On the excitation of free oscillations on the Moon

Since the Moon’s outer shells are very inhomogeneous, a global, spherically symmetric model of its interior structure is difficult to construct by using only seismic body-wave data. We study the diagnostic capabilities of the free-oscillation method. The sources of the largest moonquakes are located in the outer 200-km thick layer. Their seismic moments reach 10²² dyn. cm. Current seismometers are capable of detecting ground accelerations of ～10^?8 cm s^?2. Taking M ₀≈10²² dyn. cm, we show that torsional modes _n T _l with l≥7 and n=0 (l is the degree of oscillation, and n is the overtone number) can be detected. These modes contain information about the outer layers to a depth of ≈500 km and can allow a global model to be constructed for the outer, most inhomogeneous layers of the satellite. The largest moonquakes excite spheroidal modes _n S _l much worse, and it is unlikely that they can be detected with current instruments. We provide detailed information on the excitation of free oscillations for various moonquake focal mechanisms and focal depths.     

Internal rotation of the Sun as inferred from GONG observations

Helioseismology is a direct and most informative method of studying the structure and dynamics of the Sun. Determining the internal differential rotation of the Sun requires that the frequencies of its eigentones be estimated with a high accuracy, which is possible only on the basis of continuous long-term observations. The longest quasi-continuous series of data have been obtained by the Global Oscillation Network Group (GONG). The parameters of each individual mode of solar acoustic oscillations with low spherical degrees l=0, 1, 2, 3, 4, 5, 6 are determined by using 1260-day-long series of GONG observations. The mean frequency splitting by rotation for the modes of each radial order n is calculated by using all possible combinations between the eigenfrequencies in multiplets. As a result, it has become possible to statistically estimate the splitting and its measurement errors for the modes of each radial order. The mean splitting for each given degree l=1–6 is presented under the assumption of its independence of oscillation frequency, which holds for the achieved accuracy. The frequencies and splittings for the modes with low spherical degrees l, together with the MDI group results for higher degrees l, are used to invert the radial profile of solar angular velocity. Using the SOLA method to solve the inverse problem of restoring the rotation profile has yielded solutions sensitive to the deepest stellar interiors. Our results indicate that the solar core rotates faster than the surface, and there may be a local minimum in angular velocity at its boundary.     

Emden-chandrasekhar axisymmetric,solid-body rotating polytropes

According to the general results of a previous work (Caimmi, 1980; hereafter referred to as Paper I), solutions to EC equation, which expresses a necessary and sufficient condition for equilibrium of Emden-Chandresekhar axisymmetric, solid-body rotating polytropes (EC polytropes), are taken into consideration, of the type $$\vartheta (\xi ,\mu ) = A_0 \vartheta _0 (\upsilon ,\xi ) + \sum\limits_l^\infty {_l {\rm A}_{2l} (\upsilon )\vartheta _{2l} (\xi )P_{2l} (\mu ),} $$ with ? _2l later defined as the EC associated function of degree 2l. Thus the EC equation, involving (?, μ), is found to be equivalent to the infinite set of EC associated equations, involving ? _2l (μ). We approximate g (?, μ) by neglecting all terms of degree higher than 2 which appear in the above expression, and then search power series solutions to EC associated equations of degree 0 and 2, corresponding to any choice ofn (polytropic index, related to density distribution) andv (related to rotational distorsion). To this aim, we extend the methods used by Seidov and Kuzakhmedov (1977), and Mohan and Al-Bayaty (1980), to construct power series of the type outlined above, related to solid-body rotating configurations and originating both inside and outside the radial boundary (defined as the first zero of ?₀(μ)=0). The corresponding expressions of ?₀ and ?₂ may serve to derive an approximate expression of, and future work becomes possible concerning the determination of some physical parameters (such as volume, mass, potential energy, angular momentum) related to any choice ofn andv. Computations have been performed forn=k/4 (0≤k≤20, i.e. 0≤n≤5) andv=0,v≈v _R/2,v≈v _R, withv _R lowest value ofv leading to balance between gravitation and centrifugal force at the equator of the system. An upper limit to the error, ε^*(μ), done in computing ? _2l , ?? _2l , and ?? _2l at any point ? for a given choice ofn andv, is estimated, ranging from large values (ε^*=1E-2) forn close enough to 0 and ? close enough or outside the radial boundary, to low values (ε^*=1E-10) forn far enough from 0 and no constraint on ?. Comparison between results of this paper and the accurate results by Linnell (1977, 1981) obtained using a different approach and available forn=2,v=0, andn=3,v=0, lead to a fair agreement (up to (1E?5?1E?6). It is apparent that the method followed here continues to hold when the first EC associated functions up to degree 2l are taken into account, leading — at least in way of principle — to a more refined approximation to the EC function; this would only make the related calculations much more complicated.     

