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NASA NTRS1992

Search for evidence of a clock related to the solar 154 day complex of periodicities

Evidence that has recently been compiled (Bai and Sturrock 1991) indicates that the enigmatic 154-day periodicity in solar activity may be viewed as part of a complex of periodicities that are approximate multiples of 25.8 days, suggesting that the Sun contains a 'clock' with frequency in the range 440 to 463 nano Hz. The clock may comprise either an oscillator or a rotator, each of which may be either real or virtual. We have reconsidered a previous spectrum analysis of the Zurich sunspot-number sequence by Knight, Schatten, and Sturrock (1979) which revealed a sharp, persistent and significant periodicity with a period of 12.072 days, corresponding to a frequency of about 958.8 nano Hz. This periodicity may be regarded as the (second) upper sideband of the second harmonic (2nu(sub R) + 2nu(sub E)) of a fundamental frequency of 447.7 nano Hz that is clearly within the search band. In this expression, nu(sub R) is the sidereal frequency of the hypothetical rotator and nu(sub E) is the frequency (31.69 nano Hz) of the Earth in its orbital motion around the Sun. In analyzing sunspot area data derived from the Greenwich data set, and on noting that any frequency is defined only to within the Nyquist frequency, we find clear evidence not only for the upper sideband of the second harmonic, but also for the second harmonic (2nu(sub R)) and the lower sideband of the second harmonic (2nu(sub R) - 2nu(sub E)). There is no strong peak at the fundamental frequency in the Greenwich data, but there is in the Zurich sunspot data. The effect of a linear oscillator is, to the lowest order in the amplitude, the same as the combined effect of two rotators of opposite polarities. A rotator that has arbitrary orientation with respect to the ecliptic may influence the outer layers of the Sun and thereby modulate the occurrence of solar activity such as sunspots. By analyzing a simple model, we find that such a rotator would influence surface activity in such a way that the spectrum of a 'signal' (such as the record of sunspots), as seen from the Earth, would contain components with frequencies that are certain integral combinations of nu(sub R) and nu(sub E). The amplitudes of the various components depend sensitively on theta, the angle between the axis of the rotator and the axis of the Earth's orbital motion. This simple model therefore offers a kinematical (but not dynamical) interpretation of the sunspot spectrum. The present analysis, while offering support of our conjectures that the Sun contains a clock that regulates the 154-day complex of periodicities, cannot distinguish between an osillator or a rotator (that might be a traveling wave), nor between a real rotator or a virtual rotator (that might be an apparent traveling wave due to the aliasing effect of an oscillator in a rotating system). Further analysis of sunspot and other data sets will be required to confirm the existence of such clock and (if it is real) to determine its physical nature.

Sturrock, P. A.↗
NASA NTRS1992

The effect of secular resonances in the asteroid region between 2.1 and 2.4 AU

The asteroid region between 2.1 and 2.4 AU appears to be depopulated at inclinations i greater than 12 deg. This region is surrounded by the three main secular resonances nu(sub 5), nu(sub 6), and nu(sub 16) and is crossed by higher order secular resonances. Secular resonances appear to overlap in this region. Numerical integrations of the orbits of seventeen fictituous asteroids with initial inclinations 12 deg less than or equal to i less than or equal to 20 deg show the following: (1) this particular asteroid region is not depopulated in our computer experiment on timescales of 2.7 Myrs; (2) inclinations are pumped up by successive crossings through higher order secular resonances while eccentricities are not increased sufficiently to produce planet-crossers; (3) bodies located in the bordering nu(sub 6) resonance with semi-major axes a less than or equal to 2.4 AU become Earth-crossers on a time scale of 1 Myr; and (4) we confirm the result that modes due to higher order secular resonances must be eliminated when proper elements are computed.

