Franck-condon factors and -centroids for certain band systems of astrophysical molecular ions CN+ and N+2

The Franck-Condon factors and r-centroids, which are very closelyrelated to relative vibrational transition probabilities, have beenevaluated by the more reliable numerical integration procedure forthe bands of c ¹ - a ¹ and f ¹ - a ¹ systems of CN ⁺ and C ^{2 +} _u- X ^{2 +} _g and D ² _g- A ² _u systems of N ⁺ ₂ molecular ions of astrophysical interest,using a suitable potential.     

RKRV Potential Energy Curves, Dissociation Energies, γ-Centroids And Franck-Condon Factors Of YO, CrO, BN, ScO, SiO And AlO Molecules

The potential energy curves for the electronic ground states of astrophysically important YO, CrO, BN, ScO, SiO and AlO molecules are constructed techniques using the five-parameter Hulburt-Hirschfelder function. The estimated dissociation energies are 7.235±0.15, 4.337 ± 0.09, 3.917 ± 0.09, 6.899 ± 0.14, 8.181 ± 0.17 and 5.202 ± 0.11 eV for YO, CrO, BN, ScO, SiO and AlO, respectively. The estimated D₀ values are in reasonably good agreement with literature values. The r-Centroids and Franck-Condon factors for the bands of B^{2 +} – X^{2 +} of YO, B⁵ –X⁵ > of CrO, A³ – X³ of BN, B^{2 +} –X^{2 +} of ScO, E^{1 +} – X^{1 +} of SiO and D^{2 +} – X^{2 +} and B^{2 +} –X^{2 +} of AlO molecules have been determined. The Franck-Condon factors are evaluated by the approximate analytical method of Jarmain and Fraser. The absence of the bands in these systems is explained.     

The leblanc bands of the CN radical in the spectra of comets

Spontaneous emission rates and absorption oscillator strengths for prominent V4 sequence bands of theB ²⁺-A ²_i transition of the CN molecule are estimated. The wavelengths of some lines observed in the coma spectrum of the comet Bradfield 1980t as well as in several comets coincide with these V4 sequence LeBlanc bands of the CN radical. Formation and destruction of the CN radical in the coma of a comet are discussed in the framework of gas phase reactions.Work supported by CNPq, Brasília, under contract numbers: Processos 401236-83 and 4076/77-FA01.     

YO molecule in the sun

Vibrational transition probabilities, namely Franck—Condon factors and -centroids have been evaluated by an approximate analytical method for the (A–X), (A–X), and (A–X) system of YO molecule. Morse potential energy curves forX ²⁺,A ²₂,A²₂, andA²₂, states of YO have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to decrease linearly with the corresponding wavelengths. We show results for two new transitions of (A–X) and (A–X) and five new bands of (A–X) of YO in the umbral spectrum of the Sun.     

Isotopes of magnesium in the solar atmosphere

We have analysed MgH A ² -X ²(0.0), (1.1), (2.2), (0.1) and (1.2) absorption bands in a sunspot spectrum. By two different methods, which are almost independent of the estimated value of the correction for stray light, we have determined the solar isotopic ratios of magnesium. These ratios are equal to the terrestrial ones - ²⁴Mg²⁵Mg²⁶Mg = 801010.     

Does the principle of special relativity really hold?

We start from a reference frame for which the pseudo-Euclidean geometry holds, i.e., all laws in have the form of special relativity. The geometry of a reference frame , moving with constant velocity with regard to , is received by using the well-known Galilei-transformation for the covariant space-time vector. In the geometry is different from the pseudo-Euclidean one, i.e., the principle of special relativity does not hold. The velocity of light in is direction dependent but the null result of the Michelson-Morley experiment is received. Several useful transformation formulae are given. In particular, we obtain the Marinov-transformation as transformation from the frame to , and conversely. Maxwell's equations and the equations of motion in the reference frame are given. The theory is applied to some examples, e.g., the Doppler effect, the Fizeau experiment, the field of a charged particle, etc. The method can be generalized to an accelerated reference frame .     

Spectrum variability of 25 Sextantis

Vibrational transition probabilities: namely, Franck-Condon factors andr-centroids, have been evaluated using an approximate analytical method for theB-A system of MgO. Morse potential energy curves forB ¹⁺ andA ¹ states of MgO have been constructed by use of the latest spectroscopic data. The value ofr-centroids for the band have been found to decrease linearly with the corresponding wavelength. We show results for six new bands in the umbral spectrum of the Sun.     

24MgH+ in the solar photospheric spectrum

The²⁴MgH⁺ (A ¹⁺ –X ¹⁺) molecular lines have been identified in the photospheric spectrum. The rotational excitation temperature determined from the analysis of molecular line intensities of²⁴MgH⁺ is found to be of the order of 4850 K which corresponds to the photospheric temperature of the Sun. The CNDO/2 dipole moments of²⁴MgH⁺ for internuclear distance range: (1.3–2.1) Å in theX ¹⁺ state can be approximated byM(R)=4.92+1.33R. Estimations for the spontaneous emission Einstein coefficients (A _{v v} ) and the absorption oscillator strengths (f _{v v} ) for the (1, 0), (2, 0), and (2, 1) transitions in theX ¹⁺ state of the²⁴MgH⁺ ion are also made.Work partially supported by the CNPq, Brasilia under contract number 30.4076/77.     