On the excitation of oscillations of the Sun (numerical models)

Numerical solutions of the general time-dependent gas-dynamical equations in linear adiabatic approximation are given for initial conditions imitating: (a) a central perturbation, (b) a boundary perturbation (in the convective envelope), and (c) a ‘shrinking’ of the Sun as a whole. For a variety of models of the Sun it is found that at the surface the radial component v _r of velocity is much greater than the tangential component v _t , and that the period T of stationary oscillations does not exceed 131^m. The appearance at the surface of a g mode with period 160^m is found to be improbable. With the initial conditions adopted, a propagating wave is produced which is reflected successively from the centre to the periphery and back, producing 5-min oscillations at the surface of the Sun. Expansion of this wave into separate modes leads to a power spectrum qualitatively similar to that observed.     

Non-radial oscillations and convective instability of a polytrope with a toroidal magnetic field

We examine the non-radial modes of oscillation, belonging to spherical harmonics of ordersl=1 andl=3, of a gaseous polytrope with a toroidal magnetic field. We find that a toroidal magnetic field increases the growth rate of convective instability for deformations belonging to the spherical harmonicl=1 whereas it decreases the growth rate of convective instability for deformations belonging to the harmonicsl=2 andl=3. The frequencies of the ‘acoustic’ mode and the ‘Kelvin’ mode are decreased by the presence of the toroidal magnetic field.     

Brightness of the O2 atmospheric bands in the daytime thermosphere

The Fabry-Perot interferometer on Dynamics Explorer 2 was used as a low sensitivity photometer to study the O₂ Atmospheric A band during the daytime. A study of the brightness of the emission showed that the assumed source of O₂(b¹Σ_g⁺) in the thermosphere, O(¹D), can account for the observed intensity up to about 250 km but with a significantly different scale height. This combined with an enhanced brightness above this altitude suggests an additional source for this emission.     

Periods and stability of solar g-modes

We consider the rotation independent (m = 0) frequencies of Hill and Gu (1988) and Henning and Scherrer (1988). Comparison with Cox, Guzik, and Kidman (CGK) frequencies shows that CGK are systematically 5.7 ± 0.7% larger. This effect may be due to the larger central density in this model (162 g cm^–3) compared to the real Sun. A known systematic error of about one percent in the pressure calculated by the Iben (1965) procedure can account for the higher CGK central helium and density. A check of this increase of g-mode frequency with central density is made by calculating g-mode frequencies for a WIMP model with a central density of 210 g cm^–3. This 30% density increase gives a 17% frequency increase, and implies a law with frequency increasing with the 17/30 power of the central density. Thus the 5.7% decrease of frequencies from the model to the real Sun indicates a central density decrease of about 9.7% to about 147 g cm^–3. Comparison with the recent van der Raay g-mode frequencies shows that the CGK model frequencies are about 14% larger, as one would expect for these observed frequencies with a large P ₀ of 41.2 min.Destabilizing mechanisms of the normal -effect at the top of the convection zone and convection blocking at the bottom of the convection zone for low order and low-l g-modes produces pulsation driving that does not seem to be damped by radiation and convection effects at the surface. Since the surface motions are very small, photospheric damping does not stabilize these modes at it does for the 5-min p-modes. For higher-order and degree modes, deep damping by radiation flow across nodes overwhelms the destabilization and any small effect.     

Do we need a surface wave approach to the magnetospheric resonances?

