Some effects of elasticity on lunar rotation

A general Hamiltonian for a rotating Moon in the field of the Earth is expanded in terms of parameters orienting the spin angular momentum relative to the pricipal axes of the Moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love numberk ₂. The principal periodic terms in the longitude of a point on the Moon due to variations of the tide caused by the Earth are shown to have amplitudes between 3.9 × 10^–3 and 1.6 × 10^–2 with a period of an anomalistic month, 3.0 × 10^–4 and 1.2 × 10^–3 with a period of one-half an anomalistic month and 2.4 × 10^–4 and 9.6 × 10^–4 with a period of one-half of a nodical month. The extremes in the amplitudes correspond to rigidities of 8 × 10¹¹ cgs and 2 × 10¹¹ cgs, respectively, the former rigidity being comparable to that of the Earth. Only the largest amplitude given above is comparable to that detectable by the projected precision of the laser ranging to the lunar retrorereflectors, and this amplitude corresponds to an improbably low rigidity for the Moon. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given, where it is shown that elasticity can alter the period of the free wobble of 75.3 yr by only 3 × 10^–4 to 10^–3 of this period. Also, the effect of elasticity on the period of free libration is completely negligible by many orders of magnitude. If the Moon's rigidity is close to that of the Earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the Moon can be determined from variations in the rotation.Currently on leave from the Dept. of Physics, University of California, Santa, Barbara, California.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

On the lifetime of bright X-ray sources

The lifetime of massive X-ray binaries is (2–5)×10⁵ yr, this time close to the nuclear one. The lifetime of nonmassive X-ray binaries close to thermal one, (0.5–1)×10⁷ yr. Massive systems may be conserved at supernova explosion, the probability of the conservation of nonmassive system is (1–3)×10^–3.     

Period study of XY Ceti

A first period study of the eclipsing binary XY Ceti is presented. A new period (P=2^d.7807135), based on all available times of minima, is given. Period changes in different portions of the O–C diagram, with a new period, have been estimated. The total change in period (P/P) ranges from 1.1×10^–5 d to 1.2×10^–4 d, thus, P ranges from 3.1×10^–5 d to 3.3×10^–4 d. The O–C diagram suggests that the trend of the period has changed around the year 1959. Two portions of increasing and decreasing trends also reveal that the period changes (P/P) of the order of 10^–5 d are present, which are appreciably large.     

An expanding circumstellar cloud of Zeta Aurigae

Strong absorption satellite lines of CaI 6572 were found on spectrograms taken on three successive days just after the fourth contact of the 1971–72 eclipse of Zeta Aurigae. The radial velocities of the satellite lines are –88 km s^–1, –74 km s^–1, and –180 km^–1, respectively, relative to the K-type primary star (K4 Ib). These absorptions should be due to a circumstellar cloud in which the column density of neutral calcium atoms is 1×10¹⁷ cm^–2 and the turbulent velocities come to 20–50 km s^–1. It is suggested that the cloud may be formed by the rocket-effect of the Lyman quanta of the B-type component (B6 V). We estimate the density in the cloud to be 2×10¹¹ atoms cm^–3 fors=10R _K and 2×10¹⁰ atoms cm^–3 fors=10² R _K, wheres denotes the distance of the cloud from the K star andR _K the K star's radius. The mass loss rate of the K-type component is also estimated to be about 10^–7 M yr^–1, assuming that the expansion of the K star occurs isotropically.     

Steady mass-loss from supermassive stars

Structures of Newtonian super-massive stars are calculated with the opacity for Comptor effectK ₀/(1 + T), whereK ₀=0.21(1 +X and =2.2×10^–9K^–1. The track of the Main-Sequence is turned right in the upper part of the HR diagram. Mass loss will occur in a Main-Sequence stage for a star with mass larger than a critical mass. The cause of mass loss and the expansion of the radius is continuum radiation pressure. The critical mass for mass loss is 1.02×10⁶ M for a Population I star, and 1.23×10⁵ M for Population III star. Mass loss rates expected in these stars are 3.3×10^–3 and 4.0×10^–3 M yr^–1, respectively.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Models of the universe compatible with present observations

