Electro-hydromagnetic waves in a fully ionized gas-II

The propagation of hydromagnetic and low frequency radio waves in all directions in a fully ionized gas containing a magnetic field is examined. For longitudinal and transverse propagation the addition of one extra term in the magneto-ionic formulae (without collisions) accounts for the presence of heavy ions.

The partition of energy of disturbance between kinetic (K) and magnetic (M) for longitudinal propagation of all frequencies is given by

where V is the Alfvén speed. Thus approximate equipartition may exist for some audio- and radio-frequencies in the Earth's exosphere.

Some errors in Paper I of this series are corrected.     

The effect of an electric field induced by a time-dependent ring current on the particle drift motion

The effect of an electric field induced by a rapidly decaying ring current on the motion of charged particles in the magnetosphere has been investigated using Euler potentials. For a model consisting of the earth dipole and the symmetric ring current, the electric field satisfies the condition E . B = 0.

Under this circumstance, the E × B drift of the particle can be identified as the motion of the magnetic field lines and vice versa. The time dependent electric field induced can be evaluated in a Spherical polar coordinate system by the formula

where and β are Euler potentials.

A model calculation on the particle drift velocity v_D = E × B/B² shows that the radial component of the drift velocity is in good agreement with those deduced from whistler duct studies.     

Electro-hydromagnetic waves in a fully ionized gas—I

Transport equations are used to determine coefficients which are generalizations for any frequency of electric field of the parallel, Pedersen and Hall conductivities in a fully ionized gas.

These coefficients are used in an investigation of the propagation of weak electromagnetic and hydromagnetic waves of all frequencies across a homogeneous and constant magnetic field in a rarefied fully ionized gas. For propagation perpendicular to the magnetic field it is found for all frequencies

(i)

(ii)

where V² = H²/4π and v, h are the perturbations of the velocity, magnetic field. Similar relationships are deduced for propagation at any angle to the field for frequencies greater than about 10 times the gyrofrequency of electrons.

The theory is applied to discuss transmission of disturbance across the interplanetary medium, the temperature of the solar corona and the earth's outer atmosphere, the emission of non-thermal solar radio noise, cosmic radio noise and the anomalous emission of light from shock fronts.     

Nature of solar-cycle and heliomagnetic-polarity dependence of cosmic rays, inferred from their correlation with heliomagnetic spherical surface harmonics in the period 1976–1985

Correlation of cosmic-ray intensity (I) with the solar magnetic field expanded into the spherical surface harmonics, B_ns(n 9), by Hoeksema and Scherrer has been studied using the following regression equation:

, where are subgroups of B_ns classified in ascending order of n, and τ_i is the time lag of I behind correlation coefficient between the observed and simulated intensities (I_obs, I_sml) in the period 1976–1985 is 0.87 and considerably better than that derived from any single index of solar activity. The lag time τ₃ is greater than others, indicating that the higher order magnetic disturbances effective to the cosmic-ray modulation have a longer lifetime in space than the lower order disturbances. The rigidity spectrum of the cosmic-ray intensity variation responsible for A_I due to the dipole moment is harder than those for others (A₂,A₃), indicating that the lowest order (i.e. largest scale) magnetic disturbances can modulate cosmic rays more effectively than the higher order disturbances. As another result of the present analysis, it has been found that the intensity depends also on the polarity of the polar magnetic field of the Sun; the residual (I_obs−I_sml) of the simulation changes its sign from positive to negative with a time lag (0–5 Carrington rotation periods) behind the directional change of the solar magnetic dipole moment from northward to southward, and has a softer rigidity spectrum than A_iS. The dependence is consistent with the result having been obtained in the previous period, 1936–1976, by one (K.N.) of the present authors. The polarity dependence can be found also in the 22-year variation of the time lags obtained every solar cycle in the period 1936–1985. The theoretical interpretation of these polarity dependences is discussed on the basis of the diffusion-convection-drift model.     