In this paper we study a possible existence of surface wave (SW) global modes of the outer magnetosphere. The SW modes are supported by two plasma discontinuities: the plasmapause and the boundary between the open and closed field lines of the magnetosphere. Conditions under which the SW global modes can propagate azimuthally and along the magnetic field lines are examined. The ionosphere at the ends of the field lines is considered as reflecting boundaries of these SW modes. As a result SW standing wave structures along the magnetic field fluxes can be formed. Two branches of SW modes are derived. The low frequency branch, f_s,1 falls in the Pc5 range, while the high frequency branch, f_s,2—in the Pc4 range, where f_s,1(2) is the fundamental SW global mode frequency. Their frequencies possess quantized properties in the following way: f≡(1,2,3, …)f_s,1(2). The high frequency SW branch, f_s,2 exists only for relatively great azimuthal wavenumbers k_⊥. It is pointed out that most of the SW global mode characteristics are similar to those of the FLR. These results are applied to 1.8 mHz global mode observations on 11 January 1997. Spectral, phase and polarization properties of this Pc5 pulsation event under northward IMF conditions are examined as we see them from ground-based (L’Aquila and TNB observatories) and satellite (POLAR and INTERBALL) observations.     

The excitation of O2(b1Σg+) in the nightglow

It is proposed that the available measurements of the O₂(b¹Σ_g⁺ ?X³Σ_g^?) atmospheric bands both in the nightglow and in the laboratory indicate that the excitation mechanism is a two-step process rather than the direct three body recombination of atomic oxygen. It is shown that such a two-step mechanism can explain observations of the atmospheric bands both in altitude and intensity.     

Observations of low-degree solar oscillations with few detector elements

The detection of low-degree solar oscillation modes with a specific low-resolution detector configuration is investigated. The detector is part of an instrument (the Luminosity Oscillations Imager) in the VIRGO package, to be flown on SOHO. Various problems such as p- and g-mode sensitivity, B and roll angle effects, modes isolation, cross-talk and guiding effects are treated for a given detector configuration. The computed sensitivity will enable the instrument to detect any type of modes for l < 6.B and roll angle effects can be compensated by using adequate filters for mode isolation. Guiding effects are small for p-modes. Also some other complex high-degree mode effects are treated.     

Ground-based observations of O2 (b1Σ+g−X3Σ−g) atmospheric bands in high latitude auroras

Analysis of observed spectrograms is based on comparison with synthetic spectra. The O₂(b¹Σ⁺_g?X³Σ^?_g Atm. (1,1) band in high latitude auroras observed from the ground is found to be the strongest in the Δv = 0 sequence. It is enhanced with altitude relative to the N₂ 1P(2, 0)and N⁺₂ M(2,0) bands, but the O₂ Atm. (2, 2) band has an unexpected low intensity. The range of rotational temperatures of the O₂ Atm. bands varies from approx. 200 to above 500 K which indicates that the altitude of the centroid of the emission region varies from about 100 km to the F-region. The highest temperature is found in the midday aurora associated with the magnetospheric cusp. Conspicuous relative variations between the intensities of N₂ and O₂ spectra are documented, but a satisfactory explanation of the variety is not given. Deviations of the observed O₂ Atm. band intensities from the vibrational intensity distribution predicted by Franck-Condor factors indicate that the excitation of the O₂ Atm. bands in aurora is not mainly due to particle impact on O₂, and the contribution due to energy transfer from hot O(¹D) atoms has to be found in future research.     

Study on Properties of the k − ω Model for Stellar Convection

For applying the k − ω model proposed by Li to the general stellar environment, it is necessary to study the physical meanings of the parameters in this model, in order to set a limit for the range of their values. It is indicated by the study that the variation of the parameter c^l_μ impacts all the Péclet number, kinetic energy, characteristic timescale and characteristic length of turbulent ?ows. Besides, as the model parameter c^l_μ increases, the damping rate of turbulent kinetic energy in the bottom convective overshoot region can be accelerated evidently. Both the model parameter c^l_μ and the equivalent mixing length parameter α are proportional to the effciency of convective heat transfer in the convection zone, and their logarithms have a linear relation. There is also a linear relation between the logarithms of the model parameter c^l_μ and the damping index θ of turbulent kinetic energy in the convective overshoot region. For the Sun, a group of appropriate model parameters are obtained to be: c^l_μ = 0.004, and α = 1.7.     

