Photoionization and Electron–Ion Recombination in Astrophysical Plasmas
Abstract
:1. Introduction
2. Stellar Interiors
3. Photoionization
3.1. Inner Shell Ionization
4. Recombination
4.1. Direct Radiative Recombination
4.2. Low Temperature Dielectronic Recombination (LTDR)
- The LTDR rate is very sensitive to when is of order unity or larger.
- When , the LTDR recombination rate scales as and thus increases more quickly with decreasing temperature than the radiative recombination rate, which typically scales as with . (see, e.g., [83]).
- The LTDR process will be most important for those states with a large Einstein A coefficient and for those states lying closest to, but above, the ion ground state.
- The process is very dependent on the details of the atomic structure. In the above case, the energy of the 2p 4d F state is crucial for determining the LTDR rate. As the LTDR autoionizing states lie well above the C iii ground state, and can have large energy widths, the energies of the states are not necessarily known. Theoretical calculations can provide estimates, but will have difficulties for states that lie ”very close” to the ionization limit since a small error in the energy level can make a big difference in the recombination rate, particularly at low temperatures.
4.3. High Temperature Dielectronic Recombination (HTDR)
5. Suppression of Dielectronic Recombination
5.1. Collisional Processes
5.2. The Importance of the Radiation Field
6. Astrophysical Examples
6.1. Recombination Processes
6.2. The Sun
6.3. O, WR, and LBV Stars
6.3.1. N iii and N iv lines in Of and WN stars
6.3.2. Carbon in WC stars
6.4. C ii in [WC] Stars
6.5. Supernovae
7. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ADS | Astrophysics Data System |
ESA | European Space Agency |
HST | Hubble Space Telescope |
LTE | Local thermodynamic equilibrium |
nLTE | Non-local thermodynamic equilibrium |
LTDR | Low temperature dielectronic recombination |
HTDR | High temperature dielectronic recombination |
LBV | Luminous blue variable |
LS coupling | Total orbital angular momentum (L) is coupled with the total spin (S) |
NASA | National Aeronautics and Space Administration |
SN | Supernova |
WD | White dwarf |
WR star | Wolf–Rayet star |
WN | Wolf–Rayet star belonging to the nitrogen sequence |
WC | Wolf–Rayet star belonging to the carbon sequence |
1 | The effective temperature of the star is defined by the relation where L is the stellar luminosity (energy emitted per second), the Stefan–Boltzmann constant, and is the radius of the star. |
2 | The meaning of “accurate” is highly context dependent. Atomic data calculations can, in some cases, give energy levels accurate to 1% and for some purposes this is sufficient. However, for spectral modeling such energy levels cannot be used to compute transition wavelengths—a 1% shift (which will be potentially larger if the levels are close in energy) will move a line far from its correct location, influencing spectral synthesis calculations. Moreover, in non-LTE a wrong wavelength will influence how a line interacts with neighboring transitions. In O supergiants two weak Fe iv lines, that overlap with He i 304, influence the strength of He i singlet transitions in the optical and accurate wavelengths (and oscillator strengths) of these Fe iv lines are crucial for understanding the He i singlet transitions [1]. |
3 | Strictly speaking, a radiation temperature is only well defined if the radiation field is Planckian. However, astronomers often use color temperatures, defined by fitting a scaled blackbody ratio to the flux at two wavelengths, to characterize the nature of the radiation field in some pass band. In nLTE, astronomers may also use the excitation temperature to characterize the excitation or ionization state of a gas. In general these will not be the same as the local electron temperature, and will vary with level and ionization stage (though possibly in a systematic way). |
4 | The Sun’s atmosphere is cool and dense enough for molecules to form and 50 molecular species have been identified [8]. In the solar spectrum, spectral features due, for example, to CO, SiO, H, OH, CH, C, and CN, have been identified [8,9]. Dust formation in red giants and supergiants is common but not well understood [10], and in some cases may be associated with non-equilibrium chemistry [11]. |
5 | Throughout the article we neglect full shells when providing the electron configuration. We use the principal quantum number (n), orbital angular momentum number ( s, p, d, f, g …), and spin () to describe the state of an electron. Thus, 2p indicates an electron with and . LS-coupling (in which the orbital angular momenta are coupled and the electron spins are coupled) is used to provide the term designation. A term designation has the format 2S+1Lx where S is the sum of the (valence) electron spins, L is the total orbital angular momentum, and “o” is used to indicate that the arithmetic sum of the electron orbital angular momenta is odd (o) or even (in which case e is omitted by convention). An excellent primer on atomic spectroscopy is provided by [63]. |