Galactic cosmic-ray anisotropy and its heliospheric modulation, inferred from the sidereal semidiurnal variations observed in the rigidity range 300–600 GV with multidirectional muon telescope at Sakashita underground station

The existence of sidereal semidiurnal variation of cosmic-ray intensity in a rigidity region 10²-10³ GV has been reported by many researchers, but there is no consensus of opinion on its origin. In this paper, using the observed semidiurnal variations in a rigidity range (300–600 GV) with 10 directional muon telescopes at Sakashita underground station (geog. lat. = 36°, long. = 138°E, DEPTH = 80 m.w.e.), the authors determine the magnitudes (η₁, η₂) and directions (a₁, a₂) of the first- and second-order anisotropies in the following galactic cosmic-ray intensity distribution (j)

jdp = j₀{1 + η₁P₁(cos χ₁) + η₂P₂(cos χ₂)}dp

, where P_nis the nth order spherical function and χ_n is the pitch angle of cosmic rays with respect to a_n. For the determination, the influence of cosmic-ray's heliomagnetospheric modulation, geomagnetic deflection and nuclear interaction with the terrestrial material and also of the geometric configuration of the telescopes are taken into account. Usually, the semidiurnal variation is produced by the second-order anisotropy. The present observation, however, requires also the first-order anisotropy which usually produces only the diurnal variation, but can produce also the semidiurnal variation as a result of the heliospheric modulation. The first- and second-order anisotropies are characterized with η₁) > 0 and η₂ < 0 have almost the same direction (a₁ a₂) specified by the right ascension ( 0.75 h) and declination (δ 50°S) and, therefore, they can be expressed, as a whole, by an axis-symmetric anisotropy of loss-cone type (i.e. deficit intensities in a cone). It is noteworthy that this anisotropy approximately coincides with that inferred from the air shower observation at Mt Norikura in the rigidity region 10⁴ GV.     

Studies of three-dimensional disk-shaped galaxies. II. Projected surface density in the central region and for the whole galaxy

Based on the method of Paper I and concentrating on the rigidly rotating, inner region of the galaxy, a theoretical investigation is carried out here on the asymptotic property of the projected surface density σ(r); combining with the asymptotic solution of Paper I for the outer region with flat rotation curve, I suggest the form

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as a possible, reasonable mass model for the whole galactic disk. In the course of the study, an important relation between the masses of the bulge and the disk and certain parameters characterizing the distribution was found.     

A combined photometric and spectroscopic solution for aa ursae majoris

From the photometric and spectroscopic data on AA UMa obtained by us in 1987 and 1986 and using the Wilson-Devinney program, we made a simultaneous solution. We found mass-ratio q = 1. 8157 ± 0.0099, M₁ = 0.85 M, M₂ = 1. 55 M , A = 3.39 R , R₁ = 1.50 R , and degree of over-contact f = 0.15 ± 0.01. Adding six minimum times obtained by us to the literature, a new epoch formula is derived: Min.I(J.D.Hel) = 2 446 885.1119+0.468 125 83 E.     

A synthesized method for determining the azimuth of solar transverse magnetic field

The analyses have been made with the emphasis on four existing criteria for calibrating the azimuth of the photospheric transverse magnetic field measured with a heliomagnetograph. The results indicate that the potential criterion, Krall's criterion, i.e. B_t · B_z < 0 and Wu-Ai's criterion, i.e.

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, are applicable to different cases, and the criterion based on the assumption about azimuth continuity of the transverse field is unreliable for the magnetograms with discrete data. On the basis of these analyses, a synthesized method for determining the azimuth of the transverse magnetic field on solar photosphere has been suggested in this paper. The main points of the method are as follows:

The transverse magnetic field observed with a heliomagnetograph could be calibrated, respectively, by means of potential criterion and Krall's criterion, and two different results could be obtained. By comparing the both results with one another, we can find that the azimuth distributions of transverse field are the same in some areas, which are named as areas with certain transverse field (CA), and different in other areas, which are named as areas with uncertain transverse field(UA). In order to determine the transverse field in UA, we introduce an assumption that the values of (the factor of force-free magnetic field) at neighbouring points are close. According to this assumption, the distribution of in UA could be determined through extrapolating from the CA, and hence the azimuth distribution of the transverse field in UA could be determined as well.

