Open Access This article is
- freely available
Galaxies 2018, 6(3), 72; https://doi.org/10.3390/galaxies6030072
The Collisional Atomic Processes of Rydberg Hydrogen and Helium Atoms: Astrophysical Relevance
Institute of Physics, Belgrade University, Pregrevica 118, 11080 Zemun, Belgrade, Serbia
Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia
LERMA, Observatoire de Paris, UMR CNRS 8112, UPMC, 92195 Meudon CEDEX, France
Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia
Author to whom correspondence should be addressed.
Received: 17 June 2018 / Accepted: 12 July 2018 / Published: 16 July 2018
Elementary processes in astrophysical environments traditionally attract researchers’ attention. We present the data needed for the inclusion of the specific atomic collisional processes in the investigation of the optical and kinetic properties of weakly ionized stellar atmosphere layers. The first type of processes are collisional ionisation (chemi-ionization) processes, and the second ones are excitation and de-excitation (i.e., ()-mixing processes). We give the rate coefficients of the aforementioned processes for the conditions that exist in the solar photosphere, the atmosphere of DB white dwarfs, M-type red dwarfs, etc.
Keywords:atomic data; molecular data; atomic and molecular databases
Many fields in astrophysics, especially the modelling of various stellar atmospheres and the kinetics of stellar and other astrophysical plasmas, depend on data for atomic and molecular collisions [1,2,3,4,5,6]. Modern codes for stellar atmosphere modelling (e.g., [7,8]) require knowledge of atomic data, so the accuracy of these data becomes very important. Among these data there are atomic and molecular processes and spectral regions that even today are poorly investigated. Therefore, there is a need for further investigation and development of methods for improving the existing ones [9,10,11]. Recently, the research community has become aware of the need for better atomic data which could be important in modelling of AGN BLR clouds .
In this paper we analyze the current state of research on ionisation (chemi-ionization) processes and excitation and de-excitation (()-mixing) processes in collisional reaction involving hydrogen and helium atoms.
Since these processes have already been treated for a long time on the basis of the so-called dipole resonant mechanism (DRM), we will briefly describe its main features. In this description of collisional ionisation and excitation events, it is envisaged that processes are induced by the dipole part of the electrostatic interaction between the outer Rydberg electron and the inner ion-atom system. Figure 1 schematically illustrates the chemi-ionization/recombination and ()-mixing processes. A detailed description of the mechanism can be found in .
The inelastic collisions of hydrogen atoms is an important factor in the modelling of stellar atmospheres [9,14]. This kind of calculation requires accurate atomic data (e.g., hydrogen collisional excitation/ionization cross-sections and rate coefficients) [11,15]. The reason is that even if the cross-sections for such collisions are quite small, their abundance is large (number of neutral hydrogen atoms are a few orders of magnitude higher than electrons in the atmospheres of solar-type stars).
It can be seen from Reference  that there exists a difference in collision rate data. In view of the present large uncertainties in the data for excitation/ionization by collisions with hydrogen atoms, it is important to further investigate the H(n) + H(1s) system, especially for higher values of n where uncertainties are very noticeable.
2.1. Collisional Ionization
The collisional ionisation (chemi-ionization) includes two possible channels: the associative ionisation and the non-associative one:where is the hydrogen atom in the excited state with the principal quantum number n, is the molecular ion in the ground electronic state, and e is a free electron.
The values of the total chemi-ionization and recombination rate coefficients and are presented in Figure 2 and Figure 3, respectively. These figures cover the regions and 10,000 , which are relevant for the solar photosphere [1,16], some atmospheres of late type (M) stars , etc. The values for and are from . By analyzing the partial rate coefficients of both possible channels of chemi-ionization, we conclude that the associative channel (1a) is dominant for lower n and T. This gives important information about the presence of the molecular ion H. The importance of the associative channel (1a) decreases with temperature increase when the non-associative channel (1b) takes the dominant place.
2.2. Collisional Excitation and De-Excitation
Collisional excitation process by hydrogen atoms includes two possible channels—the direct excitation process and the excitation process involving excitation transfer:
The inverse de-excitation processes are:where is a Rydberg state hydrogen atom with principal quantum number and e is a free electron.
