The absorption due to pairs of H₂ molecules is an important opacity source in the atmospheres of various types of planets and cool stars, such as late stars, low mass main sequence stars, brown dwarf stars, cool white dwarf stars, the ambers of the smaller, burnt out main sequence stars, exoplanets, etc., and therefore of special astronomical interest. Astronomers are interested in the outer planets as they still contain primordal matter. Furthermore, recent observations by the Hubble space telescope (in operation since 1990) have revealed several thousand cool white dwarf stars with temperatures of several thousand Kelvin. It is surprising that none of them has temperatures lower than roughly 4000 K. This means that the white dwarf stars have not had enough time to cool down to the temperature of the cosmic background radiation. Astrophysicists believe that this information can be used for an alternative and more accurate method of cosmochronology. However, the emission spectra of cool white dwarf stars differ significantly from the expected blackbody spectra of their cores, largely due to collision-induced absorption by collisional complexes of residual hydrogen and helium in the stellar atmospheres. In order to model the radiative processes in these atmospheres, which have temperatures of several thousand kelvin, one needs accurate knowledge of the induced dipole and potential energy surfaces of the absorbing collisional complexes, such as H₂--H₂, H₂--He, and H₂--H. These come from quantum-chemical calculations, which, for the high temperatures and high photon energies under consideration in this work, need to take into account that the H₂ bonds can be stretched or compressed far from equilibrium length. Since no laboratory measurements for these high temperatures and photon energies exist, one has to undertake \textit{ab initio} calculations which take into account the high vibrational and rotational excitation of the involved hydrogen molecules. However, before one attempts to proceed to higher temperatures and photon energies where no laboratory measurements exist it is good to check that the formalism is correct and reproduces the results at temperatures and photon energies where laboratory measurements exist, that is, at and below room temperature and for photon energies up to about 1.5 eV. In this work a formalism is developed to compute the binary collision-induced absorption of simple molecular complexes up to temperatures of thousands of kelvin and photon energies up to 2.5 eV, properly taking into account vibrational and rotational dependencies of the induced dipole and potential energy surfaces. In order to make the computational effort feasible, the isotropic potenial approximation is employed. The formalism is applied to collisional complexes of H₂--H₂, D₂--D₂, H₂--He, D₂--He, T₂--He, and H₂--H, and compared with existing laboratory measurements. / text

The absorption due to pairs of H2 molecules is an important opacity source in the atmospheres of various types of planets and cool stars, such as late stars, low-mass stars, brown dwarfs, certain white dwarfs, etc., and therefore of special astronomical interest [13]. The emission spectra of cool white dwarf stars differ signicantly from the expected blackbody spectra of the cores, due to collision-induced absorption by collisional complexes of hydrogen and helium in the stellar atmospheres. In order to model the radiative processes in these atmospheres, which have temperatures of several thousand kelvin, one needs accurate knowledge of the induced dipole and potential energy surfaces of collisional complexes such as H2-H2. These come from quantum-chemical calculations with the H2 bonds stretched or compressed far from equilibrium length. Since no measurements of the collision-induced absorption for these high temperatures exist, one has to undertake ab initio calculations which take into account the high vibrational excitations of the hydrogen molecules. However, before one attempts to proceed to higher temperatures where no laboratory measurements exist it is good to know that the formalism is correct and reproduces the results at temperatures where measurements exist. Therefore, in order to make sure that the calculations are reliable one compares the results of the calculations with existing laboratory measurements where possible before proceeding to higher temperatures. Molecular hydrogen has always played a special role in the collision-induced spectroscopies. The rotational transition frequencies of H2 are widely separated so that translational, rotational and vibrational induced spectral bands can be studied separately. Moreover, the H2 molecule has a small anisotropy of the intermolecular interactions which may often be ignored in first order approximations. In general hydrogen gas is a mixture of para- and ortho-hydrogen. Para-hydrogen at sufficiently low temperature