Amplitude Of Anisotropy Research Articles

Diurnal variation of cosmic ray intensity, 1. Two approaches to the study

The investigation of the daily variation of cosmic ray intensity has been carried out over the past two decades by either of two approaches: the traditional Fourier series method and the more recently introduced power spectral method. A comparison of the two approaches is essential to the proper understanding of the results derived from them. The present study, for the first time, adopts both approaches for investigating the data from the Sulphur Mountain super neutron monitor for the period of mid‐December 1965 to April 1966 (extending over five solar rotations), when interplanetary magnetic field data from Pioneer 6 were also available. Problems relating to the analyses of both data sets on a day‐to‐day basis and on a statistical basis over a number of days are discussed. The power spectral analysis method cannot provide information on the phase of the diurnal variation or information on the diurnal amplitude on a day‐to‐day basis. This method, however, provides excellent estimates of the diurnal anisotropy amplitude independent of any daily phase shifts in the anisotropy. In addition, this method provides a measure of the ambient anisotropy amplitude which, for the entire period studied, has a mean value of ∼0.1%. The Fourier series method can yield reliable measures of the amplitude and phase on a day‐to‐day basis, provided the time series is reasonably stationary. This method cannot estimate the ambient anisotropy amplitude which, for small amplitudes, contributes to large uncertainties in the Fourier coefficients. We find that there is a general agreement between the observed diurnal variation over each period considered and that predicted theoretically from parameters derived from the interplanetary data. However, for most of the periods examined the ratio of the perpendicular diffusion coefficient to the parallel diffusion coefficient is rather small (K⊥/K∥ ≲ 0.1). As such the diurnal variation amplitude is generally most sensitive to the interplanetary field direction and the solar wind velocity and not to the calculated values of the diffusion coefficients. Further tests of the theory will require analyses of other periods when perhaps the perpendicular diffusion is larger and/or measurements of cosmic rays outside the atmosphere are available in order to obtain better energy resolution on the detected particles.

Limitations of the COS approximation as applied to the cosmic-ray anisotropy

A systematic study is presented of the COS approximation as applied to the class of spinning charged particle detectors that measure solar and galactic cosmic-ray anisotropies. This study includes the derivation of: (1) the general COS approximation equations and their limitations for any harmonic component of the anisotropy, (2) the realistic errors for each harmonic component produced by the Poisson statistical fluctuations, and (3) the first order geometric smoothing effects caused by real charged particle telescopes. A computer simulation of the COS approximation is developed to test the reliability of the derived error relations and to examine effects associated with limited count rates. We find that not only anisotropy amplitude increased above its proper value at low count rates, but at any count rate an isotropic background anisotropy exists and is equal to ∼✓(3/C)±✓(1/C), where C is the total number of counts.

Field dependent cosmic ray streaming at high rigidities

Data from underground µ meson telescopes at depths of 25, 40, and 80 mwe covering the period 1965–1973 have been analyzed as a function of interplanetary magnetic field direction. Cosmic ray streaming both in and perpendicular to the ecliptic plane, with directions dependent on the sense of the interplanetary magnetic field, is observed throughout the period at all depths. The field dependent streaming in the ecliptic plane exhibits some variability in amplitude and phase but contains a component in the direction perpendicular to the interplanetary magnetic field direction which is consistent with B × ▽N streaming due to a perpendicular cosmic ray density gradient pointing southward (higher density below the ecliptic plane than above it). In the case of the field dependent streaming perpendicular to the ecliptic plane the direction of the streaming has remained remarkably consistent over the 9-year period. One possible source of this streaming is B × ▽N streaming due to a radial heliocentric cosmic ray density gradient; this possibility is discussed along with other possible sources. There does not appear to be an obvious variation in the amplitude of the field dependent streaming either in or perpendicular to the ecliptic plane with increasing rigidity; both effects are still apparent at rigidities well above the 52-GV threshold rigidity of the Socorro 80-mwe telescope. The amplitudes of both anisotropies appear larger at solar maximum than at solar minimum.

Supergalactic Studies. V. The Supergalactic Anisotropy of the Redshift-Magnitude Relation Derived from Nearby Groups and SC Galaxies

The amplitude of the north-south anisotropy and its level of significance is shown to increase rapidly with increasing angular resolution ..cap omega../4..pi..; in particular the null result of the Sandage-Tammann analysis is accounted for by insufficient resolution (..cap omega../4..pi..approx. =0.4). At high resolution (..cap omega../4..pi..<0.1) the logarithmic redshift anisotropy in the range 31<..mu../sub 0/<33 approaches 0.3 (i.e., a factor of 2 in velocity ratio) at significance levels greater than 5< or =. In Appendix A the free-space or low density, asymptotic value of the Hubble constant H/sub 0/=75 km s/sup -1/ Mpc/sup -1/ is derived from sky areas (anticenter sector and polar caps) not dominated by the Local Supercluster. Some galaxies with discrepant or questionable redshifts are discussed in Appendix B. (AIP)