The processes (2) and (3) are characterized by the excitation and de-excitation rate coefficients and , where T is the local temperature of the atomic particles. The values of excitation rate coefficients for K are from . In the extended region of temperature coefficients are determined here using the semi-classical approach similar to that described in  or . The de-excitation rate coefficients are determined according to the principle of thermodynamical balance. All necessary expressions are given and explained in Mihajlov et al. .
2.3. Astrophysical Targets
Solar atmosphere modelling: The influence of collision processes and the corresponding ()-mixing processes on hydrogen atom excited-state populations in the solar photosphere has been examined. It has been concluded that the considered collision processes dominate over the relevant concurrent electron–atom and electron–ion processes in almost the entire solar photosphere [17,21]. It is shown that these processes are important for the non-local thermodynamic equilibrium modelling.
Atmospheres of late type (M) stars: In  it is shown that the examined processes influence the populations of all hydrogen atom excited states. This suggests that the examined processes, due to their influence on the excited state populations and the free electron density, should also influence the atomic spectral line shapes. Figure 5 (from ) shows the line profiles of H, H, H Pa with and without the inclusion of (1a) and (1b) processes. Profiles are synthesized with PHOENIX code  with Stark broadening contribution. The presented results suggest that the processes (1) influence the atomic spectral line shapes. Line shape changes, especially in the wings, show the influence of the electron density change having a direct influence on the Stark broadening of hydrogen lines in the atmospheres of late type (M) stars (see also ).
AGN BLR clouds: The possibility that the atom–Rydberg atom collisions (i.e., chemi-ionization processes as well as the inverse chemi-recombination processes) may be useful for the diagnostics, modelling, and confirmation of the existence or non-existence of very dense weakly ionised domains in clouds in BLR and NLR regions of AGN has been investigated recently. The preliminary results are presented in . The importance of ()-mixing processes in H*(n) + H(1s) collisions, for the principal quantum number , in AGN BLR clouds has been investigated as well. The preliminary results show that the corresponding processes must have an influence on the populations of hydrogen highly excited atoms in moderately ionized layers of sufficiently dense parts of the BLR clouds, if such exist.
Non-LTE modelling, especially for helium plasma, needs accurate rate coefficients for all relevant elementary processes, including collisional ionization/recombination and excitation/de-excitation processes, because the great departure from LTE in laboratory conditions is more easily realized in helium than in hydrogen plasmas . Such investigation of non-equilibrium helium plasmas is still current and of interest (see [26,27,28,29,30]).
Helium atoms play an important role in astrophysics [4,31,32]. Ionization processes of excited states of helium and their inverse recombination processes are significant for helium plasmas in the very low-density environment which exists in stellar atmospheres with weakly ionized layers . Chemi-ionization/recombination and ()-mixing processes in low-temperature layers of white dwarf atmospheres are very important for the helium atom Rydberg states population where the gaseous mixture of hydrogen and helium exists.
The helium molecular ion He is also present in stellar medium, as well as in the chemistry of the early universe [4,33,34]. Dissociative recombination (right side of Equation (4a)) is an inverse process occurring through the neutralization of the He ion. It has been widely studied due to its importance in a relatively low-temperature system .
3.1. Collisional Ionization
The total chemi-ionization and chemi-recombination rate coefficients and , in the temperature range 30,000 and principal quantum numbers , are shown in Figure 6 and Figure 7. The data were calculated in . The dependence of both coefficients and on the quantum number decreases with the increase of the temperature.
As in the case of hydrogen, by analyzing the partial rate coefficients of both possible channels of chemi-ionization, we concluded that the associative channel (4a) is noticeable for lower n and T ( and 10,000 K). This gives important information about presence of the helium molecular ion He. The importance of the associative channel (4a) decreases with temperature increase when the non-associative channel (i.e., dissociation (4b)) takes the dominant place.
3.2. Collisional Excitation and De-Excitation
3.3. Astrophysical Targets
White dwarfs modelling: The influence of chemi-ionization processes (4) in reference to the other ionization processes was examined in the photospheres of the DB white dwarfs with 12,000 20,000 . On the basis of the data from Koester  it was established that in the parts of the considered photosphere (where 20,000 ), these chemi-ionization processes dominate over the concurrent electron–Rydberg atom impact ionization processes. It is concluded that these processes should be included in the model atmospheres from the beginning in a consistent way.
