Theorie de Weyl et principe de moindre action: Application a l'etude des mouvements

Sommaire Les lois du mouvement dans une variété riemannienneV ₄ peuvent être déduites d'un principe de moindre action. Nous établissons dans cet article l'équivalence des relations ds=0 et dL=-L _k d^k, où ds ²=L ² est une métrique riemannienne et d _k /dt une fonction homogène de degré 1 des variables dx ⁱ/dt qui définit un espace de Weyl. Ce théorème permet de ramener une théorie de jaugen à un principe de moindre action. Il peut être utilisé dans la théorie de la double métrique de Dirac, obtenue en choissant la théorie des grands nombres comme condition de jauge. Une fibration de l'espace physiqueV ₃ basée sur le théorème de Huyghens permet de déduire les propriétés dynamiques des particules des propriétés des photons dansV ₃, et constitue en ce sens une unification des propriétés dynamiques des particules.

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The laws of motion in a RiemannianV ₄ manifold can be deduced from the principle of least action. We state in this work the equivalence between the equations ds=0 and dL=-L _k d^k, where ds ² =L ² is the Riemannian metric and d _k /dt the homogeneous functions of first degree of the dx ⁱ/dt which define a Weylian space. This theorem can then reduce a gauge theory to a principle of least action. It can be used in the double metric theory of Dirac, obtained by means of the Large Number Hypothesis as a gauging condition. A fibration of the physical spaceV ₃ based on Huyghens' theorem allows the deduction of the dynamical properties of particles by means of the properties of photons inV ₃, and constitutes in this way an unification of the dynamical properties of particles.

     

VR c photometry of dwarf cepheids (I)

In this paper, we present VRc photometric observations of four dwarf cepheids: YZ Boo (P = 0 _. ^d 104, V = 0 _. ^m 5), AD CMi (P = 0 _. ^d 123, V = 0 _. ^m 5), XX Cyg (P = 0 _. ^d 135, V = 0 _. ^m 5), EH Lib (P = 0 _. ^d 088, V = 0 _. ^m 7). The light curves were obtained at West Mountain Observatory, Provo, Utah on 14 nights from 1983 through 1986 and contain 589 data points in each of theV andR bands in the Cousin photometric system. A detailed study of these stars, based on the present light curves, will be published separately.     

Spectral investigation of some Be stars for NRP variability

Spectroscopic observations of the Be stars Eri, Oph, 66 Oph, and Ori for the period 1982–1988 are reported. The NRP hypothesis was verified on the ground of rapid line profile variability, radial velocities, and equivalent widths. The star Eri is pulsating in bothl=2 andl=8 with period 0 _. ^d 7. Pulsation in modesl=2 andl=4 are observed in Hei profiles of Oph for May 1982. For radial velocities has been obtained a period 0 _. ^d 913. The H and H lines of 66 Oph for April–August 1983 are in emission state with two clearly expressed components with intensity variations. All the parameters measured have the same period of variation — 0 _. ^d 025. For Ori variations in line profiles for component Ab have been observed and a period of 0 _. ^d 463 found for the radial velocities.     

Implications of liouville's theorem on the apparent brightness temperatures of solar radio bursts

Liouville's theorem for radiation, of which the generalized étendue is a consequence, implies ² d² d² A = constant along the ray path, where is the refractive index and d² and d² A are the ranges, respectively, of solid angle and of area that define a ray (actually a bundle of rays). Implications of this concept on the propagation of radio waves from the actual to the apparent source in the solar corona (i.e., the scatter image of the true source) are discussed. The implications for sources of fundamental plasma radiation include: (1)The observed solid angle (defining the directivity) and apparent area A of the source are compatible with Liouville's theorem only if the apparent source (the scatter image of the true source) corresponds to the envelope of subsources with a small filling factor f. (2) The brightness temperature T _Bof the actual source is greater than that of the apparent source by f ^-1. (3) For sources of fundamental plasma radiation the factor f is very small ( 10^-2). (4) A long-standing discrepancy between the observed low value of T _B at meter/decameter wavelengths for the quiet Sun and the known coronal temperature may be resolved by noting that the implied coronal temperature is given by T _B f and that the factor f must be significantly less than unity.A brief discussion is included of the relation between Liouville's theorem, the generalized étendue, Milne's laws, occupation numbers, extension in phase, and suppression of emission by a medium with refractive index unequal to unity.     