is not rotationally excited and is therefore an isotropic system. However, the anisotropy can be turned on and of by raising and lowering the temperature, because the ratio of para- to ortho-hydrogen depends on the temperature. What is even more, roughly 90% of all the known matter in the universe is hydrogen, in the ionized, atomic or molecular states, which makes hydrogen one of the most important species in astrophysics. The hydrogen molecule is non-polar, and some of the most important spectra in the near and far infrared and microwave region are collision-induced, due to H2-H2 complexes. At the temperature of 297.5K measurements of the collision-induced absorption spectra of H2-H2 gas are reported in the frequency range from 1900 to 2260cm^{-1} [9]. The gas densities for these measurements ranged from 51 to 610 amagat. These measurements were compared with ab initio calculations of the absorption. For these calculations the isotropic potential approximation was used. In contrast to previous ab initio calculations [9] agreement between calculations and measured spectra is now observed over the full frequency range considered. A major difference to the earlier calculations is that in this work new dipole and potential energy surfaces were used. Furthermore, measurements exist of the fundamental band and first and second overtone of H2 in dense hydrogen gas. They have been compared with ab initio calculations based on the new method. Over the full range of frequencies considered the agreement between calculations and measurements is remarkable. This work demonstrates that the new method is capable of reproducing the measured spectra where those exist with high accuracy, and predicts reliable opacities where no laboratory measurements exist. / text

The electric charge distribution of molecules such as H₂ and D₂ is inversion-symmetric so that permanent dipole moments do not exist: such molecules are infrared-inactive. It is therefore interesting that gaseous, liquid, and solid hydrogen and its isotopes actually absorb infrared radiation, for example if gas densities are sufficiently high. The observed absorption arises from electric dipole moments induced by intermolecular interactions. It is of a supermolecular origin, due to binary (or higher-order) molecular complexes that may be transient (i.e., in a collisional encounter) or relatively stable (van-der-Waals molecule). Interaction-induced electric dipoles arise from the same mechanisms that generate the intermolecular forces: exchange forces, dispersion forces, and multipolar induction. Recently the induced dipole and potential energy surfaces of H₂ pairs have been obtained by advanced quantum-chemical calculations. Interaction-induced absorption, more commonly called collision-induced absorption (CIA), by H₂ pairs is an important opacity source in the atmospheres of various types of planets and cool stars, such as late stars, low-mass stars, brown dwarfs, certain white dwarfs, etc., and therefore of special astronomical interest. The emission spectra of cool white dwarf stars differ significantly from the expected blackbody spectra of their cores, mainly due to collision-induced absorption by collisional complexes of hydrogen and helium in the stellar atmospheres. Before proceeding to the frequencies and temperatures of interest it is good to check the new potential energy surface and induced dipole surface in all possible ways by comparison with existing isotopic laboratory measurements. Furthermore, the new potential energy surface is directly compared with previously available, well established intermolecular potential energy surfaces. The electric charge distributions of deuterium and hydrogen are very similar. The new potential energy and induced dipole surfaces were originally obtained to facilitate the computation of the collision-induced absorption of hydrogen. However, by replacing the rotovibrational wavefunctions of H₂ with those of D₂ the surfaces can also be used to calculate the collision-induced absorption of deuterium pairs, thereby probing them further. At the temperature of 298K existing measurements of the collision-induced absorption of D₂--D₂ gas are compared with our quantum scattering calculations in the D₂ fundamental band (approximately 2,500cm⁻¹ to 4,500cm⁻¹). Furthermore, measurements of the collision-induced absorption of deuterium (D₂) in the D₂ first overtone band (about 5,250cm⁻¹ to 7,250cm⁻¹) at 201K are reported. These measurements are compared with ab initio calculations of the absorption spectra. Close agreement of measured and calculated spectra is seen.