6 | WR stars are a class of massive stars that evolved from O stars (stars with initial masses ≳ 15 ). They are experiencing mass loss via a stellar wind (induced by radiation pressure acting through bound–bound transitions) with a mass-loss rate typically in excess of and a terminal wind speed of ∼1000 to 3500 km s [64,65]. In many WR stars the wind is sufficiently dense that the entire spectrum we observe originates in the wind—the hydrostatic core of the star is not seen. There are two main WR classes: WN stars exhibit N and He (and sometimes H) emission lines, and exhibit enhanced N and He at the stellar surface due to the CNO cycle (the main H-fusion chain in massive stars). WC stars exhibit emission lines of He, C, and O, with a C abundance comparable to that of He (e.g., [66,67]). They have lost all of their hydrogen envelope, with the enhanced C abundance arising from the triple alpha process (3 HeC). |
7 | A P Cygni profile is formed when continuum radiation is absorbed and scattered by outflowing material. Outflowing gas along the line of sight absorbs continuum radiation and scatters it out of the line of sight, producing blue-shifted absorption. Radiation absorbed in other directions can be scattered into the line of sight and, for a spherically symmetric expanding gas, the combination with the blue-shifted absorption will give rise to red-shifted emission. |
8 | The ejecta of Type Ia SNe are composed primarily of intermediate mass elements (Ca, Si) and iron group (Fe, Ni, Co) elements. In such ejecta we may need to treat Auger ionization more rigorously since it could potentially affect the ionization state of the gas and the thermalization of non-thermal electrons. The non-thermal electrons are initially produced via Compton scattering of gamma-ray photons produced from decay of radioactive Ni and Co. In this case inner shell ionization will most likely occur via non-thermal electrons. However the subsequent Auger ionization and fluorescence are independent of how the K-shell hole was created. |
9 | From autostructure calculations made by a collaboration of researchers at Auburn University, Rollins College, the University of Strathclyde, and other universities. Tables produced by N. R. Badnell and are available at Atomic Data from AUTOSTRUCTURE. |
10 | A signal processing term that refers to the distortion of data due to sampling which is too coarse. In the present case a narrow but strong resonance could be missed in the photoionization cross-section when the frequency sampling is too coarse. Alternatively, its influence could be artificially enhanced if it is not fully resolved. |
11 | The Sun is simultaneously oscillating in thousands of different vibration modes. The frequency and strength of these modes depends on the internal structure of the Sun (e.g., the depth of the convection, the sound speed). |
12 | At the Eddington limit the force arising from the scattering of radiation by free electrons matches the gravitational force. |
13 | The strength of most emission lines in WR stars is proportional to the density squared. Thus, a clumped wind can yield the same line strengths for a lower mass-loss rate (i.e., for a lower average density). On the other hand electron scattering line wings arise from Thomson scattering of line photons by free electrons and hence scale with density. Thus, the strength of electron scattering wings relative to their neighboring emission line can act as a global diagnostic of clumping. In WR stars the wings are offset to the red from their originating transition because of the large outflow velocities. |
14 | In this process a strong transition (typically in the UV) absorbs continuum photons, a process whose efficiency is enhanced by the velocity field which allows the UV transitions to intercept more continuum radiation. In many cases the absorbed photons will typically be re-emitted in the same transition. However, in some cases the upper levels have an alternate decay route—decay via this transition can then lead to emission in this bound–bound transition. This is also known as the Swings mechanism [109]. |
15 | C ii emission is also predicted but this is masked by blending with other lines. |
16 | The 11 appended to WC denotes the ionization class of the star—in this case, a spectrum dominated by C ii with little evidence for C iii. |
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Hillier, D.J. Photoionization and Electron–Ion Recombination in Astrophysical Plasmas. Atoms 2023, 11, 54. https://doi.org/10.3390/atoms11030054
Hillier DJ. Photoionization and Electron–Ion Recombination in Astrophysical Plasmas. Atoms. 2023; 11(3):54. https://doi.org/10.3390/atoms11030054
Chicago/Turabian StyleHillier, D. John. 2023. "Photoionization and Electron–Ion Recombination in Astrophysical Plasmas" Atoms 11, no. 3: 54. https://doi.org/10.3390/atoms11030054