V792 Her=HD 155638: A totally eclipsing RS CVn binary

Photometry of HD 155638=V792 Her has been analyzed to determine the elements of this totally eclipsing RS CVn binary. The light variation outside eclipse was found to have a period of 27^d.07±0^d.07, which is slightly different from the 27^d.5384±0^d.0045 orbital period. Analysis of the eclipses was achieved by a modification of the Russell-Merrill technique. With the aid of radial velocity measures, absolute elements were obtained for the hot and cool stars, respectively;R _h=2.58R ,R _c=12.28R ,M _h=1.40M ,M _c=1.46M ,i=80^o.61 and velocity semi-amplitudesK _c=48.36 km s^–1±0.79 km s^–1, andK _h=50.50 km s^–1±0.33 km s^–1. The apparent magnitudes areV _h=9 ^m .73 andV _c=8 ^m .48. The distance to HD 155638 was estimated to be 310 parsecs.     

Interpretation of the underground muon charge ratio

The MINOS experiment has observed a rise in the underground muon charge ratio r_μ=μ⁺/μ^-. This ratio can be related to the atmospheric production ratios of π⁺/π^- and K⁺/K^-. Our analysis indicates that the relevant variable for studying the charge ratio is , rather than . We compare a simple energy dependent parameterization of the rise in the charge ratio with more detailed previously published Monte Carlo simulations and an analytical calculation. We also estimate the size of two previously neglected effects in this context: the charge sign dependency of the dE/dx in rock, and the energy dependence of heavy primaries on the derived K⁺/K^- ratio.     

Photoelectric study of the δ Scuti star HR 1225

The periodogram analysis of theV observations of the Scuti star HR 1225 has been carried out. Two frequencies of 6.415 cd (P ₀=0 _. ^d 1558) and 8.418 cd (P ₁=0 _. ^d 1188) have been determined. The period ratio ofP ₁/P ₀=0.762 indicates radial pulsation. The absolute magnitude, effective temperature and mass of the star are derived to be 1 _. ^m 05, 7600 K and 1.9M , respectively.     

Comparative analysis of photometric variability of TT ARI in the years 1994–1995 and 2001, 2004

We present the results of photometric observations of a bright cataclysmic variable TT Ari with an orbital period of 0.13755 days. CCD observations were carried out with the Russian-Turkish RTT 150 telescope in 2001 and 2004 (13 nights). Multi-color photoelectric observations of the system were obtained with the Zeiss 600 telescope of SAO RAS in 1994–1995 (6 nights). In 1994–1995, the photometric period of the system was smaller than the orbital one (0 _. ^d 132 and 0 _. ^d 134), whereas it exceeded the latter (0 _. ^d 150 and 0 _. ^d 148) in 2001, 2004. An additional period exceeding the orbital one (0 _. ^d 144) is detected in 1995 modulations. We interpret it as indicating the elliptic disc precession in the direction of the orbital motion. In 1994, the variability in colors shows periods close to the orbital one (0 _. ^d 136, b-v), as well as to the period indicating the elliptic disk precession (0 _. ^d 146, w-b). We confirm that during the epochs characterized by photometric periods shorter than the orbital one, the quasi-periodic variability of TT Ari at time scales about 20 min is stronger than during epochs with long photometric periods. In general, the variability of the system can be described as a “red” noise with increased amplitudes of modulations at characteristic time scales of 10–40 min.     

Drift in toroidal configurations

It is found that charged particles of positive energiesE, when constrained on axisymmetric isoflux surfaces , execute sinusoidal motions with typical frequencies =(2E/m)^1/2). In general, it was found that under equilibrium condition p=J ^B/cthe particles develop a non-ambipolar drift velocityv _d =(cµ/eb)[1+q ² +2(q/)²]p.     

Pulsation periods in theδ Scuti star HR 1170

All knownV data from the literature for the Scuti star HR 1170 have been reanalysed by using single-frequency Fourier and multiple-frequency least squares analysis. The calculated periods areP ₁=0 _. ^d 09942 andP ₂=0 _. ^d 08392. The second frequency has not been found before and gives better residuals and almost constant amplitudes for the individual data sets. The period ratio andQ values indicate that this star is not pulsating in pure radial modes.     