It is shown that cosmic radiation almost follows a Planck distribution, because just as matter is formed, its density of energy is negligible in comparison with that of radiation, and that the present age of the Universe does not depend on the particular manner in which the matter is formed.Thus, if the results of the latest observations (which imply a deceleration parameterq=1.6) are combined with the assumption that the present age of the Universe is at least 12×10⁹ yr, they lead to a hyperbolic oscillating universe with a negative cosmological constant (<–1.53×10^–56 cm^–2) and a present mass-density _m of less than 1.2×10^–30 g cm^–3. If the cosmological constant is taken to be zero, a solution is only possible if we are prepared to admit a rate of evolution of galaxies with a deceleration parameterq<0.52. Three types of oscillating universe are then possible, but the heperbolic type is the most probable. If Hubble's constant is greater than 63.4 km s^–1 Mpc^–1, the solutions are only hyperbolic universes with <+0.45×10^–56 cm^–2 and _m <4.8×10^-30g cm^-3.

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Sommaire On montre que le rayonnement cosmique général suit pratiquement une loi de Planck parce que la densité d'énergie de la matière au moment de sa formation est négligeable à côté de celle du rayonnement et que l'âge actuel de l'Univers ne dépend pas du mode de formation de la matière.Dans ces conditions, si l'on combine les derniers résultats d'observations (qui impliquent un paramètre de décélérationq=1.6) avec l'hypothèse que l'âge actuel de l'Univers est au moins de 12×10⁹ années on est conduit à un Univers hyperbolique oscillant à constante cosmologique négative (<–1.53×10^–56 cm^–2) et où l'actuelle densité de matière _m est moindre que 1.2×10^–30 g cm^–3. Si la constante cosmologique est supposée nulle, une solution ne peut être obtenue que si l'on admet un certain taux d'évolution des Galaxies et un paramètre de décélérationq<0.52. Alors, les trois types d'Univers oscillants sont possibles, mains les Univers hyperboliques paraissent plus probables. Enfin, si la constante de Hubble est plus grande que 63.4 km s^–1 Mpc^–1 les solutions ne peuvent être que des Univers hyperboliques avec <+0.45×10^–56 cm^–2 et _m <4.8×10^-30g cm^-3.

     

On the figure of the planet Mercury

The figure of Mercury is estimated in terms of an isostatic form of equilibrium which tends to be controlled by the situation near perihelion passage at the 32 resonance spin rate. The ratios of the principal moments of inertia for Mercury are: (1)(C–A)/C7×10^–5; (2)(C–B)/C5×10^–5 and (3)(B–A)/C2×10^–5. The thermal effect on Mercury's figure during solidification forces Mercury's rotation to be trapped in the 32 resonance lock as its spin rate is being slowed by tidal effects. It is shown that the process of trapping of Mercury has been naturally affected by the instantaneous solidification of Mercury into a shape with two thermal bulges, and that the two permanent thermal bulges stabilize the planet's rotation.     

Extreme ultraviolet spectra of solar active regions and their analysis

Extreme ultraviolet spectra of several active regions are presented and analyzed. Spectral intensities of 3 active regions observed with the NRL Skylab XUV spectroheliograph (170–630 Å) are derived. From this data density sensitive line ratios of Mg viii, Si x, S xii, Fe ix, Fe x, Fe xi, Fe xii, Fe xiii, Fe xiv, and Fe xv are examined and typically yield, to within a factor of 2, electron pressures of 1 dyne cm^–2 (n _e T = 6 × 10¹⁵ cm^–3 K). The differential emission measure of the brightest 35 × 35 portion of an active region is obtained between 1.4 × 10⁴ K and 5 × 10⁶ K from HCO OSO-VI XUV (280–1370 Å) spectra published by Dupree et al. (1973). Stigmatic EUV spectra (1170–1710 Å) obtained by the NRL High Resolution Telescope and Spectrograph (HRTS) are also presented. Doppler velocities as a function of position along the slit are derived in an active region plage and sunspot. The velocities are based on an absolute wavelength scale derived from neutral chromospheric lines and are accurate to ±2 km s^–1. Downflows at 10⁵ K are found throughout the plage with typical velocities of 10 km s^–1. In the sunspot, downflows are typically 5 to 20 km s^–1 over the umbra and zero over the penumbra. In addition localized 90 and 150 km s^–1 downflows are found in the umbra in the same 1 × 1 resolution elements which contain the lower velocity downflows. Spectral intensities and velocities in a typical plage 1 resolution element are derived. The velocities are greatest ( 10 km s^–1) at 10⁵ K with lower velocities at higher and lower temperatures. The differential emission measure between 1.3 × 10⁴ K and 2 × 10⁶ K is derived and is found to be comparable to that derived from the OSO-VI data. An electron pressure of 1.4 dynes cm^–2 (n _e T = 1.0 × 10¹⁶ cm^–3 K) is determined from pressure sensitive line ratios of Si iii, O iv, and N iv. From the data presented it is shown that convection plays a major role in determining the structure and dynamics of the active region transition zone and corona.     