Emitter velocity and anisotropy for quasi-molecular radiation in I-Au collisions

The velocity of the quasimolecular x-ray emitter is found via Doppler shift measurements. It is in agreement with the center of mass velocity. Applying Doppler shift corrections the intrinsic anisotropy of the quasi-molecularM radiation is determined as a function of x-ray energy for 6 to 45 MeV I bombardment on thin Au targets. Position and amplitude of the maximum anisotropy in the x-ray spectrum depend on impact energy.

SmecticBliquid-crystalline glass (at 77 °K) as seen by the Mössbauer effect of Sn-bearing solute molecules

By observing the orientation dependence of the recoil-free fraction for three Sn-bearing solute molecules, we have determined the lattice contribution of a smectic $B$ glass (at 77 \ifmmode^\circ\else\textdegree\fi{}K) to the anisotropy of the nuclear vibrational amplitude for the Sn-119 nucleus. The measured anisotropy depends on the solute shape and length and is explained in terms of the layered smectic structure and the difference between the character of the central core and the end-chain regions of the host liquid-crystal molecules. The resonant line position for the solute, 4-trimethyl-tin-benzylidene-4\ensuremath{'}-$n$-butylaniline (Sn-BBA), was found to be dependent on the angle ($\ensuremath{\theta}$) between the preferred direction of the aligned liquid-crystalline glass and the M\"ossbauer $\ensuremath{\gamma}$ beam. We interpret this in terms of an unresolved quadrupole splitting ($\ensuremath{\Delta}{E}_{Q}$) for this molecule. The line-shift data are shown to yield the sign of ${V}_{\mathrm{zz}}$ and the magnitude of $\ensuremath{\Delta}{E}_{Q}$ for the Sn-BBA molecule.

On the measurement of energetic particle flux anisotropies with a class of spinning detectors

Some of the charged particle telescopes on spinning spacecraft operate in an analysis-readout mode in which a Poissonlike statistical bias can significantly distort both the amplitude and the direction of the measured flux anisotropy. Briefly, if the telescope accepts the first event after telemetry readout for analysis and then accepts no further events for analysis until after the next readout, then, if the conventional computational techniques are followed, the anisotropy amplitude deduced from the analyzed events will be reduced from the true anisotropy, and the deduced direction of maximum flux will lag the true direction (in the sense of the spacecraft spin). For high enough fluxes the rates will be reduced to the sampling rate (a well-known effect), but for weak anisotropies the lag will approach 90° (an effect not discussed heretofore). However, these distortions may be computed if the incident rate of unanalyzed events is measured independently, and hence the measurements may be corrected for the statistical bias in a straightforward manner.

Quiet-time electron increases: A measure of conditions in the outer solar system

One possible explanation for the increases in the intensity range of 3- to 12-Mev interplanetary electrons that McDonald et al. (1972) have labeled as ‘quiet-time electron increases’ is discussed. It is argued that the electrons in quiet-time increases are galactic in origin but that the observed increases are not the result of any variation in the modulation of these particles in the inner solar system. It is suggested instead that quiet-time increases may occur when more electrons than normal penetrate a modulating region that lies far beyond the orbit of the earth. The number of electrons penetrating this region may increase when field lines that have experienced an unusually large random walk in the photosphere are carried by the solar wind out to the region. As evidence of this increased random walk, it is shown that five solar rotations before most of the quiet-time increases occur there is an extended period when the amplitude of the diurnal anisotropy (measured by the Deep River neutron monitor) is relatively low. A delay time of five rotations implies that the proposed modulating region lies at ∼30 AU from the sun if the average solar-wind speed is assumed to be constant at ∼400 km/sec over this distance. The implications for the correlation between periods of low-amplitude diurnal anisotropy and quiet-time increases on interplanetary conditions out to ∼30 AU and some possible models for the proposed modulating region are also considered.

