer-sized G-phase cubes and plates or, in an extreme case, produced a microstructure with all the G-phase converted to Heusler (Ni2AlHf) particles. The results of 1027 C creep strength and strain rate testing are illustrated which summarizes data from tensile and compressive testing of samples cut from all four NiAl-1Hf ingots and subjected to a variety of heat treatment schedules. With one exception, all the strength values lie in a narrow band that spans six orders of magnitude in strain rate. The only factor that produced results outside of this band was the heat treatment schedule that dissolved all the G-phase and replaced it with Heusler precipitates. The results portrayed in this figure lead to the important practical conclusion that the elevated-temperature creep properties of NiAl-1Hf single crystals are reproducible and are not affected by small variations in alloy chemistry from ingot to ingot or by different initial distributions of G-phase in the heat-treated alloy. The only variable in this study that produced a significant and delerious effect on mechanical strength was a post-solution heat treatment that lead to the complete disappearance of the G-phase in favor of Heusler precipitates.

Whittenberger, J. Daniel↗
NASA NTRS1992

Extreme ultraviolet filters for 58.4 and 83.4 nm

We report the design of an EUV filter for He I at 58.4 nm and the design and fabrication of an EUV filter for O II at 83.4 nm. Both filters are designed as combinations of three narrow-band reflection filters. The net transmittance through both EUV filters is close to 10 percent with bandwidths less than 10 nm, and blocking better than 0.005 percent for out-of-band wavelengths. A theoretical calculation of the 83.4 nm filter predicts higher values for the peak transmittance than the measured spectral performance of the fabricated filter. Since aluminum is one of the film materials used for the fabrication of EUV filters, the aluminum film oxidation can be modeled in order to explain the discrepancy between the theory and experiment. Since the filters operate at angles of incidence up to 50 deg, the optical components of a system can serve as both the filtering and imaging elements.

Zukic, Muamer↗
NASA NTRS1999

Climatic Variability of Precipitation from the Seasonal Cycle to ENSO Using GPCP's Merged Data Product and SSM/I-Based Microwave Estimates

Satellite estimates and gauge observations of precipitation are useful in understanding the water cycle, analyzing climatic variability, and validating climate models. The Global Precipitation Climatology Project (GPCP) released a community merged precipitation data set for the period July 1987 through the present, and has recently extended that data set back to 1986. One objective of this study is to use GPCP estimates to describe and quantify the seasonal variation of precipitation, with emphasis on the Asian summer monsoon. Another focus is the 1997-98 El Nino Southern Oscillation (ENSO) and associated extreme precipitation events. The summer monsoon tends to be drier than normal in El Nino ears. This was not observed for 1997 or 1998, while for 1997 the NCEP model produced the largest summer rain rates over India in years. This inconsistency will be examined. The average annual global precipitation rate is 2.7 mm day as estimated by GPCP, which is similar to values computed from long-term climatologies. From 30 deg N to 30 deg S the average precipitation rate is 2.7 mm day over land with a maximum in the annual cycle occurring in February-March, when the Amazon basin receives abundant rainfall. The average precipitation rate is 3.1 mm day over the tropical oceans, with a peak earlier in the season (November-December), corresponding with the transition from a strong Pacific Intertropical Convergence Zone (ITCZ) from June to November to a strong South Pacific Convergence Zone (SPCZ) from December to March. The seasonal evolution of C, C, the Asian summer monsoon stands out with rains in excess of 15 mm day off the coast of Burma in June. The GPROF pentad data also captures the onset of the tropical Pacific rainfall patterns associated with the 1997-98 ENSO. From February to October 1997 at least four rain-producing systems traveled from West to East in the equatorial corridor. A rapid transition from El Nino to La Nina conditions occurred in May-June 1998. GPCP and GPROF were used to construct precipitation-based ENSO indices to monitor El Ninos (EL) and La Ninas and (LI).