Vibrational stability of stars in thermal imbalance: A solution in terms of asymptotic expansions

Isentropic oscillations of a star in thermal imbalance are defined as those for which, at every istant, the entropy of each mass element of the configuration in the perturbed motion is equal to that of the same mass element in the unperturbed motion.The solution of the equations describing such isentropic oscillations and written in terms of the infinitesimal displacement r(r ₀,t) is presented in terms of asymptotic expansions up to the first order in the parameter /t _s where is the adiabatic pulsation period for the fundamental mode andt _s , a slow time scale of the order of the Kelvin-Helmholtz time.The solution obtained allows one to define, unambiguously, an isentropic part to the coefficient of vibrational stability of arbitrary stellar models in thermal imbalance, as well as to derive a general formula relating the results of a stability analysis in terms of r and r/r.Application of this general solution to the simple case of homologous motion is also given.     

Estimates for the effective electrical conductivity of the core in the interior of Jupiter and Saturn

In the deep interior of the giant planets Jupiter and Saturn, ordinary hydrogen and helium are transformed into a conducting metallic liquid at extremely high pressure. It is likely that the giant planets' observed magnetic field is constantly generated in the metallic fluid core by magnetohydrodynamic processes, converting mechanic energy in the form of convection into magnetic energy. The maximum strength of their magnetic fields is likely to be limited by magnetic field instabilities which convert the magnetic energy back into convection. The parameter which governs the occurrence of magnetic instabilities is the Elsasser number, = B ²/2, where B is the field strength, is the electrical conductivity, is the rotation rate and is the density. Since magnetic instability will be very active when exceeds a critical value _c 10 (the precise value depending on the magnetic field distribution), this imposes an upper bound on the effective electrical conductivity of the metallic fluid which comprises the bulk of Jupiter's interior and much of Saturn's.Stability calculations including both toroidal (model) and poloidal (observed) components of the magnetic field in a rapidly rotating spherical shell, have been performed. The most stable configuration of the field is when the poloidal component of field is strong and the toroidal field is weak; in this case we obtain an upper bound for electrical conductivity of 3 × 10⁶ S/m; while the most unstable configuration of the field is when the toroidal and poloidal fields are comparable, giving rise to _m 3 × 10⁵ S/m. The implications of the results for general dynamo theory are also discussed.     

Radiative and collisional processes in CNA 2Π i

In the last four years we have carried out a number of studies on the radiative and collisional processes in theA ² _i state of CN. Many of these of interest to those studying planetary atmospheres, comets and solar spectra are summarized in this paper. Data for CNA ² _i fluorescence lifetimes and quenching rates, and collisional energy transfer between CNA ² _i andX ²₊ are reported. Detailed comparisons and a discussion of the results may be found in several already published papers.     

On the presence of SH in the sunspot spectrum

The expected equivalent widths of individual rotational lines of the most intense Q ₂ branch of the 0-0 band of the A ²-X²_i; system of S³²H and S³⁴H have been calculated in the umbral spectrum for five disk positions using Zwaan's (1974) sunspot model. Percentage abundance of S³⁴ in the terrestrial case has been considered valid in our calculations.Strong lines of S³²H and S³⁴H of the A-X band system should be detectable in the sunspot spectrum. The molecule SH may play a possible role as a major opacity source in the ultraviolet spectrum of sunspots along with the molecule OH in the upper layers (up to _0.5m = 1.0) wherefrom most of the continuum arises. Study of this molecule in the umbral spectrum may also provide the solar isotopic abundance ratio N(S³²)/N(S³⁴).     

The 3410 Å band of the PH molecule in the solar photospheric spectrum

Some weak unidentified solar photospheric lines in the wavelength range: (3400–3465) Å may be due to PH lines of the (0, 0) band of the PH(A ³ _i - X ^{3 -})system. These faint PH molecular lines have resulted an excitation temperature of the order of 4500 K. Using experimental lifetime data for PH in the A ³ _i state, an absorption oscillator strength f ₀₀ = 0.0075 is derived for the 3410 Å band of the PH (A ³ _i - X ^{3 -})system. Accurate line positions, oscillator strength and transition probability for the 4.4 fundamental rotation-vibration band of the PH molecule are obtained. A comparison of positions of some lines of the 4.4 band with those obtained on new tracings of high resolution solar spectra shows many coincidences with weak solar lines.     

Changes in coronal condensations emission after solar bursts at microwaves

The amount of circular polarization of the total solar radio emission at 7 GHz present permanent changes after the occurrence of certain radio bursts associated with larger flares. For isolated S-components, associated with such flares the changes of the polarization degree _sranges between 0.004 to 0.1, and appears to be a function of the flare importance. A semi-qualitative interpretation associates _swith magnetic field reductions at the S-component, agreeing fairly well with a flare mechanism based on collisionless dissipation of magnetic energy, corresponding to energies in the range of 10³⁰ to 10³² ergs, assuming an average model for the coronal condensations.     