It is shown that in significant parts of the DB white dwarf atmospheres (which contain weakly ionized layers (ionization degree )), the influence of the studied atom–Rydberg atom processes (5) and (6) on excited helium atom populations is dominant or at least comparable to the influence of the concurrent electron–He*(n)–atom processes.
In this paper it is shown that the collisional processes of atoms and molecules in ground and Rydberg states play an important role in the astrophysics. We present the results of two groups of collisional processes which are important for the optical and kinetic properties of weakly ionized stellar atmosphere layers. Quantitative estimations of the rate coefficients of the mentioned processes were made. These data are important for the modelling and interpretation of data provided by observations and laboratory measurements. These data are important and have a notable role in many fields in atmospheric physics, chemistry, industry, etc.
Writing—review & editing, V.A.S., M.S.D., L.M.I., N.N.B. and A.N.K.
This research was funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia projects number 176002 and III44002.
The authors are thankful to the Ministry of Education, Science and Technological Development of the Republic of Serbia for the support of this work within the projects 176002 and III44002.
Conflicts of Interest
The authors declare no conflict of interest.
- Fontenla, J.M.; Avrett, E.; Thuillier, G.; Harder, J. Semiempirical Models of the Solar Atmosphere. I. The Quiet- and Active Sun Photosphere at Moderate Resolution. Astrophys. J. 2006, 639, 441–458. [Google Scholar] [CrossRef]
- Koester, D. Model atmospheres for DB white dwarfs. Astron. Astrophys. Suppl. Ser. 1980, 39, 401–409. [Google Scholar]
- Ferland, G.; Chatzikos, M.; Guzmán, F.; Lykins, M.; van Hoof, P.; Williams, R.; Abel, N.; Badnell, N.; Keenan, F.; Porter, R.; et al. The 2017 Release of Cloudy. Rev. Mex. Astron. Astrofis. 2017, 53, 385–438. [Google Scholar]
- Mihajlov, A.A.; Ignjatović, L.M.; Srećković, V.A.; Dimitrijević, M.S.; Metropoulos, A. The non-symmetric ion-atom radiative processes in the stellar atmospheres. Mon. Not. R. Astron. Soc. 2013, 431, 589–599. [Google Scholar] [CrossRef]
- Ignjatović, L.M.; Mihajlov, A.A.; Srećković, V.A.; Dimitrijević, M.S. The ion-atom absorption processes as one of the factors of the influence on the sunspot opacity. Mon. Not. R. Astron. Soc. 2014, 441, 1504–1512. [Google Scholar] [CrossRef]
- Srećković, V.A.; Mihajlov, A.A.; Ignjatović, L.M.; Dimitrijević, M.S. Ion-atom radiative processes in the solar atmosphere: Quiet Sun and sunspots. New Astron. Rev. 2014, 54, 1264–1271. [Google Scholar] [CrossRef]
- Hauschildt, P.; Baron, E. Cool stellar atmospheres with PHOENIX. Memorie della Società Astronomica Italiana Supplement 2005, 7, 140–146. [Google Scholar]
- Hauschildt, P.H.; Baron, E. A 3D radiative transfer framework-VI. PHOENIX/3D example applications. Astron. Astrophys. 2010, 509, 923–936. [Google Scholar] [CrossRef]
- Barklem, P.S. Non-LTE Balmer line formation in late-type spectra: Effects of atomic processes involving hydrogen atoms. Astron. Astrophys. 2007, 466, 327–337. [Google Scholar] [CrossRef]
- Mashonkina, L. Atomic data necessary for the non-LTE analysis of stellar spectra. Phys. Scr. 2009, T134, 014004. [Google Scholar] [CrossRef]
- Przybilla, N.; Butler, K. Non-LTE line formation for hydrogen revisited. Astrophys. J. 2004, 609, 1181–1191. [Google Scholar] [CrossRef]
