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.     

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.     

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.     

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.     

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.     

Bond dissociation energies and bond orders for some astrophysical molecules

The bond dissociation energies for astrophysically important diatomic molecules have been estimated based on the derived relation D_AB = D_AB + 32.058 Δ_χ where D_AB = (D_AA D_BB)1/2, Δ_χ represents Pauling electronegativity difference χ_A – χ_B) Based on the formula suggested by Reddyet al., bond orders are estimated. The ambiguity arising from Parr & Borkman relation is discussed. The present study supports the view of Politzer thatq/(0.5r _e)² is the correct definition of bond order. The estimated bond energies are in reasonably good agreement with the values in the literature. The bond energies estimated with the relation we suggested, for the molecules in the present study, give an error of 8.0 per cent. The corresponding error associated with Pauling’s equation is 26.8 per cent.     

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.     

Potential energy curves and dissociation energies of NbO,SiC, CP,PH+, SiF+, and NH+

The potential energy curves for the electronic ground states of astrophysically important NbO, SiC, CP, PH⁺, SiF⁺, and NH⁺ molecules are constructed by the RKRV method. The dissociation energies are determined by curve-fitting techniques using the five-parameter Hulburt-Hirschfelder function. The estimated dissociation energies are 7.86±0.16, 3.66±0.09, 5.12±0.12, 3.08±0.09, 6.46±0.14, and 3.02±0.09 eV for NbO, SiC, CP, PH⁺, SiF⁺, and NH⁺, respectively. The estimatedD ₀ values are in reasonably good agreement with literature values. If we utilizeD ₀ values of PH⁺, SiF⁺, and NH⁺, ionization potentials for PH, SiF, and NH are derived. The ionization potentials are 10.12, 7.13, and 13.66 eV, respectively, for PH, SiF, and NH. Dissociation energies for the above molecules are also estimated by use of the Birge-Sponer extrapolation and Hildenbrand and Murad methods.     

Millimeter and Submillimeter Emissions from Galactic and Extragalactic Photodissociation Regions

The galactic and Extragalactic photodissociation regions are primarily heated by photoelectrons ejected from the surface of interstellar dust grains by Far-ultraviolet (FUV) photons. But there is no direct mechanism to measure the photoelectric heating efficiency. To understand the role of dust grains in processing the Interstellar Radiation Field (ISRF) and heating the gas, we compare the intensities I _CII, I _CO and I _FIR for (² P _3/2→² P _1/2) & (J = 1→ 0) line emission of CII & CO at 158 μm & 2.6 mm and integrated far-infrared from number of photodissociation regions, HII regions, planetary nebulae, reflection nebulae and high latitude translucent clouds (HLCs). It is found that I _CII is linearly correlated with I _FIR. In the cold medium where cloud is exposed to weak radiations temperature is low and most of the cooling is due to [CII] emissions. As a result the ratio of I _CII/I _FIR provide indirect method to evaluate the photoelectric heating efficiency. For the neutral cold medium it is evaluated to be ∼0.028. The FUV radiation field G ₀ are estimated through the model calculation of I _CII and I _CO for different galactic and photodissociation regions. The intensity of FIR radiation I _FIR are well represented as 1.23×10⁻⁴ G ₀(ergs cm⁻² s⁻¹ sr⁻¹) almost same as estimated for HLCs by Ingalls et al (2002). Hydrogen density for each source has also been estimated.     

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     

Dark energy model in anisotropic Bianchi type-III space-time with variable EoS parameter

A new dark energy model in anisotropic Bianchi type-III space-time with variable equation of state (EoS) parameter has been investigated in the present paper. To get the deterministic model, we consider that the expansion θ in the model is proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i}. The EoS parameter ω is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003) and SNe Ia data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004). It has been suggested that the dark energy that explains the observed accelerating expansion of the universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Some physical aspects of dark energy model are also discussed.     