Froeschle, Christiane↗
NASA NTRS1993

Self-, N2- and Ar-broadening and line mixing in HCN and C2H2

Self-, N2- and Ar-broadening coefficients were measured for the stretch-bend infrared combination bands nu-1 + nu-1/2 (4004/cm) of HCN and nu-1 + nu-1/5 (4091/cm) of C2H2, using a tunable difference-frequency laser. At atmospheric pressures, the Q branches of these bands exhibit significant rotational narrowing or line mixing. The broadening coefficients are fit with empirical rotationally inelastic collision rate laws, which are then used to model the line mixing in the overlapped Q-branch profiles. Simple energy gap fitting laws appear to be suitable for the shorter-range intermolecular quadrupole-quadrupole and induction forces, whereas an energy-corrected-sudden scaling law works better for the longer-range dipole-dipole and dipole-quadrupole collision partners. In all cases, the line-coupling coefficients are substantially reduced from the rotationally inelastic rates fit to the broadening coefficients, indicating that 35-70 percent of the broadening may be due to other collisional mechanisms such as cross-relaxation to the degenerate H state vibrational level.

Pine, A. S.↗
NASA NTRS1993

Phasing operator for two oscillators in classical field

The origin of Dicke cooperative states was studied by considering two harmonic oscillators driven by a common field of radiation. The origin is assumed for superradiance in a system of molecules where no mutual interactions exist, but all of the molecules encounter the same field of radiation. A phasing operator as Phi(sub Nu) equals D(alpha) + P(sub Nu)D(alpha), where D(alpha) is the displacing operator and P(sub Nu) the projection operator for constant energy Nu for two oscillators, was derived. The eigenstates of the phasing operator Phi are found to show a finite correlation as in the Dicke cooperative states.

Kim, Jong-Jean↗
NASA NTRS1994

Relativistic shock spectra: A prediction

I argue that particles heated by relativistic shocks should assume an equilibrium energy distribution. This leads to a synchrotron spectrum F(sub nu) varies as nu(sup 1/3) up to approximately the critical frequency nu(sub 0) of an electron with the mean electron energy. Application to gamma ray bursts (GRB's) implies that a burst with 10(exp -5) erg/(sq cm s) of soft gamma-rays and h(nu(sub 0)) = 300 KeV should be about 18th magnitude in visible light and a few micro-Jy at 1 GHz (less if self-absorbed).

Katz, J. I.↗
NASA NTRS1995

Exact, E = 0, classical and quantum solutions for general power-law oscillators

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

Nieto, Michael Martin↗
NASA NTRS1994

Probing the large-scale velocity field with clusters of galaxies

What is the role of clusters of galaxies in probing the large-scale velocity field of the universe? We investigate the distribution of peculiar velocities of clusters of galaxies in the popular low-density (omega = 0.3) flat cold dark matter (CDM) cosmological model, which best fits many large-scale structure observations. An omega = 1 CDM model is also studied for comparison. We find that clusters of galaxies are efficient tracers of the large-scale velocity field. The clusters exhibit a Maxwellian distribution of peculiar velocities, as expected from Gaussian initial density fluctuations. The cluster three-dimensional velocity distribution for the omega = 0.3 model peaks at nu approximately greater than 400 km/s and extends to high velocities of nu approximately 1200 km/s. The rms peculiar velocity of the clusters is 440 km/s. Approximately 10% of all model clusters move with high peculiar velocities nu greater or equal to 700 km/s. The observed velocity distribution of clusters of galaxies is compared with the predictions from cosmological models. The observed data exhibit a larger velocity tail than seen in the model simulations; however, due to the large observational uncertainties, the data are consistent at approximately equal to 3 sigma level with the odel predictions, and with a Gaussian initial density field. The large peculiar velocities reported for some clusters of galaxies (nu approximately greater than 3000 km/s) are likely to be overestimated, if the current model is viable.