RS CVn-binary RW com: A possible three-body system

A first detailed period study of the eclipsing RS CVn-binary system RW Com is presented. A new period (P=0^d.2373455) based on 223 minima is given. The O–C diagrams of RW Com have been presented for the first time. Types of ten minima have been corrected judging the period trend. Period changes in different portions of the O–C diagram (Figure 2) have been estimated. The total change in period (P/P) ranges from 5.5×10^–7 to 6.4×10^–6. Thus, P ranges from 1.3×10^–7 d to 1.5×10^–6 d. Numerous minima are available in the time interval 1967 to 1986. This part of the O–C diagram (Figure 2) shows a sinusoidal variation, thus, it is suspected that RW Com could be a three-body system. The period of variation due to third body appears to be nearly 16 years.     

Relation between VLF phase deviations and solar X-ray fluxes during solar flares

Sudden phase anomalies (SPA's) observed in the phase of GBR 16 kHz VLF signals during the years 1977 to 1983 have been analysed in the light of their associated solar X-ray fluxes in the 0.5–4 Å and 1–8 Å bands. An attempt has been made to investigate the solar zenith angle () dependence of the integrated solar X-ray flux for producing SPA's. It is deduced from the observations for < 81° that the phase deviation increases linearly as a whole with increasing solar X-ray fluxes in these two bands. The threshold X-ray flux needed to produce a detectable SPA effect has been estimated to be 1.6 × 10^–4 ergcm^–2 s^–1 and 1.8 × 10^–3 ergcm^–2 s^–1 in the 0.5–4 Å and 1–8 Å bands, respectively. For both bands the average cross section for all atmospheric constituents at a height of 70 km is almost equal to the absorption cross section for the 3 Å X-ray emission.     

Vacuum energy in cosmic dynamics

The analysis of the Th/U ratio in meteorites and the evolutionary ages of globular clusters favour values of the cosmic age of (19±5)×10⁹ yr. This evidence together with a Hubble parameterH ₀>70 km s^–1 Mpc^–1=(14×10⁹ yr)^–1 cannot be reconciled in a Friedmann model with =0. It requires a cosmological constant in the order of 10^–56 cm^–2, equivalent to a vacuum density _v =10^–29 g cm^–3 The Friedmann-Lemaître models (>0) with a hot big-bang have been calculated. They are based on a present value of the baryonic matter density of ₀=0.5×10^–30 g cm^–3 as derived from the primordial⁴He and²H abundances.For a Hubble parameter ofH ₀=75 km s^–1 Mpc^–1, our analysis favours a set of models which can be represented by a model with Euclidean metric (density parameter ₀=1.0, deceleration parameterq ₀=–0.93, aget ₀=19.7×10⁹ yr) and by a closed model with perpetual expansion (₀=1.072,q ₀=–1.0, aget ₀=21.4×10⁹ yr). A present density parameter close to one can indeed be expected if the conjecture of an exponential inflation of the very early universe is correct.The possible behaviour of the vacuum density is demonstrated with the help of Streeruwitz' formula in the context of the closed model with an inflationary phase at very early times.     