Relativistic Gravity in the Solar System. II. Anisotropy in the Newtonian Gravitational Constant

view Abstract Citations (60) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Relativistic Gravity in the Solar System. II. Anisotropy in the Newtonian Gravitational Constant Will, Clifford M. Abstract The Parametrized Post-Newtonian formalism is used to show that some theories of gravity predict an anisotropy in the Newtonian gravitational constant C, as measured locally by means of Cavendish experiments. Two such theories are Whitehead's theory and a theory of gravity (devised in this paper) which predicts different flat-space propagation speeds for gravity and for light. The anisotropy in C causes the local gravitational acceleration, measured by a gravimeter at a fixed point on Earth, to vary with a period of 12 sidereal hours as the Earth rotates. Gravimeter data (measurements of "Earth tides") are shown to put a limit of 1/10 on the amplitude of any such anisotropy. This rules out Whitehead's theory which predicts an effect 200 times larger than the experimental limit. It also shows that the PPN parameter combination (A2 + - 1) is zero to within 3 percent, and hence that the speeds of gravity and of light in the theory devised in this paper should be equal to within about 2 percent. Publication: The Astrophysical Journal Pub Date: October 1971 DOI: 10.1086/151125 Bibcode: 1971ApJ...169..141W full text sources ADS | Related Materials (1) Part 1: 1971ApJ...165..409W

Amplitude of diurnal anisotropy of cosmic ray intensity

Cosmic ray intensity mean diurnal variation, taking into account angle between solar corotational velocity and earth equatorial plane

Closed rotating cosmologies containing matter described by the kinetic theory. B: Small anisotropy calculations; application to observations

We continue the discussion of anisotropy in closed, rotating cosmologies begun in the accompanying paper. We present an explicit small anisotropy model, taking parameters suggested by the observed universe. We give an explicit discussion of the geodesic equation in the small anisotropy regime, with applications to the microwave temperature anisotropy. The amplitude of the temperature anisotropy, ΔT T is of the same order as predicted by Misner for Type I cosmologies, i.e. ΔT T ∼ 10 −4 or smaller, assuming that neutrino dissipation processes were effective at T ∼ 10 10K. It is shown that deviations from the lowest order anisotropy shape (quadrupole + dipole) take the form of distortions of the anisotropy pattern over angular regions Δω of the order of ∼ |β| where |β| is a measure of the metric anisotropy. Since ΔT T is given by changes in the metric anisotropy since the last photon scattering, it is not directly correlated with |β|. The metric anisotropy need not be small and would be otherwise unmeasurable, so could give rise to large effects distorting the quadrupole ΔT T shape. Observations on the (24-h) isotropy of the black-body radiation put limits on the rotation in a realistic model, and hence the largest distorting effects are those which appear even in nonrotating models, and are not directly related to rotation. Some calculations based on a moderate value for the metric anisotropy show that these effects might be detectable but probably would be submerged in structure arising from local (i.e. noncosmological) effects, or from other possible cosmological effects ignored in our homogenous models. It is possible that the entire temperature anisotropy will be dominated by these nonhomogenous or noncosmological effects.

Inversion of the anisotropy of vibration of iron atoms in crystals of siderite

Measurements were made of the total area of Mössbauer absorption for a single crystal of siderite at temperatures between 90°K and 600°K. An inversion of the anisotropy of the mean square amplitude of vibration of the iron atoms was observed at 200–300°K. Possible interpretations of the inversion are discussed.

Sidereal-time variations in the cosmic-ray intensity

Experimental results obtained between 19 May, 1967 and 17 May, 1968 for inclined muon telescopes, responding to primaries of energy above about 20 GeV and scanning the equatorial plane, are presented. The asymptotic arrival directions for these telescopes have a narrow spread in terms of asymptotic longitude and these telescopes are therefore well suited for sidereal anisotropy studies. The sidereal analyses described yield marginal evidence for a sidereal anisotropy of amplitude ≲0.05%.

Electron component in primary cosmic rays. II. Theory

The energy spectrum of cosmic-ray electrons can be represented by a power law with a single exponent between 3 and 50 GeV, and a break in the spectrum due to the energy loss of electrons could appear at about 50 GeV or higher. It is necessary to reconcile this high value of the critical energy [Formula: see text] with the effective thickness of matter traversed [Formula: see text] as estimated from the positron flux) and with the small amplitude of anisotropy [Formula: see text]. Hence rather severe conditions are imposed on the properties of the region in which cosmic rays are stored. We have carried out an investigation of the two-component model for storing galactic cosmic rays, which consists of disk and halo components. Assuming the intensity ratio (η) of the halo to the disk components to be nearly unity, one can assign parameters explaining various properties of cosmic rays consistently. For the case of a vanishing halo component (η = 0), the mean scattering length for particle diffusion becomes about 1018 cm.