Curtis, Scott↗
NASA NTRS2003

Surface Tension and Viscosity of SCN and SCN-acetone Alloys at Melting Points and Higher Temperatures Using Surface Light Scattering Spectrometer

Succinonitrile has been and is being used extensively in NASA's Microgravity Materials Science and Fluid Physics programs and as well as in several ground-based and microgravity studies including the Isothermal Dendritic Growth Experiment (IDGE). Succinonitrile (SCN) is useful as a model for the study of metal solidification, although it is an organic material, it has a BCC crystal structure and solidifies dendriticly like a metal. It is also transparent and has a low melting point (58.08 C). Previous measurements of succinonitrile (SCN) and alloys of succinonitrile and acetone surface tensions are extremely limited. Using the Surface Light Scattering technique we have determined non invasively, the surface tension and viscosity of SCN and SCN-Acetone Alloys at different temperatures. This relatively new and unique technique has several advantages over the classical methods such as, it is non invasive, has good accuracy and measures the surface tension and viscosity simultaneously. The accuracy of interfacial energy values obtained from this technique is better than 2% and viscosity about 10 %. Succinonitrile and succinonitrile-acetone alloys are well-established model materials with several essential physical properties accurately known - except the liquid/vapor surface tension at different elevated temperatures. We will be presenting the experimentally determined liquid/vapor surface energy and liquid viscosity of succinonitrile and succinonitrile-acetone alloys in the temperature range from their melting point to around 100 C using this non-invasive technique. We will also discuss about the measurement technique and new developments of the Surface Light Scattering Spectrometer.

Tin, Padetha↗
NASA NTRS2020

Mechanisms Associated with Daytime and Nighttime Heat Waves over the United States

Heat waves are extreme climate events that have the potential to cause immense stress on human health, agriculture and energy systems, so understanding the processes leading to their onset is crucial. There is no single accepted definition for heat waves, but they are generally described as a sustained amount of time where temperature exceeds a local threshold. Multiple different temperature variables are potentially relevant, as high values of daily maximum (T(max)) and minimum (T(min)) temperatures can both be detrimental to human health. Previous studies have concluded that the frequency of global heat waves has increased over recent decades, with greater increases in T(min)- than T(max)-heat waves in several regions. In this study, we focus explicitly on the different mechanisms associated with heatwaves manifest during daytime versus nighttime hours over the United States. Heat waves are examined using the National Aeronautics and Space Administration (NASA) Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2). A daytime (nighttime) heat wave is defined as average daytime (nighttime) temperature exceeding its calendar day 90th percentile for at least 3 days. Over 1980-2018, the number of heat wave days per summer has increased over much of the United States. Trends are stronger for nighttime versus daytime heat wave frequency over the Northeast, Midwest and Southwest United States. Local and remote processes linked with daytime and nighttime heat waves are identified through composite analysis of clouds, precipitation, soil moisture, and fluxes of heat and moisture. Finally, we characterize the large-scale atmospheric circulation associated with daytime and nighttime heat waves over different regions of the United States.

Thomas, N.↗
NASA NTRS1981

Lean-limit extinction of propane/air mixtures in the stagnation-point flow

The extinction limits of lean propane/air mixtures in the stagnation-point flow of a flat surface were mapped as functions of the surface temperature and the mixture concentration, velocity, and temperature. The maximum flame temperatures and the flame locations were also measured. The results show that the extinction limits are extremely insensitive to the nature of the surface, which can be heated to 1000 C. On the other hand preheating the gas mixture increases the flame temperature by an almost equal amount and therefore significantly extends the extinction limits. It is also found that at extinction the maximum flame temperatures and the flame locations, which when scaled with the velocity gradient, assume almost constant values independent of the other system variables investigated.

Law, C. K.↗
NASA NTRS1986

Solar irradiance variations from photometry of active regions

The Extreme Limb Photometer (ELP) has been used to measure the irradiance fluctuation of the sun due to selected active regions. Forty-five active regions that were completely scanned at various disk positions are included in the analysis. The contribution of these active regions to a global solar irradiance fluctuation has been correlated with photometric sunspot and facular indices (PSI and PFI) using published values of sunspot and calcium plage areas. The measured ELP fluctuations are converted to a global brightness fluctuation, Delta B/B. The sunspot component of Delta B/B correlates with PSI with r = 0.95. The facular component of Delta B/B correlates with PFI with r = 0.72. The expression for PFI is important to the question of energy balance between sunspots and faculae and the results presented here are not incompatible with energy balance between the two phenomena; that is the energy deficit of sunspots may be balanced by the energy excess of faculae.