Nós apresentamos ajustes multicromáticos de isócronas ao diagrama cor-magnitude do aglomerado globular NGC 6366, baseados em dados fotométricos que obtivemos com o Southern Astrophysical Research (SOAR) Telescope e de arquivos do Hubble Space Telescope (HST) ACS/WFC. Nós corrigimos os dados por avermelhamento diferencial e calculamos a linha de tendência média dos diagramas cor-magnitude. Nós comparamos os dados com modelos de isócronas estelares de Dartmouth Stellar Evolution Database e PAdova and TRieste Stellar Evolution Code, ambos com a difusão microscópica começando na sequência principal. Considerando todas as determinações prévias de metalicidade desse aglomerado, nós testamos de metalicidades [Fe 111]=-1.00 até [Fe 111]=-0.50, e idades de 9 a 13 Ganos. Depois de determinar a extinção total para seletiva somente com estrelas pertencentes ao aglomerado, Rv=3.06 + 0.14, nós encontramos os parâmetros para esse aglomerado com sendo avermelhamento E (13 — V)= 0.69 ± 0.02(int) +0.04(ext), módulo de distância (m — M)v= 15.02 ± 0.07(int) ±0.13(ext), Idade= 11 ± 1.15 Ganos. Os modelos evolucionários falham em reproduzir a sequência de baixa Tef em diagramas cor-magnitude de multi-bandas, indicando que eles ainda tem uma descrição incompleta. Nós encontramos que as isócronas de Dartmouth Stellar Evolution Database ajustam melhor o ramo das sub gigantes e baixa sequência principal do que as isócronas de PAdova and TRieste Stellar Evolution Code. O uso de anãs brancas de aglomerados globulares em vez de anãs brancas do campo no estudo da formação, propriedades físicas e evolução estelar é justificado por vários fatores. Dentre eles o fato de que as anãs brancas mais frias de aglomerados globulares velhos são remanescentes das estrelas mais velhas que se formaram durante a formação do halo, ou seja, trazem informação da época em que a Galáxia estava se formando. Utilizamos as tabelas fotométricas de dados obtidos com o HST/ACS por Richer et al. (2008) e Bedin et al. (2009) dos aglomerados globulares NGC 6397 e M 4, respectivamente, que alcançam a volta para o azul da sequência de esfriamento das anãs brancas. Com a análise da sequência de esfriamento desses aglomerados, demonstramos que a cristalização de anãs brancas acontece através da liberação de calor latente. Demonstramos também, pela primeira vez, o problema dos modelos de sequência de esfriamento de anãs brancas na volta para o azul e propormos que uma possível solução é, além de considerar o efeito da absorção induzida por colisão, é também necessário considerar que na atmosfera de anãs brancas mais frias de aglomerados globulares há uma mistura de H e He, em vez de uma atmosfera de II puro. / We present multichromatic isochrone fits to the colour-magnitude data of the globular cluster NGC 6366, based on photometric data obtained with Southern Astrophysical Research (SOAR) Telescope and archive data from Hubble Space Telescope (HST) ACS/WFC. We corrected the photometric data for differential reddening and calculated the mean ridge fine of the colour magnitude diagrams. We compared the isochrones of Dartmouth Stellar Evolution Database and PAdova and TRieste Stellar Evolution Code, both with microscopic diffusion starting on the main sequence. Bracketing all previous determinations of this cluster, we tested metallicities from [FelH]=- 1.00 to [Fe/H]=-0.50, and ages from 9 to 13 Gyrs. After determining the total to selective extinction ratio only from stars belonging to this cluster, obtaining Rv=3.06 + 0.14, we found the parameters for this cluster to be reddening E(B — V)=0.69 ± 0.02(int) ±0.04(ext), distance modulus (m — M)v= 15.02 ± 0.07(int) ±0.13(ext), Age= 11 ± 1.15 Gyr. Evolutionary models fail to reproduce the low-T eff main sequence in multi-band colour magnitude diagrams, indicating that they still have an incomplete physical description. We found that the Dartmouth Stellar Evolution Database isochrones fit better the sub giant branch and low main sequence than the PAdova and TRieste Stellar Evolution Code. The use of white dwarf stars from globular clusters instead of field white dwarf stars in the study of formation, physical properties and stellar evolution is justified by several factors. Among them is the fact that the coolest white dwarf stars in old globular clusters are remnants of the oldest stars that formed during the formation of the Galactic halo, i. e., bring us information about the time that the Galaxy was still forming. We use the photometric data obtained with the HST/ACS by Richer et al. (2008) and Bedin et al. (2009) of the globular clusters NGC 6397 and M 4, respectively, that reach the blue turn of the white dwarf cooling sequence.With the analysis of the cooling sequence of these clusters, we demonstrated that the crystallization of white dwarfs occurs with the release of latent heat. Also, we demonstrate, for the first time, the problem of the blue turn in the white dwarf cooling sequence and propose that a possible solution is, in addition to considering the effect of collision-induced absorption, it is necessary to consider that the atmosphere of cooler white dwarf stars is composed by a mixture of H and He, rather than an atmosphere of pure H.