Isothermal neutron star cores

By considering the relativistic expression for isothermal NS cores,T·e ^/2 = constant, we have shown that some of the standard equations of state, when applied to NS cores, correspond to constancy of some adiabatic exponents. It has been shown that the equation of state,P=KE, corresponds to ₁ = to ₂ = ₃ 1 +K and the equation of state, dP/dE=K, corresponds to ₃ 1 +K. The conditions under which different equations of state represent isothermal cores have been obtained: For isothermal NS, the local temperatureT, can be expressed in terms of pressureP, energy densityE, and rest mass density . For example: (a)P =KE :T = constant × (E/); (b)P=KE :T = constant × (P/); (c) dP/dE =K :T ^K ; (d) = ₂ :T = constant × (P/E); and (e) = ₃ :T = constant × (P/)^1/2. Equation of state corresponding to = ₂ is obtained as:P=E/ln(K/E) and the equation corresponding to = ₃ comes out as:E=P ln(K/P). Core-envelope models can be developed for these two cases. When core equation corresponding to = ₂ or = ₃ is used in the core, we can ensure the continuity of dP/dE at the core-envelope boundary, along with the continuity ofP, E, , and . The parameters of isothermal NS cores corresponding to the cases = ₂ and = ₃, have been obtained. The maximum mass of these NS cores comes out to be 2.7 .     

Sensitivity of solar eigenfrequencies to the age of the sun

The increasing central concentration of the Sun with age modifies the acoustic eigenfrequencies. In particular, the frequency separation d _l =3(2l+3)^–1v _n,l –v _n–1,l+2 for modes with l + 1/2 n decreases as nuclear reactions augment the molecular-weight gradient in the energy-generating core. If, for example, the Sun were older than is generally believed, one might therefore expect d _l to be smaller than current theoretical predictions. On the other hand, to ensure that the luminosity is consistent with observations, the presumed initial hydrogen abundance would need to be enhanced, thereby reducing the resultant molecular-weight gradient. Thus there is some degree of cancellation of the two major factors that determine d _l .Various authors have either reported directly on the sensitivity of d _l , or have provided the information from which it can be calculated. We have added our own computations. There is broad agreement amongst the results: d _l diminishes with the presumed age of the Sun at the rate of about 1 Hz per Gy for l = 0; the magnitude of the rate appears to decline with increasing l.     

Physically realizable relativistic stellar structures

Relativistic stellar structures can be obtained both analytically and by computation, but all these models do not stand the tests of physical reality. It is shown that for a physically reasonable solution d/dr -r and d(e ^v /dr r near the centre, d(P/)/dr<-0 and (dP/d)>-(P/). If we change the variabler tox=Cr ², whereC is a constant, the field equations are reduced to a form which is easier to solve. A new set of exact solutions is obtained by consideringe ^v (1-x) ⁿ . Also, a method has been given to obtain generalized solution.It is shown that the solution discussed by Durgapal and Rawat (1980) is the only exact solution which in its most generalized form for a given density distribution stands all the tests of physical reality and for which both (P/) and (dP/d) decrase with increasing value ofr.Neutron star model is proposed by assuming >-2×10¹⁴g cm^–3. Two specific cases are considered, viz.,P<-1/3 and dP/d<-1, respectively. The structures are found to be bound and stable under radial perturbations. The models have been studied for slow rotation and the mass of the Crab pulsar has been estimated for different mechanisms.     

Chromospheric downflow velocities as a diagnostic in solar flares

We explore the dynamics of chromospheric condensations driven by evaporation during the impulsive phase of solar flares. Specifically, we find that the maximum chromospheric downflow speed obeys the approximate relation _d = 0.4 (F/ _ch )^1/3, where F is that part of the flare energy flux driving chromospheric evaporation, and _ch is the mass density in the preflare chromosphere just below the preflare transition region. This implies that chromospheric downflows as measured by H asymmetries may be a powerful probe of flare energetics.     

U - B - V photometry of the spectroscopic-visual triple HD 165590

HD 165590 is a visual binary (dG0 + dG5,P = 20 _. ^y 25,e = 0.96) whoseA component is an SB1 double (dG5 + dM:P = 0 _. ^d 88,e0.0). TheA pair (Aa +Ab) undergoes partial eclipses. PhotoelectricUBV photometry from Lines and one of the Automatic Photoelectric Telescopes, andV photometry from Scarfe are examined here. The data are from the 1977, 1984, 1985, and 1986 observing seasons. The non-eclipse light variations are analyzed with a FORTRAN program which does a sinusoidal curve fitvia least squares repeatedly to obtain the best period. Periods found from each observing season and passband are consistent with Boydet al. (1985): the greatest variations seem to be produced by a rotating (0 _. ^d 88), spotted, G0 star (theAa component). To the residuals from the first analysis a further curve fit is made to determine characteristics of the wave due to the ellipticity effect. An early limit on the spectral type of the unseenAb component, based on the primary eclpse depth and the upper limit on the depth of the unseen secondary eclipse, is K2. Eclipse depths and widths seen here suggest that theA pair's inclination = 74 _. ⁰ 9 ± 1⁰, close to theA +B inclination of 82 _. ⁰ 7 ± 2⁰ (Battenet al., 1979). TheA pair's orbital period does not appear to vary, appearing instead to be well-described by a new linear ephemeris (Hel. J.D. = 2443665.4568 + 0 _. ^d 8795045E) which does, however, take into account a variable light-travel-times as theA component orbits theA +B center of mass with a 20 _. ^y 25 period. The maximum light-travel-time O-C thus produced is + /–8 _. ^m 4 = + /–0 _. ^d 0059.     