An observational example shown in this paper preliminarily demonstrates the availability of the synthesized method.     

Spectroscopic orbits of eclipsing binaries: WX Cancri

We have determined for the first time a spectroscopic orbit for WX Cnc. The orbital elements are V₀ = +9.8 km/s, k₁ = 110.2 km/s, K₂ = 149.0 km/s, T_o = HJD 2446 480.0309. After combining with the published photometric results, we derive the the following absolute parameters: A = 6.32R, R₁ = 1.53R, R₂=1.18R, M₁ = 1.29 M, M₂ = 0.96M. The spectroscopic mass-ratio is q = 0.74.     

Constraining cosmological models with cluster power spectra

Using extensive N-body simulations we estimate redshift space power spectra of clusters of galaxies for different cosmological models (SCDM, TCDM, CHDM, ΛCDM, OCDM, BSI, τCDM) and compare the results with observational data for Abell–ACO clusters. Our mock samples of galaxy clusters have the same geometry and selection functions as the observational sample which contains 417 clusters of galaxies in a double cone of galactic latitude |b|>30° up to a depth of 240 h⁻¹ Mpc. The power spectrum has been estimated for wave numbers k in the range 0.03k0.2 h Mpc⁻¹. For k>k_max0.05 h Mpc⁻¹ the power spectrum of the Abell–ACO clusters has a power-law shape, P(k)∝kⁿ, with n≈−1.9, while it changes sharply to a positive slope at k<k_max. By comparison with the mock catalogues SCDM, TCDM (n=0.9), and also OCDM with Ω₀=0.35 are rejected. Better agreement with observation can be found for the ΛCDM model with Ω₀=0.35 and h=0.7 and the CHDM model with two degenerate neutrinos and Ω_HDM=0.2 as well as for a CDM model with broken scale invariance (BSI) and the τCDM model. As for the peak in the Abell–ACO cluster power spectrum, we find that it does not represent a very unusual finding within the set of mock samples extracted from our simulations.     

A spectroscopic orbit for the two—Spectrum eclipsing binary RT Persei

Intensified Reticon spectra have been obtained at a high dispersion for the Algol system, RT Persei. They were measured by the cross-correlation technique. The spectroscopic elements, revised for the primary component and determined for the secondary for the first time, are: T₀ = HJD 2,446,038.9332, K₁ = 55.0, K₂ = 194.7, V₀ = −8.3 km/s. A mass ratio q = m₂/m₁ = 0.282 is deduced. A circular orbit is adopted. The spectrum of the primary is F5V, and the secondary is a subgiant. With the elements determined here and the published photometric parameters, the absolute dimensions of the binary are: A = 4.20, R₁ = 1.20, R₂ = 1.08 R; M₁ = 1.08, M₂ = 0.30 M.     

Robust limits on Lorentz violation from gamma-ray bursts

We constrain the possibility of a non-trivial refractive index in free space corresponding to an energy-dependent velocity of light: c(E)  c₀(1 − E/M), where M is a mass scale that might represent effect of quantum-gravitational space-time foam, using the arrival times of sharp features observed in the intensities of radiation with different energies from a large sample of gamma-ray bursters (GRBs) with known redshifts. We use wavelet techniques to identify genuine features, which we confirm in simulations with artificial added noise. Using the weighted averages of the time-lags calculated using correlated features in all the GRB light curves, we find a systematic tendency for more energetic photons to arrive earlier. However, there is a very strong correlation between the parameters characterizing an intrinsic time-lag at the source and a distance-dependent propagation effect. Moreover, the significance of the earlier arrival times is less evident for a subsample of more robust spectral structures. Allowing for intrinsic stochastic time-lags in these features, we establish a statistically robust lower limit: M > 0.9 × 10¹⁶ GeV on the scale of violation of Lorentz invariance.     