The diatomic molecules BH,BN, and BO in sunspots and the solar abundance of boron

Absorption band spectra of BH and BO have been searched for and not found in spectra of sunspots.Electronic oscillator strengths are available only for the A ¹ -X ^{1 +} system of the BH molecule. The absence of the (0,0) band of BH at 4332 Å reflects a solar abundance of boron logA _B<2.5.The band spectra of BN are several orders of magnitude weaker in sunspots than those of BH and BO.Kitt Peak National Observatory Contribution No. 488.Visiting Astronomer, Solar Division, Kitt Peak National Observatory - Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

New hα survey of chromospherically active binaries

We had observed the high-resolution H profiles of fourteen chromospherically active binaries which are And, 3 Cam, 4 UMi, ² Sgr, Sgr, HR 7333, 33 Psc, UMi, And, UMa, 12 Cam, And, Aur and Dra from August 1990 to August 1991. The H emission and absorption equivalent widths, and the half widths and the radial velocities of these systems were determined. These data have a good supply for the information of the catalog of chromospherically active binary stars. The H profiles of HR 7333, 12 Cam, 4 UMi, UMi and And show marked emission filling in core, but 33 Psc, Sgr, Sgr and And systems show the H as the stronger absorption lines. The observed fourteen binaries presented very different activity levels.     

A new approach to the possibilities of Σ(D)-dependence and distances of the supernova remnants

A new way of choosing of the calibrators for constructing (D)-dependence of supernova remnants (SNR) is suggested. A knowledge of the distance of an SNR is not sufficient to consider it as a calibrator. It is shown that neither more accurate determination of distance to calibrators, nor an increase in their number, nor an increase in the precision of the remnant angular size and radio flux determination can lead to a considerable improvement of simple (D)-dependence which is suggested in the given work.For remnants with small surface brightnesses there is no (D)-dependence at all. The most accurate remnant distances currently known, are given: these are liable to change only after a large amount of additional observational data accurately compiled.     

A study of weak molecular and atomic lines in the photospheric spectrum

An attempt is made to detect the lines of Mg²⁵H and Mg²⁶H in the photospheric spectrum, using calculated isotope shifts. From comparisons with the Mg²⁴H lines of the ² –² transition in the (0, 0) band the ratios Mg²⁵/Mg²⁴ = 0.12 ± 0.04 and Mg²⁶/Mg²⁴ = 0.12 ± 0.02 are derived. These are essentially the same as the terrestrial ratios. The profile of one line of Mgi confirms these values.The wavelengths of MgH and C₂ lines, when corrected for the gravitational red shift, indicate that macroturbulent (or streaming) velocities die out near log ₀ = – 1.0. From the equivalent widths of the MgH lines a rotational temperature of 5132 ± 200 K is obtained and compared to predictions from various model atmospheres. The band oscillator strength is found to be 0.024 ± 0.002, in serious disagreement with the single laboratory determination.The profiles of MgH, C₂, CN and some weak atomic lines are used to derive the variation of the radial component of microturbulence with optical depth, on the assumption of streaming velocities of 2.5–3.0 km/sec. A slow increase with increasing height in the photosphere is found, over the range –1.5 < log₀< 0.2.The center-limb variation of the equivalent widths of MgH and C₂ lines for a wholly inhomogeneous model is found to be the same as for a model which is homogeneous above log ₀ = - 1.0. With such a model as the latter, the center-limb variation of the profiles of the selected molecular and atomic lines is moderately-well reproduced by an anisotropic microturbulent velocity with a tangential component of 3 km/sec which seems to be constant with height over the range considered.     

Dust emission from comets at large heliocentric distances

Possible mechanisms for the production of the extended dust coma observed in comet Bowell (1980b) at the large heliocentric distance of 7.17 AU are considered. It is concluded that a plausible mechanism is electrostatic blow-off of fine, loose dust from an electrically charged H₂O dominated nucleus, as recently proposed by Mendiset al. (1981). Of all the other processes considered, dust entrainment by a chemical species more volatile than H₂O is considered the most plausible. However, the non-observation of prominent CO⁺ lines of theA ²-X ² band, seems to mitigate against a CO dominated nucleus, particularly if its radius is 1 km. A CO₂ dominated nucleus, however, cannot be ruled out by this non-observation unless its radius is considerably larger ( 5 km). The electrostatic blow-off process predicts that the dust grains in the coma of comet Bowell at 7.17 AU must be very small (r _g0.4 ), with a total mass 4×10⁸ g, and a spatial extension 10⁵ km, which is consistent with the observations (observed coma diameter 6×10⁴ km). Both the size and spatial distribution of the dust given by electrostatic blow-off and the gas entrainment processes are shown to be different, and this would be a way of discriminating between the two processes. However, the present observations do not have the resolution to do so.Department of Physics.Department of Electrical Engineering and Computer Sciences.     

О влиянии флукаций электронной концентрации на меру дисперсии и мету вращения

, (DM) (RM). , DM RM N _e = n _e ds. M _e = n _e H cos ds ; . Lerche (1970a, b) , DM RM N _e M _e . .