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NASA NTRS1981

Galactic X-ray emission from pulsars

The contribution of pulsars to the gamma-ray flux from the galactic plane is examined using data from the most recent pulsar surveys. It is assumed that pulsar gamma-rays are produced by curvature radiation from relativistic particles above the polar cap and attenuated by pair production in the strong magnetic and electric fields. Assuming that all pulsars produce gamma-rays in this way, their luminosities can be predicted as a function of period and magnetic field strength. Using the distribution of pulsars in the galaxy as determined from data on 328 pulsars detected in three surveys, the local gamma-ray production spectrum, the longitude profile, and the latitude profile of pulsar gamma-ray flux are calculated. The largest sources of uncertainty in the size of the pulsar contribution are the value of the mean interstellar electron density, the turnover in the pulsar radio luminosity function, and the average pulsar magnetic field strength. A present estimate is that pulsars contribute from 15 to 20 % of the total flux of gamma-rays from the galactic plane.

Harding, A. K.↗
NASA NTRS1986

Compton scattering in strong magnetic fields

The relativistic cross section for Compton scattering by electrons in strong magnetic fields is derived. The results confirm and extend earlier work which has treated only transitions to the lowest or first excited Landau levels. For the teragauss field strengths expected in neutron star magnetospheres, the relative rates for excited state transitions are found to be significant, especially for incident photon energies several times the cyclotron frequency. Since these transitions must result in the rapid emission of one or more cyclotron photons as well as the Compton-scattered photon, the scattering process actually becomes a photon 'splitting' mechanism which acts to soften hard photon spectra, and also provides a specific mechanism for populating higher Landau levels in the electron distribution function. The results should be significant for models of gamma-ray bursters and pulsating X-ray sources.

Daugherty, Joseph K.↗
NASA NTRS2020

Characteristics of DSD Bulk Parameters: Implication to Radar Rain Retrieval

With the use of 213,456 one-minute measured data of droplet-size distribution (DSD) of rain collected during several National Aeronautics and Space Administration (NASA)-sponsored field campaigns, the relationships between rainfall rate R, mass-weighted diameter D(m) and normalized intercept parameter N(w) of the gamma DSD are studied. It is found, based on the simulations of the gamma DSD model, that R, D(m) and N(w) are closely interrelated, and that the ratio of R to N(w) is solely a function of D(m), independent of the shape factor μ of the gamma distribution. Furthermore, the model-produced ratio agrees well with those from the DSD data. When a power-law equation is applied to fit the model data, we have: R=aN(w)D(sup b, sub m) , where a=1.588×10(exp −4) , b=4.706 . Analysis of two-parameter relationships such as R–D(m), N(w)–R and N(w)–D(m) reveals that R and D(m) are moderately correlated while N(w) and D(m) are negatively correlated. N(w) and R, however, are uncorrelated. The gamma DSD model also reveals that variation of R–D(m) relation is caused primarily by N(w). For the application of the Ku- and Ka-band dual-frequency radar for the retrieval of the DSD bulk parameters as well as the specific radar attenuations, the study is carried out to relate the dual-frequency radar reflectivity factors to the DSD and attenuation parameters.

Liang Liao↗
NASA NTRS1988

A parameterization of the evaporation of rainfall

A general theoretical expression for the rainfall rate and the total evaporation rate as a function of the distance below cloud base is developed, and is then specialized to the gamma raindrop size distribution. The theoretical framework is used to analyze the data of Rosenfeld and Mintz (1988) on the radar observations of the rainfall rate as a function of the distance below cloud base, for rain falling from continental convective cells in central South Africa, obtaining a parameterization for the evaporation of rainfall.