Cosmic-ray propagation processes: 1. A study of the cosmic-ray flare effect

Observations of the cosmic radiation generated by solar flares are used to study the propagation of cosmic rays through the interplanetary magnetic field. The observations were made by cosmic-ray detectors flown on two identical interplanetary spacecraft, Pioneers 6 and 7. The detectors determined the directional, energy, and temporal characteristics of the cosmic radiation of energy greater than 7.5 Mev. It was found that cosmic radiation of solar origin is normally extremely anisotropic, the direction of maximum flux being aligned parallel to the interplanetary magnetic field vector at early times during flare effects. At late times a persistent anisotropy of amplitude 5-10% is observed, the maximum flux arriving from the sun-spacecraft direction. It is argued that at late times the cosmic radiation is in diffusive equilibrium, and an explanation for the persistent anisotropy is advanced in terms of expulsion of the cosmic radiation from the solar system by the combined action of the solar wind and a cosmic-ray density gradient. It is shown that the cosmic-ray fluxes and their anisotropic characteristics are sometimes very greatly influenced by interplanetary conditions, and may exhibit strong spatial inhomogeneities. It is shown that the low-energy cosmic rays tend to remain identified with the magnetic tube of force onto which they are initially injected, this being the equivalent to saying that they corotate with the sun. Under some circumstances, the propagation of cosmic rays from the sun to the orbit of earth is completely dominated by a 'bulk motion' propagation mode, in which the cosmic rays do not gain access to the spacecraft until the magnetic regime into which the cosmic rays are injected envelops the spacecraft. This bulk motion propagation mode applies both to magnetic regimes initiated by solar flares and to the regimes associated with recurring Forbush decreases, the latter being long-lived field structures imbedded in the normal solar wind. In two cases, it is shown that the anisotropy directions and cosmic-ray times of flight are such as to indicate diffusion of the cosmic rays to a point on the western portion of the solar disk before injection onto the field line that carried them to the spacecraft. The temporal decay of a cosmic-ray flare effect subsequent to impulsive injection by a solar flare is studied, an example being presented in which the decay was essentially exponential over a period of time equal to 9.2 decay time constants. Simultaneous observations by both spacecrafts when separated by about 54° in solar azimuth indicate azimuthal cosmic-ray density gradients in excess of two orders of magnitude per 60° for extended periods during the initial phases of flare effects. By studying the rate at which a known cosmic-ray flux propagating away from the sun was backscattered so as to return to the spacecraft from the antisun direction, the mean free path for large-angle scattering in the inner solar system is shown to be of the order of 1.0 AU. The application of an isotropic diffusion model to the same data is shown to yield much lower values of mean free paths, and it is argued that this latter method is, in most cases, inapplicable.

Magnetoresistance of Nickel-Copper Single-Crystal Thin Films

Single-crystal nickel-copper thin films are obtained by utilizing a simultaneous dual-deposition technique. It is observed that the transverse magnetoresistance of the films is anisotropic with respect to magnetic field orientation for a given direction of current flow. The behavior of this anisotropy is examined at the temperatures of 77°, 173°, and 298°K, for a magnetic field strength of 10 kOe, and for film compositions ranging from pure nickel to 40% Cu-60% Ni. Data are recorded under the above-mentioned conditions with the current parallel to a [100] direction and with the magnetic field oriented in the corresponding (100) plane. The following observations are made: (1) The gross amplitude of the anisotropy passes through a maximum for a copper content of approximately 10%; (2) the gross amplitude of the magnetoresistance anisotropy decreases with decreasing temperature for a pure nickel single-crystal film and increases for most of the nickel-copper alloy single-crystal films; and finally, (3) it is noted that, as the total impurity content (materials other than nickel and copper) in the films increases, the gross amplitude of the magnetoresistance anisotropy decreases.

Asymptotic cones of acceptance and their use in the study of the daily variation of cosmic radiation

The dependence of the counting rate of a cosmic ray detector on the asymptotic directions of approach of the primary cosmic radiation is discussed. By means of a simulation of the geomagnetic field that uses spherical harmonics up to the sixth degree, and an arbitrary anisotropy in the primary cosmic radiation, a method for calculating the time variations in the counting rate of a cosmic ray detector is developed. Resolving the arbitrary anisotropy as a Fourier series in longitude, the amplitude and phases of the diurnal (24-hourly) and semidiurnal (12-hourly) components of the daily variation are calculated for a number of stations. No simple relationship is observed between the phases and the latitudes and longitudes, geographic or geomagnetic. Moreover, the theoretical calculations point out that a difference of more than five hours between the diurnal phases at two different places could arise purely from the known geomagnetic configuration. A study of the time-averaged diurnal component of the daily variation experimentally observed by 22 neutron monitors during the International Geophysical Year (1957–1958) reveals good agreement with the theoretical calculations and leads to the following conclusions: (1) The results are consistent with an anisotropy that is independent of rigidity in the range 1–200 bv, the exponent of the power law which fits the data being 0.0±0.05. (2) The anisotropy varies as the cosine of the asymptotic latitude and has a maximum in the direction 85° to the east of the earth-sun line. (3) The maximum amplitude of the average anisotropy is 4×10−3 times the average cosmic ray flux.