Association of atomic oxygen and airglow excitation mechanisms

An outline is presented of a method of calculating relative rates of association of oxygen atoms by energy transfer into the different bound states of molecular oxygen. The method takes account of the detailed form of the potential energy curves for the different states. Results are presented for seven bound states of O₂ at temperatures between 100 and 600 K and are compared with laboratory and airglow data. The ⁵Π_g state, not known experimentally, accounts for over 70% of the total association below 200 K. At higher temperatures it is redissociated, and the variation in its effective association rate is primarily responsible for the variation of the total rate of oxygen association with temperature. The ⁵Π_g state is probably involved in the production at night of the a¹Δ_g and b¹Σ_g⁺ states of O₂, and in the production of $\text{O(}{}^1\text{S)}$ in the airglow. It may also be produced by electron impact on O₂, and contribute to $\text{O(}{}^1\text{S)}$ production in aurorae.     

Stochastic excitation of gravity modes in massive main-sequence stars

We investigate the possibility that gravity modes can be stochastically excited by turbulent convection in massive main-sequence (MS) stars. We build stellar models of MS stars with masses M=10?M _⊙,15?M _⊙, and 20?M _⊙. For each model, we then compute the power supplied to the modes by turbulent eddies in the convective core (CC) and the outer convective zones (OCZ). We found that, for asymptotic gravity modes, the major part of the driving occurs within the outer iron convective zone, while the excitation of low n order modes mainly occurs within the CC. We compute the mode lifetimes and deduce the expected mode amplitudes. We finally discuss the possibility of detecting such stochastically-excited gravity modes with the CoRoT space-based mission.     

Stability of zonal flows on Jupiter

Jupiter's troposphere is bounded below by a deep layer of fluid which is probably extremely close to adiabatic. This paper explores the effect of this new boundary condition on the stability of atmospheric jets. The three parameters of the problem are the Rossby number Ro = U/fl, the ratio of the deformation radius l to the horizontal scale of jets y₀, and the nondimensional value of $\text{β,}\text{β}\text{= βl}{}^2\text{/U}$. The tropospheric deformation radius is unknown; all other quantities are constrained by observation. If the deformation radius is small, then nongeostrophic instabilities are of interest, and the regime is given by $\text{Ro = O(1), l/y}{}_0\text{? 1,}\text{β}\text{? 1}$. Using an Eady model, it is found for this case that the new boundary condition suppresses baroclinic instabilities but that if Ro > 1 (corresponding to a Richardson number less than unity) then inertial instabilities exist as usual. If the deformation radius is somewhat larger, the regime of interest if $\text{Ro ? 1, l/y}{}_0\text{? 1,}\text{β}\text{? 1}$. Horizontal shear can be neglected but β cannot. In this case, it is found that Eady-type baroclinic modes $\text{(}\text{β}\text{= 0)}$ again do not grow, but that the Charney modes $\text{(}\text{β}\text{≠ 0)}$ can exist. Finally, if l/y₀ = O(1) it is found that mixed barotropic-baroclinic instability can exist. Its stability boundaries and energetics approach those of pure barotropic instability when l/y₀ exceeds unity. Observations are discussed: the l/y₀ ? 1 regime appears most relevant. The mixed barotropic-baroclinic modes in this regime display upgradient momentum fluxes.     

The free oscillations of Jupiter

The spectrum of free oscillations of Jupiter is calculated for a set of models, each of them fitting all available observational data. Diagnostic capabilities of the spectrum are studied. They could be used, as soon as relevant observations are performed, for both the identification of the observed modes and the improvement of the models themselves. The calculations were made for five-layer models. They differ in the core mass (2–10 M_⊕) and in the molecular-metallic phase transition pressure of hydrogen (1.5–3 Mbar). The spectrum of Jupiter consists of gravitational modes related to density jumps in the planetary interiors and of acoustic modes. The periods of the acoustic modes are calculated for degree up to l=30 and overtone number up to n=20. The investigated models have a characteristic frequency of ≈152–155 μHz. Two outer gravitational modes related to density jumps in the molecular envelope and at the interface with the metallic envelope have nonzero displacements at the planetary surface. These modes have good diagnostic properties. The values of the kinetic energy averaged over the period of oscillation are calculated for a 1-m amplitude of the displacement at the planetary surface. The influence of all effects of rotation on the spectrum is discussed.     