Schlesinger, Michael E.↗
NASA NTRS1986

Spatial modelling of total storm rainfall

The spatial structure of the depth of rainfall from a stationary storm event is investigated by using point process techniques. Cells are assumed to be stationary and to be distributed in space either independently according to a Poisson process, or with clustering according to a Neyman-Scott scheme. Total storm rainfall at the centre of each cell is a random variable and rainfall is distributed around the centre in a way specified by a spread function that may incorporate random parameters. The mean, variance and covariance structure of the precipitation depth at a point are obtained for different spread functions. For exponentially distributed centre depth and a spread function having quadratically exponential decay, the total storm depth at any point in the field is shown to have a gamma distribution. The probability of zero rainfall at a point is investigated, as is the stochastic variability of model parameters from storm to storm. Data from the Upper Rio Guaire basin in Venezuela are used in illustration.

Rodriguez-Iturbe, I.↗
NASA NTRS1977

The galactic halo question - New size constraints from galactic gamma-ray data

Recent satellite observations of the distribution of galactic 100-MeV gamma rays and their interpretation are used as an independent test of the existence and extent of a cosmic-ray halo around the Galaxy. The cosmic-ray halo is defined, uniform and diffusion halo models are described, and the flat diffusion model is employed to investigate the effect of a diffusion halo on the galactic cosmic-ray distribution. Cosmic-ray source distributions that are perpendicularly uniform functions of galactocentric distance are adopted in the analysis. Possible longitudinal distributions of the gamma-ray line flux from neutral-pion decay are evaluated and compared with the fluxes observed by SAS-2 for goodness of fit. The results are shown to be consistent with a thick-disk or thin-halo model having a mean half-thickness of 1 to 3 kpc.

Stecker, F. W.↗
NASA NTRS1999

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗
NASA NTRS1996

Independent Pixel and Two Dimensional Estimates of LANDSAT-Derived Cloud Field Albedo

A theoretical study has been conducted on the effects of cloud horizontal inhomogeneity on cloud albedo bias. A two-dimensional (2D) version of the Spherical Harmonic Discrete Ordinate Method (SHDOM) is used to estimate the albedo bias of the plane parallel (PP-IPA) and independent pixel (IPA-2D) approximations for a wide range of 2D cloud fields obtained from LANDSAT. They include single layer trade cumulus, open and closed cell broken stratocumulus, and solid stratocumulus boundary layer cloud fields over ocean. Findings are presented on a variety of averaging scales and are summarized as a function of cloud fraction, mean cloud optical depth, cloud aspect ratio, standard deviation of optical depth, and the gamma function parameter Y (a measure of the width of the optical depth distribution). Biases are found to be small for small cloud fraction or mean optical depth, where the cloud fields under study behave linearly. They are large (up to 0.20 for PP-IPA bias, -0.12 for IPA-2D bias) for large v. On a scene average basis PP-IPA bias can reach 0.30, while IPA-2D bias reaches its largest magnitude at -0.07. Biases due to horizontal transport (IPA-2D) are much smaller than PP-IPA biases but account for 20% RMS of the bias overall. Limitations of this work include the particular cloud field set used, assumptions of conservative scattering, constant cloud droplet size, no gas absorption or surface reflectance, and restriction to 2D radiative transport. The LANDSAT data used may also be affected by radiative smoothing.

Chambers, L. H.↗
NASA NTRS2003

Computation of Domain-Averaged Shortwave Irradiance by a One-Dimensional Algorithm Incorporating Correlations between Optical Thickness and Direct Incident Radiation

A one-dimensional radiative transfer algorithm that accounts for correlations between the optical thickness and the incident direct solar radiation is developed to compute the domain-averaged shortwave irradiance profile. It divides the direct irradiance into four components and treats the direct irradiance in two separate, clear and cloudy columns to account for the fact that clouds attenuate the direct irradiance more than clear-sky. The horizontal inhomogeneity of clouds in the cloudy column is treated by the gamma weighted two-stream approximation, which assumes that the optical thickness of clouds follows a gamma distribution. The algorithm inputs the cloud fraction, cumulative cloud fraction as a function of height, and a parameter expressing the shape of the probability density function of the cloud optical thickness distribution in addition to inputs required for a two-stream radiative transfer model. These cloud property inputs can be obtained using ground- and satellite-based instruments. Therefore, the algorithm can treat realistic cloud overlap features and horizontal inhomogeneity of clouds in a framework of one- dimensional radiative transfer. Heating rates computed by the algorithm using cloud fields generated by cloud resolving models agree with those computed with a Monte Carlo model. If optical properties in computational layers that divide a vertically extensive cloud are correlated, the irradiance profile computed by the algorithm further improves.

