H(2) infrared line emission from the ionized region of planetary nebulae

Context. The analysis and interpretation of the H(2) line emission from planetary nebulae have been done in the literature by assuming that the molecule survives only in regions where the hydrogen is neutral, as in photodissociation, neutral clumps, or shocked regions. However, there is strong observational and theoretical evidence that at least part of the H(2) emission is produced inside the ionized region of these objects. Aims. The aim of the present work is to calculate and analyze the infrared line emission of H(2) produced inside the ionized region of planetary nebulae using a one-dimensional photoionization code. Methods. The photoionization code Aangaba was improved in order to calculate the statistical population of the H(2) energy levels, as well as the intensity of the H(2) infrared emission lines in the physical conditions typical of planetary nebulae. A grid of models was obtained and the results then analyzed and compared with the observational data. Results. We show that the contribution of the ionized region to the H(2) line emission can be important, particularly in the case of nebulae with high-temperature central stars. This result explains why H(2) emission is more frequently observed in bipolar planetary nebulae (Gatley's rule), since this kind of object typically has hotter stars. Collisional excitation plays an important role in populating the rovibrational levels of the electronic ground state of H(2) molecules. Radiative mechanisms are also important, particularly for the upper vibrational levels. Formation pumping can have minor effects on the line intensities produced by de-excitation from very high rotational levels, especially in dense and dusty environments. We included the effect of the H(2) molecule on the thermal equilibrium of the gas, concluding that, in the ionized region, H(2) only contributes to the thermal equilibrium in the case of a very high temperature of the central star or a high dust-to-gas ratio, mainly through collisional de-excitation.

New limits on the possible variation of physical constants

Recent detections of high-redshift absorption by both atomic hydrogen and molecular gas in the radio spectra of quasars have provided a powerful tool for measuring possible temporal and spatial variations of physical 'constants' in the Universe. We compare the frequency of high-redshift hydrogen 21-cm absorption with that of associated molecular absorption in two quasars to place new (1 sigma) upper limits on any variation in y = g(p) alpha(2) (where alpha is the fine-structure constant, and g(p) is the proton g-factor) of \Delta y/y\ < 5 x 10(-6) at redshifts z = 0.25 and 0.68. These quasars are separated by a comoving distance of 3000 Mpc (for H-0=75 km s(-1) Mpc(-1) and q(0) = 0). We also derive limits on the time rates of change of \(g) over dot (p)/(g) over dot (p)\ < 1 x 10(-15) yr(-1) and \(alpha) over dot/(a) over dot\ < 5 x 10(-16) yr(-1) between the present epoch and z = 0.68, These limits are more than an order of magnitude smaller than previous results derived from highredshift measurements.

Modelling the warm H(2) infrared emission of the Helix nebula cometary knots

Molecular hydrogen emission is commonly observed in planetary nebulae. Images taken in infrared H(2) emission lines show that at least part of the molecular emission is produced inside the ionized region. In the best studied case, the Helix nebula, the H(2) emission is produced inside cometary knots (CKs), comet-shaped structures believed to be clumps of dense neutral gas embedded within the ionized gas. Most of the H(2) emission of the CKs seems to be produced in a thin layer between the ionized diffuse gas and the neutral material of the knot, in a mini-photodissociation region (mini-PDR). However, PDR models published so far cannot fully explain all the characteristics of the H(2) emission of the CKs. In this work, we use the photoionization code AANGABA to study the H(2) emission of the CKs, particularly that produced in the interface H(+)/H(0) of the knot, where a significant fraction of the H(2) 1-0 S(1) emission seems to be produced. Our results show that the production of molecular hydrogen in such a region may explain several characteristics of the observed emission, particularly the high excitation temperature of the H(2) infrared lines. We find that the temperature derived from H(2) observations, even of a single knot, will depend very strongly on the observed transitions, with much higher temperatures derived from excited levels. We also proposed that the separation between the H alpha and [N II] peak emission observed in the images of CKs may be an effect of the distance of the knot from the star, since for knots farther from the central star the [N II] line is produced closer to the border of the CK than H alpha.

Silicon monosulphide radiative association

Rate coefficients for radiative association of silicon and sulphur atoms to form silicon monosulphide (SiS) molecule are estimated. The radiative association is due mainly to approach in the E(1)Sigma(+) and A(1)Pi states of SiS. For temperatures ranging from similar to 1000 to similar to 14 000 K, the rate coefficients are found to vary from 8.43 x 10(-17) to 2.69 x 10(-16) cm(3) s(-1). Our calculated rate coefficient is higher than the values used in modelling the chemistry of Type Ia supernovae.