Bahcall, Neta A.↗
NASA NTRS1994

Magnetic shaping of planetary nebulae and other stellar wind bubbles

As in the case of the solar wind, the magnetic field in the wind from a magnetized, rotating star becomes increasingly toroidal with distance from the star. The strength of the magnetic field can be characterized by sigma, the ratio of toroidal magnetic energy density to kinetic energy density in the equatorial plane of the wind. A fast wind shocks against the external medium and creates a bubble whose volume is dominated by shocked gas. The toroidal magnetic field increases in the shocked bubble and can dominate the thermal pressure. Because of the low velocities in the bubble, hydrostatic equilibrium is a good approximation and allows the calculation of the thermal and magnetic pressure in the bubble, as in the model of Begelman and Li (1992) for the Crab Nebula. The structure, which is axisymmetric and extended in the polar direction, depends on two parameters: sigma nu(sub w)/w(sub 0), where nu(sub w) is the wind velocity and w(sub 0) is the shell velocity in the polar direction, and lambda = nu(sub a)/w(sub 0), where nu(sub a) is the velocity of the slow wind. For small values of lambda, there is a cusp in the shell in the equatorial plane, i.e., there is an equatorial ring. For larger values of lambda, the maximum of the surface density moves away from the equator i.e., a double ring structure. Our models should apply to planetary nebulae, if their central stars are sufficiently magnetized; the calculated shapes do resemble the observed shapes of planetaries. In all cases, our model predicts that X-ray emission from the bubble is concentrated toward the polar axis. Finally, we briefly discuss the asymmetry of the Crab Nebula and 3C 58.

Chevalier, Roger A.↗
NASA NTRS1994

Low-frequency spectra of gamma-ray bursts

Particles with energies below the mean energy E(sub 0) in relativistic shocked plasmas should assume an equilibrium energy distribution. This leads to a synchrotron spectrum F(sub nu) proportional to nu(exp 1/3) up to approximately the critical frequency nu(sub 0) of an electron with the energy E(sub 0). Application to gamma-ray bursts (GRBs) implies that a burst with 10(exp -5) ergs/sq cm/s of soft gamma rays and h nu(sub 0) = 300 keV should simultaneously be about 18th magnitude in visible light and a few micro-J at 1 GHz (less if self-absorbed); the low-freqency intensities peak later at higher values.

Katz, J. I.↗
NASA NTRS1995

BATSE observations of gamma-ray burst spectra. 2: Peak energy evolution in bright, long bursts

We investigate spectral evolution in 37 bright, long gamma-ray bursts observed with the Burst and Transient Source Experiment (BATSE) spectroscopy detectors. High-resolution spectra are chracterized by the energy of the peak of nu F(sub nu), and the evolution of this quantity is examined relative to the emission intensity. In most cases it is found that this peak energy either rises with or slightly precedes major intensity increases and softens for the remainder of the pulse. Interpulse emission is generally harder early in the burst. For bursts with multiple intensity pulses, later spikes tend to be softer than earlier ones, indicating that the energy of the peak of nu F(sub nu) is bounded by an envelope which decays with time. Evidence is found that bursts in which the bulk of the flux comes well after the event which triggers the instrument tend to show less peak energy variability and are not as hard as several bursts in which the emission occurs promptly after the trigger. Several recently proposed burst models are examined in light of these results and no qualitative conflicts with the observations presented here are found.

Ford, L. A.↗
NASA NTRS1994

On the vertical thermal structure of Io's atmosphere

A radiative-thermal conduction model for the vertical thermal structure of Io's atmosphere is developed with solar heating by SO2 absorption in UV and near-IR bands and non-local thermodynamic equilibrium (LTE) cooling by SO2 nu(sub 1), nu(sub 2), nu(sub 3), vibrational bands and rotational lines. The model predicts the existence of a mesopause in Io's atmosphere when the surface pressure exceeds approximately 10 nbar. The radiative time constant for establishing a mesosphere/mesopause on Io is only approximately 20 min, whereas the thermospheric radiative time constant is about 1 hr. These time constants are significantly shorter than the diurnal time scale and competitive with dynamic time scales. In the thermosphere when solar UV heating dominates, the asymptotic thermospheric temperature is approximately 270 K, only 140 K greater than the surface temperature because at high altiudes non-LTE cooling by SO2 rotation lines exceeds cooling in the nu(sub 2) virbrational band. Solar-heating-only modles are incapable of generating warm enough atmospheres to satisfy the observational inferences from UV and especially millimeter-wave meausrements. Joule heating driven by the penetration of Jupiter's corotational electric field into Io's conducting ionosphere is demonstrated to be the dominant heating mechanism in the subnanobar regions of Io's atmosphere with tempertures ranging from 150 to 1000 K as a function of decreasing pressure from 1 to 0.1 nbar, The asymoptotic thermospheric temperature can attain a value as high as 1800 K.