Cosmic neutrinos of ultra-high energies and detection possibility

The fluxes and spectra of galactic and extragalactic neutrinos at energy 10¹¹–10¹⁹ eV are calculated. In particular, the neutrino flux from the normal galaxies is calculated taking into account the spectral index distribution. The only assumption that seriously affects the calculated neutrino flux atE _v 10¹⁷ eV is the power-like generation spectrum of protons in the entire considered energy region.The normal galaxies with the accepted parameters generate the metagalactic equivalent electron component (electrons+their radiation) with energy density _e8.5×10^–7 eV cm^–3, while the density of the observed diffuse X-ray radiation alone is 100 times higher. This requires the existence of other neutrino sources and we found the minimized neutrino flux under two limitations: (1) the power-law generation spectrum of protons and (2) production of the observed energy density of the diffuse X-an -radiation. These requirements are met in the evolutionary model of origin of the metagalactic cosmic rays with modern energy density _M83.6×10^–7 eV cm^–3.The possibility of experiments with cosmic neutrinos of energyE _v 3×10¹⁷ eV is discussed. The upper bound on neutrino-nucleon cross-section <2.2×10^–29 cm² is obtained in evolutionary model from the observed zenith angular distribution of extensive air showers.In Appendix 2 the diffuse X-and -ray flux arising together with neutrino flux is calculated. It agrees with observed flux in the entire energy range from 1 keV up to 100 MeV.     

Upper limit on the steady emission of the 2.223 MeV neutron capture γ-ray line from the Sun

Data accumulated by the Solar Maximum Mission Gamma Ray Spectrometer (GRS) have been searched for evidence of the 2.223 MeV neutron capture line from the Sun, outside the times of -ray-emitting solar flares. Background-corrected spectra accumulated over 3-day intervals between 1980 and 1989 show no evidence of the line. Upper limits are reported separately for periods of high and low solar activity.A conservative 3 upper limit of 5.7 × 10^–5 (cm² s)^–1 is placed on the steady flux in the 2.223 MeV line during inactive periods, which is nearly two orders of magnitude lower than previously published results. After correction for limb darkening of the line emission from off-center positions, this upper limit becomes 7.1 × 10^–5 (cm²s)^–1. Our 3 upper limit on the steady flux in the line during periods of high solar activity is 6.9 × 10^–5 (cm² s)^–1, or 8.6 × 10^–5 (cm² s)^–1 after correction for limb darkening. Our results imply that the quiescent solar corona cannot be heated by ions accelerated above 1 MeV in microflares (or a continuous acceleration process), so long as the ion energy spectrum is similar to that measured in large flares. We also use our results to derive the rate of tritium production at the solar surface; our upper limit of 9 nuclei (cm² s)^–1 is about a factor of 9 below the upper limit from searches for ³H in the solar wind. We place upper limits of the order 10³³ on the number of energetic (> 30 MeV) protons which can be stored in active regions prior to being released in solar flares, which imply that the strongest observed flares cannot be produced by such a mechanism.     

Intergalactic suprathermal grains

The physical conditions under which suprathermal grains may loose energy and the processes involving the grains (a3×10^–6 cm) destruction are investigated. It is found that the dust grain once attaining the velocityU (10⁵ cm s^–1) may attain suprathermal energy (v _g3×10⁸ cm s^–1) and subsequently may also attain relativistic energy are almost indestructible in the accelerating phase.     

The Hypothesis of Additional Acceleration in the Motion of Comet Harrington–Abell from Jupiter

By processing 494 observations of Comet Harrington–Abell, we obtained a unified system of elements that includes its turn around the Sun during which it closely approached Jupiter to a minimum distance of 0.037 AU in 1974. A study of the cometary orbit before and after the approach showed that, probably, at the approach of the comet to Jupiter, apart from the well-known gravitational perturbations, its motion was affected by an additional force. An improvement of the cometary orbit by assuming that an additional acceleration inversely proportional to the square of the distance to Jupiter exists in its motion yielded the following values: (4.57 ± 0.42) × 10^–10 and (–7.20 ± 0.42) × 10^–10 AU day^–2 for the radial and transversal acceleration components, respectively. As a plausible explanation of the changes in the cometary orbit, we additionally considered a model based on the hypothesis of partial disintegration of the cometary nucleus. The parameter that characterizes the instant displacement of the center of inertia along the jovicentric radius vector was estimated to be –1.83 ± 0.75 km. Based on a unified numerical theory of cometary motion, we determined the nongravitational parameters using Marsden's model for two periods: A ₁ = (11.68 ± 1.74) × 10^–10 AU day^–2, A ₂ = (0.53 ± 0.0357) × 10^–10 AU day^–2 for 1975–1999 and A ₁ = (5.92 ± 5.86) × 10^–10 AU day^–2, A ₂ = (0.08 ± 0.028) × 10^–10 AU day^–2 for 1955–1969, under the assumption that the nongravitational acceleration changed at the approach of the comet to Jupiter.     