Chapman, G. A.↗
NASA NTRS2011

Martian Atmospheric Modeling of Scale Factors for MarsGRAM 2005 and the MAVEN Project

For spacecraft missions to Mars, especially the navigation of Martian orbiters and landers, an extensive knowledge of the Martian atmosphere is extremely important. The generally-accepted NASA standard for modeling (MarsGRAM), which was developed at Marshall Space Flight Center. MarsGRAM is useful for task such as aerobraking, performance analysis and operations planning for aerobraking, entry descent and landing, and aerocapture. Unfortunately, the densities for the Martian atmosphere in MarsGRAM are based on table look-up and not on an analytical algorithm. Also, these values can vary drastically from the densities actually experienced by the spacecraft. This does not have much of an impact on simple integrations but drastically affects its usefulness in other applications, especially those in navigation. For example, the navigation team for the Mars Atmosphere Volatile Environment (MAVEN) Project uses MarsGRAM to target the desired atmospheric density for the orbiter's pariapse passage, its closet approach to the planet. After the satellite's passage through pariapsis the computed density is compared to the MarsGRAM model and a scale factor is assigned to the model to account for the difference. Therefore, large variations in the atmosphere from the model can cause unexpected deviations from the spacecraft's planned trajectory. In order to account for this, an analytic stochastic model of the scale factor's behavior is desired. The development of this model will allow for the MAVEN navigation team to determine the probability of various Martian atmospheric variations and their effects on the spacecraft.

Martian atmosphere↗
NASA NTRS1980

Reducing the error of geoid undulation computations by modifying Stokes' function

The truncation theory as it pertains to the calculation of geoid undulations based on Stokes' integral, but from limited gravity data, is reexamined. Specifically, the improved procedures of Molodenskii et al. are shown through numerical investigations to yield substantially smaller errors than the conventional method that is often applied in practice. In this improved method, as well as in a simpler alternative to the conventional approach, the Stokes' kernel is suitably modified in order to accelerate the rate of convergence of the error series. These modified methods, however, effect a reduction in the error only if a set of low-degree potential harmonic coefficients is utilized in the computation. Consider, for example, the situation in which gravity anomalies are given in a cap of radius 10 deg and the GEM 9 (20,20) potential field is used. Then, typically, the error in the computed undulation (aside from the spherical approximation and errors in the gravity anomaly data) according to the conventional truncation theory is 1.09 m; with Meissl's modification it reduces to 0.41m, while Molodenskii's improved method gives 0.45 m. A further alteration of Molodenskii's method is developed and yields an RMS error of 0.33 m. These values reflect the effect of the truncation, as well as the errors in the GEM 9 harmonic coefficients. The considerable improvement, suggested by these results, of the modified methods over the conventional procedure is verified with actual gravity anomaly data in two oceanic regions, where the GEOS-3 altimeter geoid serves as the basis for comparison. The optimal method of truncation, investigated by Colombo, is extremely ill-conditioned. It is shown that with no corresponding regularization, this procedure is inapplicable.

Jekeli, C.↗
NASA NTRS1990

Reexamination of data from the asteroid/meteoroid detector

A reexamination of the results of the Pioneer 10 and 11 Asteroid Meteoroid Detector, or Sisyphus, was carried out in the light of a recently derived theory characterizing interplanetary matter and the Zodiacal Light (ZL). Sisyphus measured individual meteoroids from reflected sunlight and ZL between meteoroid events. The results were questioned because meteoroid orbits could not be calculated as intended and the ZL as computed from individual meteoroids did not agree with values determined from the ZL mode and from the other ZL sensor on the spacecraft. It is first shown that, independent of any explanation, the measurements are, with high probability, valid and strongly correlated with the ZL. The model which explains the strange behavior of the Sisyphus instrument also resolves the enigma why the three dust experiments on the Pioneer 10 and 11 spacecraft produced extreme disparate results for the distribution and orbits of meteoric particles and the ZL. The theory based primarily on these measurements requires a population in the inner solar system of cold meteoroid material composed mainly of volatile molecules. These meteoroids in orbits of high eccentricity are called cosmoids. They are impulsively disrupted from solar heating, resulting in order of magnitude increases in optical cross section. The dispersed particles, predominantly micron sized, scatter most of the ZL and supply the polarization. The sublimation time in sunlight for micron sized particles of volatile composition opposes the gravitational flux increase expected in approaching the sun. The other two Pioneer 10/11 dust experiments were: the Imaging Photopolarimeter for the ZL, and the Meteoroid Detection Experiment that measured penetration of 25 micron (Pioneer 10) and 50 micron (Pioneer 11) thick walls of pressurized gas cells.