The formation of CN and CN+ by direct radiative association

Rate coefficients for direct radiative association of carbon and nitrogen atoms to form CN, and of carbon ions and nitrogen atoms to form CN+ ions, are calculated for temperatures in the range of 300 to 14,700 K. For the CN molecule, the rate coefficients can be represented by the standard expression, k(CN)(T) = 7.87 x 10(-19)(T/300)(0.056) exp (-96.0/T) cm(3) s(-1) for temperatures between 300 and 2700 K and k(CN)(T) = 1.37 x 10(-18)(T/300)-0.128 exp (-520.1/T) cm(-3) s(-1) at T > 2700 K. For the CN+ ion, the corresponding expression is k(CN+)(T) = 1.08 x 10(-18)(T/300)(0.071) exp (-57.5/T) cm(-3) s(-1) for the temperature range studied. Calculated rate coefficients k(CN) are about 2 orders of magnitude lower than the canonical value used in the modeling of the chemistry of various astrophysical environments.

SPH simulations of clumps formation by dissipative collisions of molecular clouds - II. Magnetic case

We performed computer simulations of interstellar cloud-cloud collisions using the three-dimensional smoothed particle magnetohydrodynamics method. In order to study the role of the magnetic field on the process of collision-triggered fragmentation, we focused our attention on head-on supersonic collisions between two identical spherical molecular-clouds. Two extreme configurations of the magnetic field were adopted: parallel and perpendicular to the initial clouds motion. The initial magnetic field strength was approximately 12.0 muG. In the parallel case, much more of the collision debris were retained in the shocking region than in the non-magnetic case where gas escaped freely throughout the symmetry plane. Differently from the non-magnetic case, eddy-like vortices were formed. The regions of highest vorticity and the the regions of highest density are offset. We found clumps formation only in the parallel case, however, they were larger, hotter and less dense than in the analogous non-magnetic case. In the perpendicular case, the compressed field works as a magnetic wall, preventing a stronger compression of the colliding clouds. This last effect inhibits direct contact of the two clouds. In both cases, we found that the field lines show a chaotic aspect in large scales. Also, the field magnitude is considerably amplified in the shock layer. However, the field distribution is almost coherent in the higher density regions.

SPH simulations of clumps formation by dissipative collision of molecular clouds - I. Non magnetic case

Computer experiments of interstellar cloud collisions were performed with a new smoothed-particle-hydrodynamics (SPH) code. The SPH quantities were calculated by using spatially adaptive smoothing lengths and the SPH fluid equations of motion were solved by means of a hierarchical multiple time-scale leapfrog. Such a combination of methods allows the code to deal with a large range of hydrodynamic quantities. A careful treatment of gas cooling by H, H(2), CO and H II, as well as a heating mechanism by cosmic rays and by H(2) production on grains surface, were also included in the code. The gas model reproduces approximately the typical environment of dark molecular clouds. The experiments were performed by impinging two dynamically identical spherical clouds onto each other with a relative velocity of 10 km s(-1) but with a different impact parameter for each case. Each object has an initial density profile obeying an r(-1)-law with a cutoff radius of 10 pc and with an initial temperature of 20 K. As a main result, cloud-cloud collision triggers fragmentation but in expense of a large amount of energy dissipated, which occurred in the head-on case only. Off-center collision did not allow remnants to fragment along the considered time (similar to 6 Myr). However, it dissipated a considerable amount of orbital energy. Structures as small as 0.1 pc, with densities of similar to 10(4) cm(-3), were observed in the more energetic collision.

Formation of SO, SO+, and S-2 by radiative association

Rate coefficients for radiative association of SO, SO+, and S-2 are estimated. For temperatures ranging from 300 to 14,000 K, the direct radiative association rate coefficients are found to vary with temperature from 1.73 x 10(-19) to 7.29 x 10(-19) cm(3) s(-1) and from 1.49 x 10(-21) to 3.70 x 10(-19) cm(3) s(-1) for S-2 and SO, respectively. The rate coefficients for formation through the inverse predissociation for S-2 are found to vary from 3.59 x 10(-18) to 1.44 x 10(-20) cm(3) s(-1). For SO+, the direct rate coefficient varies rapidly with temperature from 3.62 x 10(-27) cm(3) s(-1) at 2000 K to 2.34 x 10(-20) cm(3) s(-1) at 14,000 K. The direct radiative association rate coefficients increase with the increase in temperature, but the inverse predissociation rate coefficients decrease with the increase in temperature.