Nós apresentamos ajustes multicromáticos de isócronas ao diagrama cor-magnitude do aglomerado globular NGC 6366, baseados em dados fotométricos que obtivemos com o Southern Astrophysical Research (SOAR) Telescope e de arquivos do Hubble Space Telescope (HST) ACS/WFC. Nós corrigimos os dados por avermelhamento diferencial e calculamos a linha de tendência média dos diagramas cor-magnitude. Nós comparamos os dados com modelos de isócronas estelares de Dartmouth Stellar Evolution Database e PAdova and TRieste Stellar Evolution Code, ambos com a difusão microscópica começando na sequência principal. Considerando todas as determinações prévias de metalicidade desse aglomerado, nós testamos de metalicidades [Fe 111]=-1.00 até [Fe 111]=-0.50, e idades de 9 a 13 Ganos. Depois de determinar a extinção total para seletiva somente com estrelas pertencentes ao aglomerado, Rv=3.06 + 0.14, nós encontramos os parâmetros para esse aglomerado com sendo avermelhamento E (13 — V)= 0.69 ± 0.02(int) +0.04(ext), módulo de distância (m — M)v= 15.02 ± 0.07(int) ±0.13(ext), Idade= 11 ± 1.15 Ganos. Os modelos evolucionários falham em reproduzir a sequência de baixa Tef em diagramas cor-magnitude de multi-bandas, indicando que eles ainda tem uma descrição incompleta. Nós encontramos que as isócronas de Dartmouth Stellar Evolution Database ajustam melhor o ramo das sub gigantes e baixa sequência principal do que as isócronas de PAdova and TRieste Stellar Evolution Code. O uso de anãs brancas de aglomerados globulares em vez de anãs brancas do campo no estudo da formação, propriedades físicas e evolução estelar é justificado por vários fatores. Dentre eles o fato de que as anãs brancas mais frias de aglomerados globulares velhos são remanescentes das estrelas mais velhas que se formaram durante a formação do halo, ou seja, trazem informação da época em que a Galáxia estava se formando. Utilizamos as tabelas fotométricas de dados obtidos com o HST/ACS por Richer et al. (2008) e Bedin et al. (2009) dos aglomerados globulares NGC 6397 e M 4, respectivamente, que alcançam a volta para o azul da sequência de esfriamento das anãs brancas. Com a análise da sequência de esfriamento desses aglomerados, demonstramos que a cristalização de anãs brancas acontece através da liberação de calor latente. Demonstramos também, pela primeira vez, o problema dos modelos de sequência de esfriamento de anãs brancas na volta para o azul e propormos que uma possível solução é, além de considerar o efeito da absorção induzida por colisão, é também necessário considerar que na atmosfera de anãs brancas mais frias de aglomerados globulares há uma mistura de H e He, em vez de uma atmosfera de II puro. / We present multichromatic isochrone fits to the colour-magnitude data of the globular cluster NGC 6366, based on photometric data obtained with Southern Astrophysical Research (SOAR) Telescope and archive data from Hubble Space Telescope (HST) ACS/WFC. We corrected the photometric data for differential reddening and calculated the mean ridge fine of the colour magnitude diagrams. We compared the isochrones of Dartmouth Stellar Evolution Database and PAdova and TRieste Stellar Evolution Code, both with microscopic diffusion starting on the main sequence. Bracketing all previous determinations of this cluster, we tested metallicities from [FelH]=- 1.00 to [Fe/H]=-0.50, and ages from 9 to 13 Gyrs. After determining the total to selective extinction ratio only from stars belonging to this cluster, obtaining Rv=3.06 + 0.14, we found the parameters for this cluster to be reddening E(B — V)=0.69 ± 0.02(int) ±0.04(ext), distance modulus (m — M)v= 15.02 ± 0.07(int) ±0.13(ext), Age= 11 ± 1.15 Gyr. Evolutionary models fail to reproduce the low-T eff main sequence in multi-band colour magnitude diagrams, indicating that they still have an incomplete physical description. We found that the Dartmouth Stellar Evolution Database isochrones fit better the sub giant branch and low main sequence than the PAdova and TRieste Stellar Evolution Code. The use of white dwarf stars from globular clusters instead of field white dwarf stars in the study of formation, physical properties and stellar evolution is justified by several factors. Among them is the fact that the coolest white dwarf stars in old globular clusters are remnants of the oldest stars that formed during the formation of the Galactic halo, i. e., bring us information about the time that the Galaxy was still forming. We use the photometric data obtained with the HST/ACS by Richer et al. (2008) and Bedin et al. (2009) of the globular clusters NGC 6397 and M 4, respectively, that reach the blue turn of the white dwarf cooling sequence.With the analysis of the cooling sequence of these clusters, we demonstrated that the crystallization of white dwarfs occurs with the release of latent heat. Also, we demonstrate, for the first time, the problem of the blue turn in the white dwarf cooling sequence and propose that a possible solution is, in addition to considering the effect of collision-induced absorption, it is necessary to consider that the atmosphere of cooler white dwarf stars is composed by a mixture of H and He, rather than an atmosphere of pure H.