On origin of ultra high energy cosmic rays

Propagation of UHE protons through CMB radiation leaves the imprint on energy spectrum in the form of Greisen–Zatsepin–Kuzmin (GZK) cutoff, bump (pile-up protons) and dip. The dip is a feature in energy range 1×10¹⁸–4×10¹⁹ eV, caused by electron-positron pair production on CMB photons. Calculated for power-law generation spectrum with index γ _g =2.7, the shape of the dip is confirmed with high accuracy by data of Akeno—AGASA, HiRes, Yakutsk and Fly’s Eye detectors. The predicted shape of the dip is robust: it is valid for the rectilinear and diffusive propagation, for different discretenesses in the source distribution, for local source overdensity and deficit etc. This property of the dip allows us to use it for energy calibration of the detectors. The energy shift λ for each detector is determined by minimum χ ² in comparison of observed and calculated dip. After this energy calibration the absolute fluxes, measured by AGASA, HiRes and Yakutsk detectors remarkably coincide in energy region 1×10¹⁸–1×10²⁰ eV. Below the characteristic energy E _c ≈1×10¹⁸ eV the spectrum of the dip flattens for both diffusive and rectilinear propagation, and more steep galactic spectrum becomes dominant at E<E _c . The energy of transition E _tr<E _c approximately coincides with the position of the second knee E _2kn , observed in the cosmic ray spectrum. The dip-induced transition from galactic to extragalactic cosmic rays at the second knee is compared with traditional model of transition at ankle, the feature observed at energy ∼1×10¹⁹ eV.      

A New Pumping Mechanism for A Series of Class II Methanol Masers in the J 0 - J -1 E Transitions

A new pumping mechanism – methanol masers without population inversion is presented in this paper. It can be used to explain the formation of a series of J ₀ → J _-1 E methanol masers, while the 2₁ → 3₀ A ⁺ methanol masers are regarded as a driving coherent micrwave field. In the new mechanism, the intensities of J ₀ - J _-1 E methanol masers are increased with the decreasing transition frequencies (or with rotational number J, approximately). These results agree with Slysh et al. (1995) and Slysh et al. (1999) J ≤ 5 observations for G3345.01+1.79 and W48, in which both J ₀ → J _-1 E and 2₁ → 3₀ A ⁺ methanol masers are detected coincidentally. Other astronomical conditions, such as magnetic field, 2₁ → 3₀ A ⁺ coherent radition, incoherent pumping rate by thermal radition and so on are also discussed. The new mechanism can operate as a complement to other ordinary maser pumping mechanisms for some class II methonal maser sources. 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.     

Observations of Ions in Comets: A Contribution Towards Understanding the Comet-Solar Wind Interaction

Since many years cometary ions have been observed by the authors and their coworkers in order to study the comet-solar wind interaction. Comets with water production rates ranging from 10²⁸(46P/Wirtanen) to 6 10³⁰molecules s⁻¹(C/1995 O1 Hale-Bopp) have been observed. In this paper we briefly introduce the physics of the comet-solar wind interaction. New observations of comet C/1996 Q1 (Tabur) are presented, where for the first time H₂O⁺and CO⁺ions have been recorded exactly simultaneously with a two-channel system. They are compared with previous observations of comets C/1989 X1 (Austin), 46P (Wirtanen) and 109P (Swift-Tuttle). We use a new method of Wegmann et al. (1998), based on the MHD scaling law, to determine the water production of comet Tabur from its H₂O⁺column density map and obtain a value of 3.3 10²⁸water molecules s⁻¹. Nonstationary phenomena like tail rays and so-called tail disconnections are very briefly reviewed. A movie of plasma envelopes observed in the light of OH⁺in comet 1995 O1 (Hale-Bopp) is presented on the attached CD-ROM. 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.     

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.     

Electronic Sputtering Analysis of Astrophysical Ices

Experimental results on fast ion collision with icy surfaces having astrophysical interest are presented. ²⁵²Cf fission fragments projectiles were used to induce ejection of ionized material from H₂O, CO₂, CO, NH₃, N₂, O₂ and Ar ices; the secondary ions were identified by time-of-flight mass spectrometry. It is observed that all the bombarded frozen gas targets emit cluster ions which have the structure X_nR^±, where X is the neutral ice molecule and R^± is either an atomic or a molecular ion. The shape of the positive or negative ion mass spectra is characterized by a decreasing yield as the emitted ion mass increases and is generally described by the sum of two exponential functions. The positive ion water ice spectrum is dominated by the series (H₂O)_nH₃O⁺ and the negative ion spectrum by the series (H₂O)_nOH⁻ and (H₂O)_nO⁻. The positive ion CO₂ ice spectrum is characterized by R⁺ = C⁺, O⁺, CO⁺, O₂⁺ or CO₂⁺ and the negative one by R⁻ = CO₃⁻. The dominant series for ammonia ice correspond to R⁺ = NH₄⁺ and to R⁻ = NH₂⁻. The oxygen series are better described by (O₃)_nO_m⁺ secondary ions where m = 1, 2 or 3. Two positive ion series exist for N₂ ice: (N₂)_nN₂⁺ and (N₂)_nN⁺. For argon positive secondary ions, only the (Ar)_nAr⁺ series was observed. Most of the detected molecular ions were formed by one-step reactions. Ice temperature was varied from ∼20 K to complete sublimation.     

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.