Presence of LaO, ScO and VO Molecular Lines in Sunspot Umbral Spectra

High-resolution Fourier Transform Spectrometer sunspot umbral spectra of the National Solar Observatory/National Optical Astronomy Observatory at Kitt Peak were used to detect rotational lines from 19 electronic transition bands of the molecules LaO, ScO and VO, in the wavenumber range of 11 775 to 20 600 cm⁻¹. The presence of lines from the following transitions is confirmed: A ² Π _r1/2 – X ² Σ ⁺(0, 0; 0, 1), A ² Π _r3/2 – X ² Σ ⁺(1, 0), B ² Σ ⁺ – X ² Σ ⁺(0, 0; 0, 1; 1, 0) and C ² Π _r1/2 – A′²Δ _r3/2(0, 0; 1, 1) of LaO; A ² Π _r3/2 – X ² Σ ⁺(0, 0), A ² Π _r1/2 – X ² Σ ⁺(0, 0) and B ² Σ ⁺ – X ² Σ ⁺(0, 0) of ScO; and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 1; 1, 0; 0, 2) and (2, 0) of VO. However, the presence of A ² Π _r3/2 – X ² Σ ⁺(0, 0) and C ² Π _r3/2 – A′²Δ _r5/2(0, 0; 1, 1) of LaO and C ⁴ Σ ⁻ – X ⁴ Σ ⁻(0, 0) of VO are found to be doubtful because the lines are very weak, and detections are difficult owing to heavy blending by strong rotational lines of other molecules. Equivalent widths are measured for well-resolved lines and, thereby, the effective rotational temperatures are estimated for the systems for which the presence is confirmed.     

Astrophysical Molecules AlD and CaH: Transition Probabilities and Dissociation Energy

The Franck-Condon (FC) factors and r-centroids for the bands systemC ¹ Σ ⁺ → X ¹ Σ ⁺ of AlD and E ² Π → X ² Σ ⁺ of CaH have been evaluated by means of a reliable numerical integration procedure by using a suitable potential. The dissociation energy, D _e, for the electronic ground states of AlD and CaH have been estimated by the curve fitting method to the RKRV experimental potential curve turning out to be 3.01 eV and 2.32 eV, respectively. This revised version was published online in July 2006 with corrections to the Cover Date.     

Astrophysically Useful Parameters for Some Vibronic Transitions of AlH and BH

For molecular identification in astrophysical sources, an astrophysicist needs some spectroscopic parameters such as dissociation energy, vibrational or rotational temperature of the source, band or line wavelengths, transition probability parameters, etc. The Franck-Condon(FC) factors are proportional to the transition probabilities. In this study, the FC factors and r-centroids for the vibronic (vibration-electronic) transitions C ¹ Σ ⁺ → X ¹ Σ ⁺ of aluminium hydride (AlH), b ³ Σ ^{( −)} → a ³ Π, C ¹ Σ ⁺ → A ¹ Π & C ^′1 Δ → Δ ¹ Π of boron hydride (BH) have been evaluated and the results are presented in tables which include band origin/head wavelengths. The physical & astrophysical significances of our evaluated FC factors & r-centroids have been discussed and the possible presence of AlH in sunspot umbral spectra is also predicted. PACS: 33 · 70 · Ca     

Spectroscopic Studies on Astrophysically Interesting TaO TaS, ZrS and SiO+ Molecules

The true experimental potential energy curves for the electronic ground states of astrophysically important TaO, TaS, ZrS and SiO⁺molecules are constructed by using the Rydberg–Klein–Rees method as modified by Vanderslice et al. The ground state dissociation energies are determined by curve fitting techniques using the five parameters Hulburt-Hirschfelder (H-H) function. The estimated dissociation energies are 8.19 ± 0.17, 6.9 ±0.14, 5.89 ± 0.12 and 5.75 ± 0.12 eVfor TaO, TaS, ZrS and SiO⁺ respectively. These values are in good agreement with the literature values. The r-centriods and Franck–Condon factors (FC Factors) for the bands of K ² φ _5/2 - X ² Δ _3/2 (K-X) system of TaO, A-X ² Δ (A-X) and B-X ² Δ (B-X)systems of TaS, B ¹ Π - X¹ Σ⁺ (B-X) system of ZrS and B ²Σ⁺ - X² Σ⁺ (B-X) and A ² Π - X² Σ⁺ (A-X)systems of SiO⁺ molecules have been calculated. The Franck–Condon factors (FC factors) are evaluated by the approximate analytical methods of Jarmain and Fraser. The absence of the bands of these systems is explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimation of potential energy curves, dissociation energies, franck-condon factors and r-centroids of comet interesting molecules