- Dimitrijević, M.S.; Srećković, V.A.; Ignjatović, L.M. Chemi-ionization processes in Narrow-Line Seyfert 1 Galaxies. In Proceedings of the Revisiting Narrow-Line Seyfert 1 Galaxies and Their Place in the Universe, Padua, Italy, 9–13 April 2018. Proceeding of Science, NLS1-2018, 049 (1–4). [Google Scholar]
- Mihajlov, A.A.; Srećković, V.A.; Ignjatović, L.M.; Klyucharev, A.N. The Chemi-Ionization Processes in Slow Collisions of Rydberg Atoms with Ground State Atoms: Mechanism and Applications. J. Clust. Sci. 2012, 23, 47–75. [Google Scholar] [CrossRef]
- Mason, N. The status of the database for plasma processing. J. Phys. D 2009, 42, 194003. [Google Scholar] [CrossRef]
- Przybilla, N.; Nieva, M.F.; Butler, K. Testing common classical LTE and NLTE model atmosphere and line-formation codes for quantitative spectroscopy of early-type stars. J. Phys. Conf. Ser. 2011, 328, 012015. [Google Scholar] [CrossRef][Green Version]
- Vernazza, J.E.; Avrett, E.H.; Loeser, R. Structure of the solar chromosphere. III—Models of the EUV brightness components of the quiet-sun. Astrophys. J. Suppl. Ser. 1981, 45, 635–725. [Google Scholar] [CrossRef]
- Mihajlov, A.A.; Ignjatović, L.M.; Srećković, V.A.; Dimitrijević, M.S. Chemi-ionization in Solar Photosphere: Influence on the Hydrogen Atom Excited States Population. Astrophys. J. Suppl. Ser. 2011, 193, 2. [Google Scholar] [CrossRef]
- Mihajlov, A.A.; Ignjatovic, L.M.; Djuric, Z.; Ljepojevic, N.N. The rate coefficients for the processes of (n-n′)-mixing in collisions of Rydberg atoms H*(n) with H(1s) atoms. J. Phys. B 2004, 37, 4493–4506. [Google Scholar] [CrossRef]
- Srećković, V.A.; Mihajlov, A.A.; Ignjatović, L.M.; Dimitrijević, M.S. Excitation and deexcitation processes in atom-Rydberg atom collisions in helium-rich white dwarf atmospheres. Astron. Astrophys. 2013, 552, A33. [Google Scholar] [CrossRef]
- Mihajlov, A.A.; Ignjatović, L.M.; Srećković, V.A.; Djurić, Z. The influence of (n-n′)-mixing processes in He*(n) + He(1s2) collisions on He*(n) atoms’ populations in weakly ionized helium plasmas. J. Quant. Spectrosc. Radiat. Transf. 2008, 109, 853–862. [Google Scholar] [CrossRef]
- Mihajlov, A.A.; Srećković, V.A.; Ignjatović, L.M.; Dimitrijević, M.S. Atom-Rydberg-atom chemi-ionization processes in solar and DB white-dwarf atmospheres in the presence of (n-n′)-mixing channels. Mon. Not. R. Astron. Soc. 2016, 458, 2215–2220. [Google Scholar] [CrossRef]
- Mihajlov, A.; Ignjatović, L.M.; Dimitrijević, M.; Djurić, Z. Symmetrical chemi-ionization and chemi- recombination processes in low-temperature layers of helium-rich DB white dwarf atmospheres. Astrophys. J. Suppl. Ser. 2003, 147, 369. [Google Scholar] [CrossRef]
- Mihajlov, A.A.; Jevremović, D.; Hauschildt, P.; Dimitrijević, M.S.; Ignjatović, L.M.; Alard, F. Influence of chemi-ionization and chemi-recombination processes on hydrogen line shapes in M dwarfs. Astron. Astrophys. 2007, 471, 671–673. [Google Scholar] [CrossRef][Green Version]
- Gnedin, Y.N.; Mihajlov, A.A.; Ignjatović, L.M.; Sakan, N.M.; Srećković, V.A.; Zakharov, M.Y.; Bezuglov, N.N.; Klycharev, A.N. Rydberg atoms in astrophysics. New Astr. Rev. 2009, 53, 259–265. [Google Scholar] [CrossRef]
- Djurić, Z.; Mihajlov, A.A. The influence of chemi-recombination and chemi-ionization processes on kinetics of non-equilibrium helium plasma. J. Quant. Spectrosc. Radiat. Transf. 2001, 70, 285–305. [Google Scholar] [CrossRef]