Nós apresentamos ajustes multicromáticos de isócronas ao diagrama cor-magnitude do aglomerado globular NGC 6366, baseados em dados fotométricos que obtivemos com o Southern Astrophysical Research (SOAR) Telescope e de arquivos do Hubble Space Telescope (HST) ACS/WFC. Nós corrigimos os dados por avermelhamento diferencial e calculamos a linha de tendência média dos diagramas cor-magnitude. Nós comparamos os dados com modelos de isócronas estelares de Dartmouth Stellar Evolution Database e PAdova and TRieste Stellar Evolution Code, ambos com a difusão microscópica começando na sequência principal. Considerando todas as determinações prévias de metalicidade desse aglomerado, nós testamos de metalicidades [Fe 111]=-1.00 até [Fe 111]=-0.50, e idades de 9 a 13 Ganos. Depois de determinar a extinção total para seletiva somente com estrelas pertencentes ao aglomerado, Rv=3.06 + 0.14, nós encontramos os parâmetros para esse aglomerado com sendo avermelhamento E (13 — V)= 0.69 ± 0.02(int) +0.04(ext), módulo de distância (m — M)v= 15.02 ± 0.07(int) ±0.13(ext), Idade= 11 ± 1.15 Ganos. Os modelos evolucionários falham em reproduzir a sequência de baixa Tef em diagramas cor-magnitude de multi-bandas, indicando que eles ainda tem uma descrição incompleta. Nós encontramos que as isócronas de Dartmouth Stellar Evolution Database ajustam melhor o ramo das sub gigantes e baixa sequência principal do que as isócronas de PAdova and TRieste Stellar Evolution Code. O uso de anãs brancas de aglomerados globulares em vez de anãs brancas do campo no estudo da formação, propriedades físicas e evolução estelar é justificado por vários fatores. Dentre eles o fato de que as anãs brancas mais frias de aglomerados globulares velhos são remanescentes das estrelas mais velhas que se formaram durante a formação do halo, ou seja, trazem informação da época em que a Galáxia estava se formando. Utilizamos as tabelas fotométricas de dados obtidos com o HST/ACS por Richer et al. (2008) e Bedin et al. (2009) dos aglomerados globulares NGC 6397 e M 4, respectivamente, que alcançam a volta para o azul da sequência de esfriamento das anãs brancas. Com a análise da sequência de esfriamento desses aglomerados, demonstramos que a cristalização de anãs brancas acontece através da liberação de calor latente. Demonstramos também, pela primeira vez, o problema dos modelos de sequência de esfriamento de anãs brancas na volta para o azul e propormos que uma possível solução é, além de considerar o efeito da absorção induzida por colisão, é também necessário considerar que na atmosfera de anãs brancas mais frias de aglomerados globulares há uma mistura de H e He, em vez de uma atmosfera de II puro. / We present multichromatic isochrone fits to the colour-magnitude data of the globular cluster NGC 6366, based on photometric data obtained with Southern Astrophysical Research (SOAR) Telescope and archive data from Hubble Space Telescope (HST) ACS/WFC. We corrected the photometric data for differential reddening and calculated the mean ridge fine of the colour magnitude diagrams. We compared the isochrones of Dartmouth Stellar Evolution Database and PAdova and TRieste Stellar Evolution Code, both with microscopic diffusion starting on the main sequence. Bracketing all previous determinations of this cluster, we tested metallicities from [FelH]=- 1.00 to [Fe/H]=-0.50, and ages from 9 to 13 Gyrs. After determining the total to selective extinction ratio only from stars belonging to this cluster, obtaining Rv=3.06 + 0.14, we found the parameters for this cluster to be reddening E(B — V)=0.69 ± 0.02(int) ±0.04(ext), distance modulus (m — M)v= 15.02 ± 0.07(int) ±0.13(ext), Age= 11 ± 1.15 Gyr. Evolutionary models fail to reproduce the low-T eff main sequence in multi-band colour magnitude diagrams, indicating that they still have an incomplete physical description. We found that the Dartmouth Stellar Evolution Database isochrones fit better the sub giant branch and low main sequence than the PAdova and TRieste Stellar Evolution Code. The use of white dwarf stars from globular clusters instead of field white dwarf stars in the study of formation, physical properties and stellar evolution is justified by several factors. Among them is the fact that the coolest white dwarf stars in old globular clusters are remnants of the oldest stars that formed during the formation of the Galactic halo, i. e., bring us information about the time that the Galaxy was still forming. We use the photometric data obtained with the HST/ACS by Richer et al. (2008) and Bedin et al. (2009) of the globular clusters NGC 6397 and M 4, respectively, that reach the blue turn of the white dwarf cooling sequence.With the analysis of the cooling sequence of these clusters, we demonstrated that the crystallization of white dwarfs occurs with the release of latent heat. Also, we demonstrate, for the first time, the problem of the blue turn in the white dwarf cooling sequence and propose that a possible solution is, in addition to considering the effect of collision-induced absorption, it is necessary to consider that the atmosphere of cooler white dwarf stars is composed by a mixture of H and He, rather than an atmosphere of pure H.