The experimental potential energy curves for the different electronic states of molecules like CN, CO and CS observed in comets are constructed by using the Rydberg-Klein-Rees method as modified by Vanderslice et al. The ground state dissociation energies are determined by curve fitting technique using the five parameter Hulburt-Hirschfelder (H-H)function. The estimated dissociation energies are 7.63 ± 0.187, 10.95 ±0.224 and 7.27 ± 0.152 eV for CN, CO and CS respectively. These values are in good agreement with the literature values. Estimated dissociation energies of CN, CO and CS are used in the relation given by Gaydon and ionization potentials are evaluated for CO and CS molecules. The estimated ionization potentials are 13.92and 12.15 eV for CO and CS molecules respectively. The r-centroids and Franck-Condon factors (FC Factors) for the band system of a ³Π_r – X¹Σ⁺ (a – X) and A¹Π – X ¹Σ⁺ (A -X) of CN, A ²Π_i – X²Σ⁺ (A – X) and B²Σ⁺-X²Σ⁺ (B – X) of CO and a ³Π_r – X¹Σ⁺ (a – X) of CS molecules have been calculated employing an approximate analytical methods of Jarmain and Fraser and Nicholls and Jarmain. The absence of the bands in these systems are explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Franck-Condon factors and <Emphasis Type="Italic">r</Emphasis>-centroids for certain band systems of astrophysical molecules SrF and ScF

The Franck-Condon factors and r-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable numerical integration procedure for the bands of B ²∑⁺ − X ²∑⁺, F ²∑⁺ − X ²∑⁺ systems of SrF and C ¹∑⁺ − X ¹∑⁺, G ¹Π − X ¹∑⁺ systems of ScF molecules of astrophysical interest, using a suitable potential.     

Estimation of the dissociation energy of CO+ from spectroscopic data

The potential energy curves for theX ² Σ⁺ andB ² Σ⁺ states of CO⁺ have been constructed by the Rydberg-Klein-Rees (RKR) method as modified by van der Sliceet al. The dissociation energy is estimated to be 7.70±0.19 eV by the method of curve fitting using the five parameter Hulburt-Hirschfelder’s function. The estimated value is in good agreement with the value (7.839 eV) given by Misraet al. Carefull observation of the results reveals that accurateD ₀ value for CO⁺ is 8.33 eV     

Identification of SrF molecular lines in the spectrum of sunspot umbra

A high resolution spectrum of a sunspot umbra is used for identification of rotational lines due to (0, 0) band of the A ²Π–X ²Σ⁺ system and (0, 0), (1, 1), and (2, 2) bands of the B ²Σ⁺–X ²Σ⁺ system of the molecule SrF. The published sunspot umbral spectrum obtained with Fourier Transform Spectrometer and solar telescope of National Solar Observatory/National Optical Astronomy Observatory at Kitt Peak was used for the study. The new identification of more than 200 SrF lines in the umbral spectrum confirms that this molecule accounts for the majority of lines in the spectral range 15050 to 15360 cm⁻¹ and 17240 to 17300 cm⁻¹. Equivalent widths have been measured for well-resolved lines of these bands and the effective rotational temperatures have been estimated for which the presence is confirmed.     

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.     

r-Centroids and Franck-Condon factors of the CP,SiC, and CO+ molecules

Ther-centroids and Franck-Condon factors for the bands of theA ² –X ²⁺ of CP,C ³ –X ³ of SiC, andB ²⁺ –X ²⁺ of CO⁺ 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.     

Astrophysically useful radiative transition parameters for?the?e1Π–X1Σ+ and 1Σ+–X1Σ+ systems of zirconium oxide

The zirconium oxide (ZrO) is well known for its astrophysical importance. The radiative transition parameters that include Franck-Condon (FC) factor, r-centroid, electronic transition moments, Einstein coefficient, band oscillator strengths, radiative life time and effective vibrational temperature have been estimated for e ¹Π–X ¹Σ⁺ and ¹Σ⁺–X ¹Σ⁺ band systems of ⁹⁰ZrO molecule for the experimentally known vibrational levels using RKR potential energy curves. A reliable numerical integration method has been used to solve the radial Schr?dinger equation for the vibrational wave functions of upper and lower electronic states based on the latest available spectroscopic data and known wavelengths. The estimated radiative transition parameters are tabulated. The effective vibrational temperatures of these band systems of ⁹⁰ZrO molecule are found to be below 4200 K. Hence, the radiative transition parameters help us to ascertain the presence of ⁹⁰ZrO molecule in the interstellar medium, S stars and sunspots.     

Comet Hale–Bopp: Velocity Field Of Ions From Fabry-Pérot Imaging

Fabry-Pérot interferograms of comet Hale-Bopp were obtained on several nights in March and April 1997. For this purpose we utilized the 2-channel focal reducer of the Max-Planck-Institute for Aeronomy at the 2-m telescope of the Pik Terskol Observatory. Solid Fabry-Pérot etalons of resolving power 30000 were used in both channels of the focal reducer. The main aim of this study is to measure the velocities and abundances of OH⁺ and H₂O⁺, both ions closely related to the same parent molecule, H₂O. In the blue channel interferograms we identified several individual OH⁺ rotational lines of the A³Π_i - X³Σ⁻ (0-0) transition and measured their Doppler shifts. The target emissions in the red channel were the H₂O⁺ lines of the A²A₁ − X²B₁ (10-0) band. We found that the line of sight velocities, obtained from the Doppler shifted wavelengths of emissions in the comet are higher in sunward direction than in the plasma tail and do not exceed 20 km s^–1. The corresponding values, deprojected in antisolar direction, are consistent with predictions by magnetohydrodynamical models of the solar-wind-comet interaction, when one accounts for the extremely high gas production rate of comet Hale-Bopp. This revised version was published online in July 2006 with corrections to the Cover Date.     