Strobel, Darrell F.↗
NASA NTRS1995

Measurements of the millimeter-wave spectrum of interstellar dust emission

We report measurements of the differential brightness of interstellar dust emission near the Galactic plane and at high Galactic latitudes. The data were obtained as part of a program to measure anisotropy in the cosmic microwave background (CMB). The measurements were made with a 0.5 deg beam size and a 1.3 deg sinusoidal chop, in broad bands (Delta nu/nu approximately 0.3) centered near frequencies of 6, 9, and 12 cm(exp -1). A measurement made toward the Galactic plane, at longitude 1 = 23.7 deg, is compared with the contrast observed in the 100 micrometers IRAS data. Assuming the dust emission has a brightness I(sub nu) proportional to nu(sup n)B(sub nu)(T(sub d)), where B(sub nu) is the Planck function, a best fit yields n = 1.6 +/- 0.4, T(sub d) = 24 +/- 5 K. In a region near the star mu Pegasi (mu PEG l = 91 deg, b = -31 deg), the comparison of our data with the 100 micrometers IRAS data yields n = 1.4 +/- 0.4, and T(sub d) = 18 +/- 3 K. In a second region near the star gamma Ursa Minoris (GUM l = 108 deg, b = 41 deg), an upper limit is placed on contrast in dust emission. This upper limit is consistent with spectrum measured at mu PEG and the IRAS 100 micrometer emission contrast at GUM, which is approximately 8 times lower than mu PEG.

Fischer, M. L.↗
NASA NTRS1996

Improved Limits on Gamma-Ray Burst Repetition from BATSE

We tighten previous upper limits on gamma-ray burst repetition by analyzing the angular power spectrum of the BATSE 3B catalog of 1122 bursts. At 95% confidence, we find that no more than 2% of all observed bursts can be labeled as repeaters, even if no sources are observed to repeat more than once. If a fraction f of all observed bursts can be labeled as repeaters that are observed to burst nu times each, then all models with (nu - 1)f greater than or equal to 0.05 are ruled out at 99% confidence, as compared to the best previous 99% limit (nu - 1)f greater than or equal to 0.27. At 95% confidence, our new limit is (nu - 1)f greater than or equal to 0.02. Thus, even a cluster of six events from a single source would have caused excess power above that present in the 3B catalog. We conclude that the current BATSE data are consistent with no repetition of classical gamma-ray bursts and that any repeater model is severely constrained by the near-perfect isotropy of their angular dis- tribution.