Soberman, Robert K.↗
NASA NTRS1995

Epsilon Canis Majoris and the ionization of the local cloud

The Lyman continuum radiation from the brightest extreme ultraviolet (EUV) source, the B2 II star epsilon Canis Majoris (Adara), is so intense that it dominates the local stellar EUV radiation field at wavelengths longer than 450 A and therefore sets a lower limit to the ionization of hydrogen in the Local Cloud. Using the EUV (70-730 A) spectrum of epsilon CMa taken with the Extreme Ultraviolet Explorer Satellite (EUVE) and simple models that extrapolate this spectrum to the Lyman edge at 912 A, we have determined the local interstellar hydrogen photionizatin parameter Gamma solely from epsilon CMa to be 1.1 x 10(exp -15)/s. This fiugre is a factor of 7 greater than previous estimates of Gamma calculated for all nearby stars combined (Bruhweiler & Cheng 1988). Using measured values of the density and temperature of neutral interstellar hydrogen gas in the Local Cloud, we derive a particle density of ionized hydrogen n(H(+)) and electrons n(sub e) of 0.015-0.019/cu cm assuming ionization equilibrium and a helium ionization fraction of less than 20%. These values correspond to a hydrogen ionizatin fraction, chi(sub H) from 19% to 15%, respectively. The range of these derived quantities is due to the uncertainties in the local values of the neutral hydrogen and helium interstellar densities derived from both (1) solar backscatter measurements of Ly alpha lines of hydrogen and helium (1216 and 584 A), and (2) the average neutral densities along the line of sight to nearby stars. The local proton density produced by epsilon CMa is enough to allow the ionization mechanism of Ripken & Fahr (1983) to work at the heliopause and explain the discrepancy between the neutral hydrogen density derived from solar backscatter measurements and line-of-sight averages to nearby stars. A large value of electron density in the Local Cloud of n(sub e) is approximately 0.3-0.7/cu cm (T = 7000 K) has recently been reported by Lallement et al. (1994) using observations of Mg II and Mg I toward Sirius A. We show that if such a high value exists, it cannot result from the EUV stellar radiation field and, therefore, must be due to a strong diffuse source of EUV radiation.

Vallerga, J. V.↗
NASA NTRS1979

Variability of Lyman-alpha emission from Jupiter

The Jovian Lyman-alpha emission line was again observed in 1978 using the high resolution spectrometer on the Copernicus satellite. In intensity of 8.4+3.0 kilo Rayleighs was measured. This value represents a significant increase in intensity over previous (1976) Copernicus observations, but is lower than the recent (1979) values obtained by Voyager I and IUE. The increase in intensity was accompanied by a significant increase in line width, giving strong support to the theory that the emission results from resonant scattering of the solar Ly-alpha line by H atoms in the upper Jovian atmosphere. The strength of Jovian Ly-alpha emission correlates well with the level of solar activity. The solar extreme ultraviolet radiation varies with the solar cycle. This radiation causes the dissociation of H2 and CH4 into H atoms in the Jovian atmosphere. Therefore, in times of high solar activity, the H column density will increase, causing the observed stronger Jovian Ly-alpha emission.

Source record↗
NASA NTRS1992

Radiation-pressure-supported obscuring tori around active galactic nuclei

Radiation pressure acting on dust grains can support the vertical thickness of the obscuring tori believed to exist in active galactic nuclei. Using the results of 2D radiation transfer calculations, we evaluate the radiation force acting on these tori. We find that on the inner edge of the torus the radiation force is about 350 l(E) times the gravitational force of the nucleus, where l(E) is the Eddington ratio. Beyond a few torus heights from the inner edge, the radiation force is negligible with respect to gravity. However, between these two extremes lies a region of considerable size where the ratio of radiation force to gravity is nearly constant and can be of order unity for l(E) about 0.1. If the distribution of material within the torus is sufficiently lumpy, there is a significant time-varying component to the radiation force. This drives the random motions of the constituent clouds, thickening the torus at lower values of l(E).

Pier, Edward A.↗