On a Property of Gravitational Systems

If one attributes to each component i of a gravitational system a dimensionless parameter ψ _i equal to the ratio of its relative mass (with respect to the mass of the system) to its relative position (with respect to a generally defined radius) and sums up the ψ _i values of all components outside the central core, one obtains a mass distribution index Σψ of the order of unity irrespective of the size or the type of the system. In the case of spiral galaxies (and probable other galactic systems) this property applies not only to the whole galaxy, but also to the matter inside any radius larger than the core radius. The mass distribution index in these systems has a maximum Σψ_* at a certain radius r _*, which strongly correlates with the surface brightness at r _* in galaxies with similar mass to light ratio. The gravitational acceleration of all galaxies at r _* divided by (Σψ_*)² is constant and approximately equal to MOND acceleration parameter. Also, at this radius all galaxies have a surface temperature of the order of the temperature of the cosmic microwave background radiation. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Transition probabilities and dissociation energy of astrophysical molecule GeH

The Franck-Condon factors andr-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable numerical integration procedure for the bands of A ² Δ - X² π_r system of astrophysical molecule GeH, using a suitable potential. The dissociation energy for the electronic ground state of astrophysical molecule GeH has been estimated precisely as D ⁰ ₀ = 2.69 ± 0.05 eV by fitting the empirical potential function to the experimental potential energy curve using correlation coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

On the effective temperature of large sunspot umbra using CrH sextets electronic state molecular lines

A high-resolution spectrum clearly shows the presence of A ⁶Σ⁺–X ⁶Σ⁺(0,0;0,1;1,0;2,0;2,1) and (2,2) bands system of CrH molecular lines in the spectral range 10,000 cm⁻¹ to 14,050 cm⁻¹. At least 3928 lines of the six bands, accounting for 57% of the lines registered in the laboratory can be identified with certainty in the sunspot spectrum. Most of the lines are found blended with TiO, CaH, MgH and other atomic species. These molecular lines are typically much more temperature sensitive than atomic lines, which make them ideal, complementary tool for studying cool stellar atmospheres as well as the internal structure of sunspots. Equivalent width for an adequate number of well identified molecular lines of these bands using the Gaussian-profile approximation method versus rotational quantum number J has been used to determine the effective rotational temperature of the CrH molecule. The range of effective rotational temperature value obtained from these bands is 1766 K to 2442 K. This range agrees well with the effective rotational temperatures derived for other molecules in sunspot umbrae.     

Well-behaved relativistic charged super-dense star models

A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g ₄₄ with that of Durgapal’s fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ _b =2×10¹⁴ g/cm³ and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22M _Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059K+4.22)M _Θ and r _b ≈−0.021464K+20 km respectively.     

Note on the Generalized Hansen and Laplace Coefficients

Recently, Breiter et al. [Celest. Mech. Dyn. Astron., 2004, 88, 153–161] reported the computation of Hansen coefficients X _k ^{γ ,m} for non-integer values of γ. In fact, the Hansen coefficients are closely related to the Laplace b _s ^(m), and generalized Laplace coefficients b _s,r ^(m) [Laskar and Robutel, 1995, Celest. Mech. Dyn. Astron., 62, 193–217] that do not require s,r to be integers. In particular, the coefficients X ₀ ^{γ ,m} have very simple expressions in terms of the usual Laplace coefficients b _{γ +2} ^(m), and all their properties derive easily from the known properties of the Laplace coefficients.     

An experimental study of the reaction kinetics of C2(XΣg) with hydrocarbons (CH4, C2H2, C2H4, C2H6 and C3H8) over the temperature range 24-300 K: Implications for the atmospheres of Titan and the Giant Planets

The reactivity of C₂(X¹Σ⁺_g) with simple saturated (CH₄, C₂H₆ and C₃H₈) and unsaturated (C₂H₂ and C₂H₄) hydrocarbons has been studied in the gas phase over the temperature range 24-300 K using the CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme or Reaction Kinetics in a Uniform Supersonic Flow) technique. All reactions have been found to be very rapid in this temperature range and the rate coefficients are typically ?10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ with the exception of methane for which the rate coefficient is one order of magnitude lower: ∼10⁻¹¹ cm³ molecule⁻¹ s⁻¹. These results have been analyzed in terms of potential destruction sources of C₂(X¹Σ⁺_g) in the atmospheres of Titan and the Giant Planets. It appears that the rate coefficient of the reaction ¹C₂ + CH₄ should be updated with our new data and that reactions with C₂H₂, C₂H₄ and C₂H₆ should also be included in the existing photochemical models.