Tegmark, Max↗
NASA NTRS1959

Heat Transfer from Cylinders in Transition From Slip Flow to Free-Molecule Flow

Over 600 measured heat-transfer coefficients in the transition from slip to free-molecule flow have been correlated by using the Nusselt number Nu as a function of the Knudsen Kn and Reynolds Re (or Mach M) numbers. The experimental range for these heat-transfer data from transverse cylinders in air corresponds to the following dimensionless groups: M, 0.10 to 0.90; Re, 0.03 to 11.5; Kn, 0.10 to 5.0. The total air temperature T(sub t) was maintained constant at 80 F, but wire temperature was Varied from 150 to 580 F. At Kn=0.10, Nu extrapolates smoothly into slip-flow empirical curves that show Nu as a function of Re and M or Kn. The correlation gradually changes from the square root of Re(sub t) dependence characteristic of continuum flow to first-power Re dependence as Kn increases (decreasing Re). At the experimental limit Kn ft 5.0, the Nu data correlate with a mean fractional error of 413 percent by the prediction of free-molecule-flow theory. In comparing experimental results with theory, an accommodation coefficient of 0.57+/-0.07 was inferred from the heat-transfer data, which were obtained with etched tungsten wire in air. The wire recovery temperature T(sub e) was measured and compared with existing data and theory in terms of a ratio eta(equivalent to T(sub e)/T(sub t). The results can be divided into three groups by Kn criteria: For Kn less than 2.01, eta is independent of Kn, and eta decreases from 1.0 to 0.97 as M increases from 0 to 0.90; for 2.0 less than Kn less than 5.0, eta is a function of both Kn and M in this transition region to fully developed free-molecule flow; and for Kn greater than 5.0, eta predicted by free-molecule-flow theory is observed and increases from 1.0 to 1.08 as M increases from 0 to 0.90, again independent of Kn. Therefore, these T(sub e) data provide a guide to the boundary of fully developed free-molecule flow, which is.inferred from this research to exist for Kn greater than 5.0. This boundary criterion is substantiated by other published data on T(sub e) at supersonic speeds.

Cybulski, Ronald J.↗
NASA NTRS2003

Phase Coherent Timing of RX J0806.3+1527 with ROSAT and CHANDRA

RX 50806.3+1527 is an ultra-compact, double degenerate binary with the shortest known orbital period (321.5 s). Hakala et.al., have recently reported new optical measurements of the orbital frequency of the source which indicate that the frequency has increased over the approx.= 9 years since the earliest ROSAT observations. They find two candidate solutions for the long term change in the frequency; nu approx. = 3 or 6 x 10(exp -16)Hz/s. Here we present the results of a phase coherent timing study of the archival ROSAT and Chandra data for RX 50806.3+1527 in the light of these new constraints. We find that the ROSAT - Chandra timing data are consistent with both of the solutions reported by Hakala et al., but that the higher nu = 6.1 x 10(exp -16)Hz/s solution is favored at the approx. 97% level. This large a nu can be accomodated by an approx. = 1 solar mass detached double degenerate system powered in the X-ray by electrical energy. With such a large nu the system provides a unique opportunity to explore the interaction of gravitational radiation and electromagnetic torques on the evolution of an ultracompact binary.

Strohmayer, Tod E.↗
NASA NTRS2004

Precision X-ray Timing of RX J0806.3+1527 with CHANDRA: Evidence for Gravitational Radiation from an Ultracompact Binary

RX J0806.3+1527 is a candidate double degenerate binary with possibly the shortest known orbital period. The source shows an approximately equal to 100% X-ray intensity modulation at the putative orbital frequency of 3.11 mHz (321.5 s). If the system is a detached, ultracompact binary gravitational radiation should drive spin-up with a magnitude of nu(sup dot) approximately 10(exp -16) Hz per second. Efforts to constrain the X-ray frequency evolution to date have met with mixed success, principally due to the sparseness of earlier observations. Here we describe the results of the first phase coherent X-ray monitoring campaign on RX J0806.3+1527 with Chandra. We obtained a total of 70 ksec of exposure in 6 epochs logarithmically spaced over 320 days. With these data we conclusively show that the X-ray frequency is increasing at a rate of 3.77 plus or minus 0.8 x 10(exp -16) Hz per second. Using the ephemeris derived from the new data we are able to phase up all the earlier Chandra and ROSAT data and show they are consistent with a constant nu(sup dot) = 3.63 plus or minus 0.06 x 10(exp -16) Hz per second over the past decade. This value appears consistent with that recently derived by Israel et al. largely from monitoring of the optical modulation, and is in rough agreement with the solutions reported initially by Hakala et al., based on ground-based optical observations. The large and stable nu(sup dot) over a decade is consistent with gravitational radiation losses driving the evolution. An intermediate polar (IP) scenario where the observed X-ray period is the spin period of an accreting white dwarf appears less tenable because the observed nu(sup dot) requires an m(sup dot) approximately equal to 4 x 10 (exp -8) solar mass yr(sup -l), that is much larger than that inferred from the observed X-ray luminosity (although this depends on the uncertain distance and bolometric corrections), and it is difficult to drive such a high m(sup dot) in a binary system with parameters consistent with all the multiwavelength data. If the ultracompact scenario is correct, then the X-ray flux cannot be powered by stable accretion which would drive the components apart, suggesting a new type of energy source (perhaps electromagnetic) may power the X-ray flux.