The properties of molecular clouds with high redshifts (z=2–3)

This paper deals with molecular clouds discovered in the absorption spectra (z=2–3) of distant quasars. It is argued that these clouds belong to the gaseous subsystems of young galaxies. We estimate the gas concentration to ben<10⁴ cm^–3 in the cloud observed in the direction of the quasar PHL957. It is shown that this cloud is exposed to ultraviolet radiation. The UV-energy flux does not exceed the value typical for our Galaxy by an order of magnitude (F2×10^–6 ergs cm^–2 s^–1 Å^–1 at =2000 Å). The mechanisms maintaining the thermal balance in this cloud are discussed.     

A mechanism for producing plasma radiation in the gigahertz range by precipitating high-energy protons

Gamma-ray observations are discussed to determine the density of protons of about 1 MeV precipitating to the photosphere. It is shown that Coulomb collisions will produce a positive slope in the proton distribution for energies less than 0.1 MeV for traversed column depths greater than 10¹⁸ cm ^–2. This could lead to plasma wave emission and radiation near the plasma frequency for densities 3.1 × 10¹⁰ cm^–3 and temperatures 4.0 × 10⁴ K where collisional and collisionless damping of the plasma waves is sufficiently weak. It is expected that these conditions will only be satisfied sporadically which leads to stationary radio emission limited in frequency and time. Recent radio observations of impulsive phase non-drifting patches in the 1–3 GHz range with duration 2–4 s are presented which could be produced by this mechanism.     

Soft x-ray emitting regions in the solar corona

The soft X-ray emission of the solar corona is investigated by comparison of the signals of several broad band photometers carried on the Solrad 9 satellite, and sensitive to the region 0.5–20 Å. Temperature from 1.5 × 10⁶ to 25 × 10⁶ K have been measured with emission measure N _e ² dV ranging between 10⁵⁰ cm^–3 to 10⁴⁷ cm^–3.By means of the observational data and assuming magnetic confinement and hydrostatic equilibrium, the model of an active region is investigated. For temperatures larger than 10⁷K the emission is due to flare activity and two sets of emission measure are observed which appear to be related to the evolution of flares.     

The masers of E-type methanol in orion KL and SGR B2

Using a simplified model the statistical equilibrium and radiative transfer equations of E-type-CH₃OH are solved for Orion KL and SgrB2. According to our calculation results and the observation data taken by Matsakiset al. (1980) and Morimotoet al. (1985a, b), the physical conditions of both sources are estimated. In theJ ₂-J ₁ E methanol maser region of Orion KL, the density, kinetic temperature, dust temperature, and the fractional abundance are 0.8–2×10⁶ cm^–3, 150, 30–90 K, 0.8–8×10^–6. In the 4_–1-3₀ E and 5_–1-4₀ E methanol maser region of Sgr B2 the correspondance physical conditions above are 10⁴ cm³, 45, 23 K, and 7×10^–7, respectively.     

X-ray observation of the Jovian impacts of comet Shoemaker - Levy 9

An ASCA observation of the Jovian impact of the comet Shoemaker-Levy 9 is reported. Four impacts of H, L, Q1 and R were observed and four impacts of B, C, G, and Q2 were observed within 60 minutes after their impacts. No significant flaring of X-ray emission was observed. Upper limit X-ray fluxes of 90 % confidence level, averaged 5 minutes just after the impacts, were 2.4 × 10^–13 erg sec^–1 cm^–2, 3.5 × 10^–13 erg sec^–1 cm^–2, 1.6 × 10^–13 erg sec^–1 cm^–2 and 2.9 × 10^–13 erg sec^–1 cm^–2 for the impacts of H, L, Q1 and R, respectively, in the 0.5(0.7 for H and Q1)–10 keV energy range. However, a hint of X-ray enhancement around Jupiter from July 17 to July 19 was detected with about 2 6 × 10^–14 erg sec^–1 cm^–2 in the 0.5–10 keV energy range.