A theoretical study of the A(2)Sigma(+)-X-2 Pi system of the SiP molecule

The A (2)Sigma(+) and X(2)Pi electronic states of the SiP species have been investigated theoretically at a very high level of correlation treatment (CASSCF/MRSDCI). Very accurate potential energy curves are presented for both states, as well as the associated spectroscopic constants as derived from the vib-rotational energy levels determined by means of the numerical solution of the radial Schrodinger equation. Electronic transition moment function, oscillator strengths, Einstein coefficients for spontaneous emission, and Franck-Condon factors for the A(2)Sigma(+)-X(2)Pi system have been calculated. Dipole moment functions and radiative lifetimes for both states have also been determined. Spin-orbit coupling constants are also reported. The radiative lifetimes for the A(2)Sigma(+) state, taking into account the spin-orbit diagonal correction to the X(2)Pi state, decrease from a value of 138 ms at v' = 0 to 0.48 ms at v' = 8, and, for the X(2)Pi state, from 2.32 s at v = 1 to 0.59 s at v = 5. Vibrational and rotational transitions are expected to be relatively strong.

Radiative association of C and P, and Si and P atoms

The rate coefficients for the formation of carbon monophosphide (CP) and silicon monophosphide (SiP) by radiative association are estimated for temperatures ranging from 300 to 14 100 K. In this temperature range, the radiative association rate coefficients are found to vary from 1.14 x 10(-18) to 1.62 x 10(-18) cm(3) s(-1) and from 3.73 x 10(-20) to 7.03 x 10(-20) cm(3) s(-1) for CP and SiP, respectively. In both cases, rate coefficients increase slowly with the increase in temperature.

Formation of SiC by radiative association

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Radiative association of Ti and O atoms

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A theoretical study of the A2 ∑+-X2∏ system of the SiP molecule

The A2∑+ and Z2∏ electronic states of the SiP species have been investigated theoretically at a very high level of correlation treatment (CASSCF/MRSDCI). Very accurate potential energy curves are presented for both states, as well as the associated spectroscopic constants as derived from the vib-rotational energy levels determined by means of the numerical solution of the radial Schrödinger equation. Electronic transition moment function, oscillator strengths, Einstein coefficients for spontaneous emission, and Franck-Condon factors for the A2∑+-X2∏ system have been calculated. Dipole moment functions and radiative lifetimes for both states have also been determined. Spin-orbit coupling constants are also reported. The radiative lifetimes for the A2∑+ state, taking into account the spin-orbit diagonal correction to the X2∏ state, decrease from a value of 138 ms at v′ = 0 to 0.48 ms at v′ = 8, and, for the X2∏ state, from 2.32 s at v″ = 1 to 0.59 s at v″ = 5. Vibrational and rotational transitions are expected to be relatively strong.

The formation of AlF by radiative association

The formation of the aluminium monofluoride molecule AlF by radiative association of the Al and F atoms is estimated. The radiative association of Al(P-2) and F(P-2) atoms is found to be dominated by the approach along the A(1) potential energy curve accompanied by spontaneous emission into the X-1 Sigma(+) ground state of the AlF. For temperatures ranging from 300 to 14 000 K, the rate coefficients are found to vary from 1.35 x 10(-17) to 9.31 x 10(-16) cm(3) s(-1), respectively. These values indicate that only a small amount of AlF molecules can be formed by radiative association in the inner envelope of carbon-rich stars and other hostile environments.

Radiative association of Ti and O atoms

Rate coefficients for the radiative association of titanium and oxygen atoms to form the titanium monoxide (TiO) molecule are estimated. The radiative association of Ti(F-3) and O(P-3) atoms is dominated by an approach along the C-3 Delta potential energy curve, accompanied by spontaneous emission into the X-3 Delta ground state of TiO. For temperatures ranging from 300-14 000 K, the total rate coefficients are found to vary from 4.76 x 10(-17) to 9.96 x 10(-17) cm(3) s(-1), respectively.