Strohymayer, Tod E.↗
NASA NTRS2005

Long-Lag, Wide-pulse Gamma-Ray Bursts

The best available probe of the early phase of gamma-ray burst (GRB) jet attributes is the prompt gamma-ray emission, in which several intrinsic and extrinsic variables determine observed GRB pulse evolution, including at least: jet opening angle, profiles of Lorentz factor and matter/field density, distance of emission region from central source, and viewing angle. Bright, usually complex bursts have many narrow pulses that are difficult to model due to overlap. However, the relatively simple, long spectral lag, wide-pulse bursts may have simpler physics and are easier to model. We have analyzed the temporal and spectral behavior of wide pulses in 24 long-lag bursts from the BATSE sample, using a pulse model with two shape parameters - width and asymmetry - and the Band spectral model with three shape parameters. We find that pulses in long-lag bursts are distinguished both temporally and spectrally from those in bright bursts: the pulses in long spectral lag bursts are few in number, and approximately 100 times wider (10s of seconds), have systemtically lower peaks in nu*F(nu), harder low-energy spectra and softer high-energy spectra. These five pulse descriptors are essentially uncorrelated for our long-lag sample, suggesting that at least approximately 5 parameters are needed to model burst temporal and spectral behavior, roughly commensurate with the theoretical phase space. However, we do find that pulse width is strongly correlated with spectral lag; hence these two parameters may be viewed as mutual surrogates. The prevalence of long-lag bursts near the BATSE trigger threshold, their predominantly low nu*F(nu) spectral peaks, and relatively steep upper power-law spectral indices indicate that Swiift will detect many such bursts.

Norris, J. P.↗
NASA NTRS2005

How to Distinguish Neutron Star and Black Hole X-ray Binaries? Spectral Index and Quasi-Periodic Oscillation Frequency Correlation

Recent studies have revealed strong correlations between 1-10 Hz frequencies of quasiperiodic oscillations (QPOs) and the spectral power law index of several Black Hole (BH) candidate sources when seen in the low/hard state, the steep power-law (soft) state, and in transition between these states. In the soft state these index-QPO frequency correlations show a saturation of the photon index GAMMA approximately equal to 2.7 at high values of the low frequency nu(sub L). This saturation effect was previously identified as a black hole signature. In this paper we argue that this saturation does not occur, at least for one neutron star (NS) source 4U 1728-34, for which the index GAMMA monotonically increases with nu(sub L) to the values of 6 and higher. We base this conclusion on our analysis of approximately 1.5 Msec of RXTE archival data for 4U 1728-34. We reveal the spectral evolution of the Comptonized blackbody spectra when the source transitions from the hard to soft states. The hard state spectrum is a typical thermal Comptonization spectrum of the soft photons which originate in the disk and the NS outer photospheric layers. The hard state photon index is GAMMA approximately 2. The soft state spectrum consists of two blackbody components which are only slightly Comptonized. Thus we can claim (as expected from theory) that in NS sources thermal equilibrium is established for the soft state. To the contrary in BH sources, the equilibrium is never established due to the presence of the BH horizon. The emergent BH spectrum, even in the high/soft state, has a power law component. We also identify the low QPO frequency nu(sub L) as a fundamental frequency of the quasi-spherical component of the transition layer (presumably related to the corona and the NS and disk magnetic closed field lines). The lower frequency nu(sub SL) is identified as the frequency of oscillations of a quasi-cylindrical configuration of the TL (presumably related to the NS and disk magnetic open field lines). We also show that the presence of Fe K(sub alpha), emission-line strengths, QPOs, and the link between them does not depend on radio flux in 4U 1728-34.

Titarchuk, Lev↗