- Rodero, A.; Quintero, M.C.; Álvarez, R.; Sola, À.; Gamero, A.; García, M.C.; Lao, C. The electron temperature determination in a non-equilibrium helium plasma induced by microwave. Czechoslov. J. Phys. Suppl. 2000, 50, 339–342. [Google Scholar] [CrossRef]
- Isakaev, E.K.; Chinnov, V.F.; Sargsyan, M.; Kavyrshin, D.I. Nonequilibrium state of highly ionized helium plasma at atmospheric pressure. High Temp. 2013, 51, 141–146. [Google Scholar] [CrossRef]
- Golding, T.P.; Carlsson, M.; Leenaarts, J. Detailed and simplified nonequilibrium helium ionization in the solar atmosphere. Astrophys. J. 2014, 784, 30. [Google Scholar] [CrossRef]
- Korshunov, O.; Chinnov, V.; Kavyrshin, D.; Ageev, A. Spectral measurements of electron temperature in nonequilibrium highly ionized He plasma. In Proceedings of the XXXI International Conference on Equations of State for Matter (ELBRUS 2016), Elbrus, Russia, 1–6 March 2016. Journal of Physics Conference Series, Volume 774, Article 012199. [Google Scholar]
- Chinnov, V.; Kavyrshin, D.; Ageev, A.; Korshunov, O.; Sargsyan, M.; Efimov, A. Study of spatial distributions of highly ionized nonequilibrium helium plasma at atmospheric pressures. In Proceedings of the XXXI International Conference on Equations of State for Matter (ELBRUS 2016), Elbrus, Russia, 1–6 March 2016. Journal of Physics Conference Series, Volume 774, Article 012200. [Google Scholar]
- Ignjatović, L.M.; Mihajlov, A.A.; Srećković, V.A.; Dimitrijević, M.S. Absorption non-symmetric ion-atom processes in helium-rich white dwarf atmospheres. Mon. Not. R. Astron. Soc. 2014, 439, 2342–2350. [Google Scholar] [CrossRef]
- Przybilla, N.; Butler, K.; Heber, U.; Jeffery, C. Extreme helium stars: non-LTE matters-Helium and hydrogen spectra of the unique objects V652 Her and HD 144941. Astron. Astrophys. 2005, 443, L25–L28. [Google Scholar] [CrossRef]
- Stancil, P. Continuous absorption by He2 (+) and H2 (+) in cool white dwarfs. Astrophys. J. 1994, 430, 360–370. [Google Scholar] [CrossRef]
- Coppola, C.M.; Galli, D.; Palla, F.; Longo, S.; Chluba, J. Non-thermal photons and H2 formation in the early Universe. Mon. Not. R. Astron. Soc. 2013, 434, 114–122. [Google Scholar] [CrossRef][Green Version]
- Royal, J.; Orel, A. Resonant dissociative excitation and vibrational excitation of He 2+. Phys. Rev. A 2007, 75, 052706. [Google Scholar] [CrossRef]
Figure 1. The graph of schematic illustration of the resonant transitions which cause the processes of chemi-ionization/recombination and ()-mixing processes in the collision.
Figure 2. Plot of the rate coefficients for collisional ionisation H*(n) + H(1s) (i.e., for chemi-ionization processes (1)) as a function of n and T.
Figure 3. Same as in Figure 2 but for inverse process (i.e., recombination processes).
Figure 4. Collisional H*(n) + H(1s) excitation rate coefficients for the transitions between the states with , as a function of n and T. Here .
Figure 5. The hydrogen line profiles ((a) H; (b) H; (c) H; (d) Pa) in the late type (M) stars’ atmospheres. Dotted black and full blue curves denote lines without and with the inclusion of chemi-ionization and chemi-recombination processes (1), respectively.
Figure 6. The plot of the and collisional ionisation He*(n) + He(1s) rate coefficients. That is, chemi-ionization processes (4) in the region 30,000 and for principal quantum numbers .
Figure 7. Same as in Figure 6, but for the inverse process (i.e., chemi-recombination).
Figure 8. Collisional excitation helium rate coefficients for the transitions between the states with , as a function of n and T. .
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).