Kato, S.↗
NASA NTRS1971

Emitted radiation characteristics of plutonium dioxide radioisotope thermoelectric generators

The nuclear and emitted radiation characteristics of the radioisotope elements and impurities in commercial grade plutonium dioxide are presented in detail. The development of the methods of analysis are presented. Radioisotope thermoelectric generators (RTG) of 1575, 3468 and 5679 thermal watts are characterized with respect to neutron and gamma photon source strength as well as spatial and number flux distribution. The results are presented as a function of detector position and light element contamination concentration for fuel age ranging from 'fresh' to 18 years. The data may be used to obtain results for given O-18 and Pu-236 concentrations. The neutron and gamma photon flux and dose calculations compare favorably with reported experimental values for SNAP-27.

Gingo, P. J.↗
NASA NTRS2012

Probabilistic Fatigue Damage Program (FATIG)

FATIG computes fatigue damage/fatigue life using the stress rms (root mean square) value, the total number of cycles, and S-N curve parameters. The damage is computed by the following methods: (a) traditional method using Miner s rule with stress cycles determined from a Rayleigh distribution up to 3*sigma; and (b) classical fatigue damage formula involving the Gamma function, which is derived from the integral version of Miner's rule. The integration is carried out over all stress amplitudes. This software solves the problem of probabilistic fatigue damage using the integral form of the Palmgren-Miner rule. The software computes fatigue life using an approach involving all stress amplitudes, up to N*sigma, as specified by the user. It can be used in the design of structural components subjected to random dynamic loading, or by any stress analyst with minimal training for fatigue life estimates of structural components.

Michalopoulos, Constantine↗
NASA NTRS2000

The BATSE Gamma-Ray Burst E-Peak Distribution

Gamma-ray burst observed by BATSE are found to have approximately the same characteristic energy, denoted as E_p. We examine whether instrumental effects can give rise to this observation. We simulate the derivation of E-p and determine that the values in the BATSE sample are accurate and complete above a minimum fluence. We simulate the triggering of BATSE on gamma-ray bursts, deriving the efficiency of detecting bursts as a function of characteristic energy. From this simulation, we model the observed E_p distribution function expected when the intrinsic distribution function is a power-law. We find that this distribution produces poor fits to the observations. We find that a log-normal intrinsic distribution with a power-law tail gives a good fit to the data. From these fits, we conclude that instrumental effects cannot produce the observed E_p distribution, and that the observed distribution is a consequence of a narrow intrinsic distribution of E_p in gamma-ray bursts.

Brainerd, Jerome J.↗
NASA NTRS2022

Markovian Statistical Model of Cloud Optical Thickness. Part I: Theory and Examples

We present a generalization of the binary-value Markovian model previously used for statistical characterization of cloud masks to a continuous-value model describing 1D fields of cloud optical thickness (COT). This model has simple functional expressions and is specified by four parameters: the cloud fraction, the autocorrelation (scale) length, and the two parameters of the normalized probability density function of (non-zero) COT values (this PDF is assumed to have gamma-distribution form). Cloud masks derived from this model by separation between the values above and below some threshold in COT appear to have the same statistical properties as in binary-value model described in our previous publications. We demonstrate the ability of our model to generate examples of various cloud-field types by using it to statistically imitate actual cloud observations made by the Research Scanning Polarimeter (RSP) during two field experiments.

binary-value Markovian model↗
NASA NTRS1994

Constraints on the luminosity function of gamma-ray bursts detected by BATSE

We have utilized the integral moment analysis technique of Horack & Emslie to extract information on the allowable form of the luminosity function for gamma-ray bursts observed by Burst and Transient Source Experiment (BATSE). Using the general properties of moments, we are able to derive constraints on the range of luminosity from which the gamma-ray bursts must be sampled. These constraints are independent of the form of the radial distribution of the gamma-ray bursts, and depend only on the assumptions that space is Euclidean and that the luminosity function phi(L) is distance independent. For power-law luminosity functions of the form phi(L) = A(sub 0)L(exp -alpha), we find that the range of luminosity from which 80% of the gamma-ray bursts must be sampled cannot exceed approximately 6.5, with a 3 sigma upper limit of 12-15, regardless of the value of alpha.