The mass ratio of Nova Muscae 1991

We report intermediate resolution H spectroscopy of the black hole candidate Nova Muscae 1991 during quiescence. We classify the companion star as a K3-K4V which contributes 85±6 percent to the total flux from the binary. The photospheric absorption lines are broadened by 106±13 kms⁻¹ with respect to template field stars, leading to a system mass ratio of q =M₁/M₂ = 7.8_−2.0^+3.4. Doppler imaging of the H line shows strong emission coming from the secondary star (EW=3.1±0.6Å) which we associate with chromospheric activity. However, the hot-spot is not detected and this may indicate a lower mass transfer rate than in other X-ray transients of comparable orbital periods. The surface brightness distribution of the accretion disk in H follows a relation I∝R^−1.1, less steep than typically observed in cataclysmic variables. Updated system parameters are also presented.     

On the effects of lunar tides in the Tianjin latitude observations

In this paper we have analysed the effect of the lunar tide on the latitude observations of 25260 star-pairs with the zenith telescope, ZTL-180 of Tianjin Latitude Station during 1960–1966. For the M₂ wave, we found an amplitude of 0.0108 and hence a value of 1 + k − 1 = 1.34. When the effect of the ocean tide is subtracted, the value of 1 + k − 1 is reduced to 1.315. This is in very good agreement with the value 1.31, deduced by geophysicists for the Asia region.     

Electron excitation and auroral emission parameters

Auroral luminosities of the main emission lines in the aurora have been calculated for excitation by an isotopic primary electron flux with spectra of the form J(E) = AE exp (−E/E₁) + B(E₂)E exp (−E/E₁). The variation of emissions from O and N₂⁺ with height are shown, as are the variations of column integrated intensities and pertinent intensity ratios with the characteristic energy E₂, this leading to a method of estimating the electron spectrum from ground observation.     

Space–time foam and cosmic-ray interactions

It has been proposed that propagation of cosmic-rays at extreme-energy may be sensitive to Lorentz-violating metric fluctuations (“foam”). We investigate the changes in interaction thresholds for cosmic-rays and gamma-rays interacting on the CMB and IR backgrounds, for a class of stochastic models of space–time foam. The strength of the foam is characterized by the factor (E/M_P)^a, where a is a phenomenological suppression parameter. We find that there exists a critical value of a (dependent on the particular reaction: a_crit3 for cosmic-rays, 1 for gamma-rays), below which the threshold energy can only be lowered, and above which the threshold energy may be raised, but at most by a factor of two. Thus, it does not appear possible in this class of models to extend cosmic-ray spectra significantly beyond their classical absorption energies. However, the lower thresholds resulting from foam may have signatures in the cosmic-ray spectrum. In the context of this foam model, we find that cosmic-ray energies cannot exceed the fundamental Planck scale, and so set a lower bound of 10⁸ TeV for the scale of gravity. We also find that suppression of p→pπ⁰ and γ→e⁻e⁺ “decays” favors values aa_crit. Finally, we comment on the apparent non-conservation of particle energy–momentum, and speculate on its re-emergence as dark energy in the foamy vacuum.     