Preliminary study of light variations of the eclipsing binary AB Cassiopeiae

Preliminary study of the eclipsing binary AB Cas is presented here by using the photometric observational data. The primary component is one of the Sct variables with period of 0^d.054, and whether the oscillation is of a radial mode or of a non-radial one is discussed. Two colour indices (B-V andU-B) data and the light curve analysis suggest that this binary system is a typical Algol type binary system, in which the primary component is near the ZAMS with about 2.3M and the secondary one is a subgiant star with about 0.5M .     

Magnetic and thermal pressures in the solar wind

Explorer 34 solar wind data for the period June to December, 1967 show that(a) The magnetic pressure, P _BB ²/8, and thermal pressure,P _kn _p kTp+n kT+n _e kTe,are variable and positively correlated on a scale of 2 days, but (b) changes in P _b and P _k are anticorrelated on a scale 1 hr (0.01 AU). Thus, dynamical hydromagnetic processes (dv/dto) must occur on the mesoscale, but the solar wind tends to be in equilibrium(P _B+P _Kconstant) on a smaller scale, the microscale. The 3-hr averages show that the most probable value of P _{k/P B} is =1.0±0.1, which implies that the most probable state of the solar wind at 1 AU is not one of equipartition between the thermal energy and magnetic energy. The average total pressure for a given bulk speed(P(V)=P ^k+P _k+P _B) is essentially independent of V, implying that P is not determined by the heating or acceleration mechanisms of the solar wind; the average pressure is P=(2.9±1.5)×10^-10dyne/cm².     

Emission cores in H and K lines

Profiles of the H and K lines of Mgii and the K line of Ca ii are computed using a two-level atom for five model atmospheres distinguished from each other mainly by the location of the temperature minimum. In the five models the temperature minimum and the chromospheric temperature are adjusted to give best agreement between computed and observed profiles. The parameters and r ₀ are prescribed as functions of from a density model of the atmosphere. By comparing computed and observed profiles of the K₃, K₂ and inner K₁ components of the lines we determine both the approximate depth variation of _D and the best of the temperature models. We find that the Doppler width increases rapidly with height in the chromosphere beginning from a value of 1.6 km/sec at ₀ 10^–2. This latter value corresponds closely to the thermal velocity of Mg atoms in the upper photosphere. The preferred temperature model is one for which the temperature minimum occurs near ₀( 2800) 10^–4–10^–5 with a value T _min 4200 ° and which has a temperatu near 7000 ° at ₀ = 10^–6 where K₂ is formed. The intensity in K₃ is determined largely by d _D/d in the K₂ and K₃ regions.     

Turbulent motions in molecular clouds

We have studied the behavior of the inner motions of OH, H₂CO, and CO molecular clouds. This study shows the existence of two main components of these clouds: the narrow one, associated to dense small clouds and a wide one representing the large diffuse clouds seen in neutral hydrogen, the large clouds are the vortex and intermediate state between turbulent and hydrodynamic motions in the Galaxy.For the dense clouds with sizesd<10 pc we have found a relationship d ^0.38 consistent with the Kolmogorov law of turbulence; the densities and sizes of these clouds behave asnd ^–1. This last relation for these molecular clouds is compared with theHII one. Also, we discuss the effects of the inner magnetic field in these clouds.     

Thermal and non-thermal soft X-ray bursts

X-ray bursts observed for energies lower than 25 keV are usually interpreted as being produced by a thermal plasma with several million degrees of temperature.A small number of events recorded at Arcetri by real time telemetry of SOLRAD 9 satellite agrees with a thermal interpretation and gives temperatures ranging between 10 × 10⁶ and 30 × 10⁶K and emission measures, N _e ² dV, between 10⁴⁷ and 10⁴⁸ cm^–3.An impulsive event recorded on January 7, 1969 shows an anomalous behaviour. In this case the emission has been attributed to bremsstrahlung radiation from electrons with a power law energy distribution dN = KE ^- dE. The values of the spectral index and of the emission measure are given.A tentative interpretation of the event is suggested and the way to produce non-relativistic electrons with a power law energy distribution is investigated.