Horack, J. M.↗
NASA NTRS1997

Internal Luminosity Distribution of Bright Gamma-Ray Bursts and its Relation to Duration and Spectral Hardness

We present first results from a comprehensive investigation into the distribution of luminosity within the 50 brightest cosmic gamma-ray bursts detected by the Burst and Transient Source Experiment (BATSE). The internal luminosity function psi(L) is defined such that the quantity psi(L)dL represents the fraction of total emission time during which the burst possesses a luminosity between L and L + dL. For these brightest bursts, the psi(L) functions are quasi-power-law-like and decrease in amplitude with increasing luminosity. Through investigation of both individual psi(L) distributions and data from the ensemble of bursts, we demonstrate a high probability for correlation between the shape of the internal luminosity function as measured by the average logarithmic slope and the burst duration as measured by the T(sub 90) parameter and, with lower significance, between the shape of psi(L) and the burst photon-fluence spectral index. We furthermore demonstrate a correlation between burst hardness ratio and duration in these brightest bursts which is opposite to that of the entire gamma-ray burst ensemble.

Horack, John M.↗
NASA NTRS1981

Galactic gamma-ray emission from pulsars

Using data from the most recent pulsar surveys, the contribution of pulsars to the gamma-ray flux from the galactic plane is examined. The assumption is made that pulsar gamma rays are produced by curvature radiation from relativistic particles above the polar cap and attenuated by pair production in the strong magnetic and electric fields. If the assumption is made that all pulsars produce gamma rays in this way, their luminosities can be predicted as a function of period and magnetic field strength. The distribution of pulsars in the Galaxy is determined using data on 328 pulsars detected in three surveys. The Z and R distributions are found to be very sensitive to the mean electron density in the galactic plane, as are the total number and birthrate of pulsars in the Galaxy. Longitude profile of pulsar gamma-ray flux are calculated for different values of the mean electron density.

Harding, A. K.↗
NASA NTRS1982

Comments on the gamma-ray burst log N /greater than S/ log S point of Beurle et al

Statistical improbability is demonstrated for the Beurle et al (1981) determination of an isotropic cumulative burst rate of 7030 + 10,000 or - 6000/year, at a fluence of 8.47 x to the -9th/erg per sq cm, from their observation of two gamma-ray bursts. The difficulty identified is Beurle's assumption that the power law cumulative distribution function index equals one. Reconsideration of the Beurle observations is undertaken, and an alternative upper limit of the annual number of bursts at the fluence cited of less than 5400/year is proposed.

Jennings, M. C.↗
NASA NTRS1974

Primary gamma rays

Within this galaxy, cosmic rays reveal their presence in interstellar space and probably in source regions by their interactions with interstellar matter which lead to gamma rays with a very characteristic energy spectrum. From the study of the intensity of the high energy gamma radiation as a function of galactic longitude, it is already clear that cosmic rays are almost certainly not uniformly distributed in the galaxy and are not concentrated in the center of the galaxy. The galactic cosmic rays appear to be tied to galactic structural features, presumably by the galactic magnetic fields which are in turn held by the matter in the arm segments and the clouds. On the extragalactic scale, it is now possible to say that cosmic rays are not universal at the density seen near the earth. The diffuse celestial gamma ray spectrum that is observed presents the interesting possibility of cosmological studies and possible evidence for a residual universal cosmic ray density, which is much lower than the present galactic cosmic ray density.

Fichtel, C. E.↗