The bulk motion of flat galaxies on scales of 100 Mpc in the quadrupole and octupole approximations

The peculiarities of non-Hubble bulk motions of galaxies are studied by analyzing a sample of 1271 thin edge-on spirals with distances determined using a multiparametric Tully-Fisher relation that includes the amplitude of the galaxy rotation, the blue and red diameters, surface brightness, and morphological type. In the purely dipole approximation, the bulk motion of galaxies relative to the cosmic microwave background frame can be described by the velocity of 336±96 km s^?1 in the direction l=321°, b=?1° within radius R _max =10000 km s^?1. An analysis of more complex velocity field models shows that the anisotropy of the Hubble expansion described by the quadrupole term is equal to ～5% on scale lengths R _max=6000–10000 km s^?1. The amplitude within the Local Supercluster (R _max=3000 km s^?1) is as high as ～20%. The inclusion of the octupole component reduces the dipole amplitude to 134±111 km s^?1 on scale lengths of ～8000 km s^?1. The most remarkable feature of the galaxy velocity field within R _max=8000 km s^?1 is the zone of minimum centered on l=80°, b=0° (the constellation of Cygnus) whose amplitude reaches 18% of the mean Hubble velocity.     

Possible H2staggered+ ultraviolet spectrum of Jupiter

An ultraviolet spectral probe for a hydrogen-rich planetary atmosphere, such as that of Jupiter, is suggested, utilizing discrete lines in the H₂^staggered+ 2pπ_u?1sσ_g electronic transition. For the Jovian atmosphere, the dominant mechanism for exciting H₂⁺ to its 2pπ_u state appears to be photoexcitation, principally through absorption of the solar Lyman-α line. We estimate that the Jovian column emission rate of the H₂⁺ 2pπ_u(ν′ = 2, J′ = 1) →1sσ_g(ν″ = 18,J″ = 0) fluorescent line at 1236.6 Å is if1 photon cmsu-2 secsu-1; i.e., that if1 photon secsu-1 of this radiation would strike a 15-cm diameter mirror in a Jupiter fly-by at an impact parameter of 3 × 10⁵km. The critical role of corrections to the Born-Oppenheimer approximation in the use of an H₂⁺ probe is discussed.     

Analysis of MDI High-Degree Mode Frequencies and their Rotational Splittings

We present a detailed analysis of solar acoustic mode frequencies and their rotational splittings for modes with degree up to 900. They were obtained by applying spherical harmonic decomposition to full-disk solar images observed by the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory spacecraft. Global helioseismology analysis of high-degree modes is complicated by the fact that the individual modes cannot be isolated, which has limited so far the use of high-degree data for structure inversion of the near-surface layers (r>0.97R _⊙). In this work, we took great care to recover the actual mode characteristics using a physically motivated model which included a complete leakage matrix. We included in our analysis the following instrumental characteristics: the correct instantaneous image scale, the radial and non-radial image distortions, the effective position angle of the solar rotation axis, and a correction to the Carrington elements. We also present variations of the mode frequencies caused by the solar activity cycle. We have analyzed seven observational periods from 1999 to 2005 and correlated their frequency shift with four different solar indices. The frequency shift scaled by the relative mode inertia is a function of frequency alone and follows a simple power law, where the exponent obtained for the p modes is twice the value obtained for the f modes. The different solar indices present the same result.     

A measurement of the O2(b1Σg+−X3Σg−) atmospheric band and the OI(1S) green line in the nightglow

Simultaneous measurements of the nightglow profiles of the O₂(b¹Σ_g⁺?X³Σ_g^?) A-band, the atomic oxygen green line and the OH (8?3) Meinel band are presented. The altitude profiles are used to determine both the excitation mechanisms for the oxygen emissions and the atomic oxygen altitude distribution. It is shown that the measurements are consistent with a green line excitation through the Barth mechanism and that the molecular oxygen emission is excited through oxygen recombination and the reaction between OH¹ and atomic oxygen. The derived atomic oxygen concentrations,6.2 × 10¹¹cm^?3at 98km, are consistent with the Jacchia (1971) model.