Synchrotron radiation from the Crab Nebula discriminates between models of space–time foam

It has been argued by Jacobson, Liberati and Mattingly that synchrotron radiation from the Crab Nebula imposes a stringent constraint on any modification of the dispersion relations of the electron that might be induced by quantum gravity. We supplement their analysis by deriving the spectrum of synchrotron radiation from the coupling of an electrically charged particle to an external magnetic fields in the presence of quantum-gravity effects of the general form (E/M_QG). We find that the synchrotron constraint from the Crab Nebula practically excludes 1.74 for M_QGm_P=1.2×10¹⁹ GeV. On the other hand, this analysis does not constrain any modification of the dispersion relation of the photon that might be induced by quantum gravity. We point out that such quantum-gravity effects need not obey the equivalence principle, a point exemplified by the Liouville-string D-particle model of space–time foam. This model suggests a linear modification of the dispersion relation for the photon, but not for the electron, and hence is compatible with known constraints from the Crab Nebula and elsewhere.     

An Observational Study of the Physical Properties of Star-forming Molecular Cores

We used the 13.7 m millimeter-wave telescope of the Qinghai Station of Purple Mountain Observatory at Delingha to carry out simultaneous mapping observations in the ¹²CO(J = 1 − 0), ¹³CO(J = 1 − 0) and CO¹⁸ (J = 1 − 0) lines towards 11 isolated star-forming molecular cores selected from the sample of Spitzer's c2d program. For all three lines, these sources were all observed to the positions of half the peak intensity of the ¹³CO(J = 1 − 0) line. The volume density, local thermodynamic equilibrium mass M_LTE and virial mass M_VIR were derived for each of the molecular cores. The obtained ratio of M_VIR to M_LTE is 0.85 ± 0.40 for the ¹³CO(J = 1 − 0) cores and 0.77 ± 0.35 for the CO¹⁸ (J = 1 − 0) cores. The density profiles of the cloud cores were also calculated.     

Mangeto-optical effects in sunspots and their vector magnetic field

The system of transfer equations of the four Stokes parameters I, Q, U, V under the action of the magneto-optical effect (i.e. the Unno-Beckers equations) are numerically solved in this paper for the magneto-sensitive lines FeI λλ 6302.499 and 5324.191 using an appropriate sunspot model. The errors in the expressions for the coefficients _r and _W in Beckers' paper [2] have been corrected for. From the results of calculations, features of the profiles of the Stokes parameters dependent on the magnetic vector have been isolated. Our computations also show that the magneto-optical effect should be taken into consideration in the measurement of the vector magnetic fields.

In the fourth section of this paper we have established a simple and convenient method for obtaining-information on the magnetic vector (including the field strength B, its inclination to the line of sight γ and its azimuth χ) from the profiles of the Stokes parameters. It consists of three steps: (1) The value of B is determined from the distance of the highest point in the V-profile from the central line. (2) γ is then found from V_max, i.e maximum value of V. (3) Lastly, the angle χ is found from Q₀, i.e. the value of Q at line centre.     

Properties of the infrared dark cloud G79.2+0.38

The MSX infrared dark cloud G79.2+0.38 has been observed over a 11′×′ region simultaneously in the J=1-0 rotational transition lines of the ¹²CO and its isotopic molecules ¹³CO and ¹⁸CO. The dense molecular cores defined by the C¹⁸O line are found to be associated with the two high-extinction patches shown in the MSX A-band image. The two dense cores have the column density N (H₂) (5 – 12) × 10²² cm⁻² and the mean number density n (3 ± 1) × 10⁴ cm⁻³. Their sizes are 1.7 and 1.2 pc in ¹³CO(1-0) line, 1.2 and 0.6 pc in C¹⁸O(1-0) line, respectively. The masses of these cloud cores are estimated to be in the range from 2 × 10² to 2 × 10³ M. The profile of radial mean density of the cloud core can be described by the exponential function ¯n(p) p^{−0.34±0.02}. Compared with the cases of typical optical dark clouds, the abundances of the CO isotopic molecules ¹³CO and C¹⁸O in this MSX infrared dark cloud appear to be depleted by a factor of 4–11, but at present there is no evidence for any obvious variation of the relative abundance ratio X_13/18 between ¹³CO and C¹⁸O with the column density.