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     

Transition probability parameters for the band systems G, H and I-B of astrophysical molecule PO

The transition probability parameters, Franck – Condon factors and r-centroids, have been evaluated by the more reliable numerical integration procedure for the bands of G, H and I-B systems of astrophysical molecule PO, using a suitable potential. 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.     

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.     

Franck-Condon factors and r-centroids for certain band systems pf astrophysical molecule BeF

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 Σ⁺ - X ² Σ⁺, C ²Σ⁺ - X ² Σ⁺ andC ² Σ⁺ - A ² Π_r systems of the astrophysical molecule BeF, using a suitable potential. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

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.     

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.     

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.     

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.     

Transition probabilities and dissociation energy of astrophysical molecule CoH

The Franck-Condon (FC) factors (transition probabilities) and r-centroids have been evaluated by the reliable numerical integration procedure for the bands of the A ³ φ₄ →X ³ φ₄ system of astrophysical molecule CoH, using a suitable potential. The dissociation energy D ⁰ ₀ = 2.5 ± 0.05 eV for the electronic ground state of CoH has been estimated by fitting Hulburt-Hirschfelder function to the experimental potential energy curve, using the correlation coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular parameters for D, E, F, and G-A band systems of the astrophysically significant molecule AlF

Franck-Condon factors and r-centroids, which are a measure of transition probabilities, have been evaluated by a numerical integration procedure for the bands of D¹Δ,E¹Π, F¹Π and G¹Σ⁺– A¹Π systems of AlF molecule.The species has been observed in circumstellar envelopes around AGB stars and spectral studies report its presence in sunspots. The molecular parameters evaluated are necessary for studying the physical and dynamical properties of these sources.     

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.     

Transition probabilities and dissociation energy of astrophysical molecule CrH

The Franck-Condon (FC) factors (transition probabilities) andr-centroids have been evaluated by the reliable numerical integration procedure for the bands of the A⁶⁺ X ⁶⁺ system of astrophysical molecule CrH, using a suitable potential. The dissociation energyD ₀ ⁰ = 2.3 eV for the electronic ground state of CrH has been estimated by fitting the Hulburt-Hirschfelder function to the experimental potential energy curve, using the correlation coefficient.     

Occurrence of AlO Molecular Lines in Sunspot Umbral Spectra

Aluminium monoxide (AlO) is widely known for its astrophysical significance. An analysis of the prominent lines of the (2,3;3,2;3,4;4,5;4,3;5,6;6,7) bands of the B ²Σ⁺?X ²Σ⁺ transition with those of sunspot umbral spectral lines suggests that the AlO molecule appears to be a non-negligible component of sunspot umbrae. Results of a recent (2008) rotational analysis were used to carry out the study. The effective rotational temperature determined for the above lines in the sunspot umbral spectrum is found to be of the order of 2900 K. The radiative-transition parameters that include Franck–Condon (FC) factors, r-centroids, electronic-transition moment, Einstein coefficient, absorption–band oscillator strength, and radiative lifetime have been estimated for the experimentally known vibrational levels using the Rydberg–Klein–Rees (RKR) potential.     

Some vibrational bands of theC-X system of V0 molecules in the umbral spectrum of the Sun

Vibrational transition probabilities namely Franck-Condon factors and r-centroids have been evaluated using an approximate analytical method for theC-X system of V0. Morse potential energy curves forX _{4 –} andC _{4 –} states of V0 have been constructed using the latest spectroscopic data. The value of r-centroids for the band have been found to increase linearly with the corresponding wavelength. We show results for new transition and ten new bands in the umbral spectrum of the Sun.     

On So In Comets

The solution of the statistical equilibrium equations for the SO molecule is used to estimate the expected intensities of microwave lines. The observed fluxes of the microwave lines of SO in Comet Hale–Bopp require approximately 1.8 10²⁸ mol/sec which give fluxes in the A³Π - X³Σ⁻bands below the observable limit, consistent with the observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Infrared Variation of BL Lacertae Object PKS 0735+178

In this paper, the long-term ( about 20 years) near-infrared data have been compiled from the published literature for BL Lac object PKS 0735+178; The light curve in the infrared (JHK) bands have been presented; The maximum variations of Δ J=2m .47, Δ H=2m .30, and Δ K = 2m.40, and color indices of J- H=0.86 ± 0.11, J- K=1.71 ± 0.16, and H-K = 0.86 ± 0.12 have been obtained from the data. It is found that the spectrum changes with the brightness of the source in the infrared bands; The variations in the optical and infrared bands are found to be correlated suggesting that the emission mechanisms in the two bands are associated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rotational excitation of aluminium monofluoride (AlF) by?He?atom at low temperature

We report on the calculation of collision induced rotational excitation cross sections and rate coefficients of AlF by He atom at low temperature. These quantities were obtained by first computing the interaction potential energy surface (PES) of the AlF(X  ¹Σ⁺)-He(¹ S) van der Waals complex at the ab initio Coupled Cluster with Single and Double and perturbative Triple excitations [CCSD(T)] level of theory. The aug-cc-pVQZ Gaussian basis, to which was added a set of bond functions, was used for that purpose. The calculations account for basis set superposition errors (BSSE). The interaction potential presents a minimum of ∼24 cm⁻¹ below the AlF-He dissociation limit. The PES was fitted on a basis of Legendre polynomial functions to allow for the calculation of cross sections in the close-coupling (CC) approach. By averaging these cross sections over a Maxwell-Boltzmann velocity distribution, rate coefficients were inferred at low temperatures (T≤300 K). From our computations, a propensity towards ΔJ=1 transitions is observed.