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Register a new userNew effective recombination coefficients for nebular N II lines
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Here we report new ${it ab initio}$ calculations of the effective recombination coefficients for the ion{N}{ii} recombination spectrum. We have taken into account the density dependence of the coefficients arising from the relative populations of the fine-structure levels of the ground state of the recombining ion, an elaboration that has not been attempted before for this ion, and it opens up the possibility of electron density determination via recombination line analysis. Photoionization cross-sections, bound state energies, and the oscillator strengths of ion{N}{ii} with $n leq 11$ and $l leq 4$ have been obtained using the close-coupling R-matrix method in the intermediate coupling scheme. Photoionization data were computed that accurately map out the near-threshold resonances and were used to derive recombination coefficients, including radiative and dielectronic recombination. Also new is including the effects of dielectronic recombination via high-$n$ resonances lying between the $^2$P$^{rm o}$,$_{1/2}$ and $^2$P$^{rm o}$,$_{3/2}$ levels. The new calculations are valid for temperatures down to an unprecedentedly low level (approximately 100 K). The newly calculated effective recombination coefficients allow us to construct plasma diagnostics based on the measured strengths of the ion{N}{ii} optical recombination lines (ORLs). The derived effective recombination coefficients are fitted with analytic formulae as a function of electron temperature for different electron densities. The dependence of the emissivities of the strongest transitions of ion{N}{ii} on electron density and temperature is illustrated. Potential applications of the current data to electron density and temperature diagnostics for photoionized gaseous nebulae are discussed. We also present a method of determining electron temperature and density simultaneously.
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The optical [N I] doublet near 5200 {AA} is anomalously strong in a variety of emission-line objects. We compute a detailed photoionization model and use it to show that pumping by far-ultraviolet (FUV) stellar radiation previously posited as a general explanation applies to the Orion Nebula (M42) and its companion M43; but, it is unlikely to explain planetary nebulae and supernova remnants. Our models establish that the observed nearly constant equivalent width of [N I] with respect to the dust-scattered stellar continuum depends primarily on three factors: the FUV to visual-band flux ratio of the stellar population; the optical properties of the dust; and the line broadening where the pumping occurs. In contrast, the intensity ratio [N I]/H{beta} depends primarily on the FUV to extreme-ultraviolet ratio, which varies strongly with the spectral type of the exciting star. This is consistent with the observed difference of a factor of five between M42 and M43, which are excited by an O7 and B0.5 star respectively. We derive a non-thermal broadening of order 5 km/s for the [N I] pumping zone and show that the broadening mechanism must be different from the large-scale turbulent motions that have been suggested to explain the line-widths in this H II region. A mechanism is required that operates at scales of a few astronomical units, which may be driven by thermal instabilities of neutral gas in the range 1000 to 3000 K. In an appendix, we describe how collisional and radiative processes are treated in the detailed model N I atom now included in the Cloudy plasma code.
In the first paper of this series, we study the level population problem of recombining carbon ions. We focus our study on high quantum numbers anticipating observations of Carbon Radio Recombination Lines to be carried out by the LOw Frequency ARray (LOFAR). We solve the level population equation including angular momentum levels with updated collision rates up to high principal quantum numbers. We derive departure coefficients by solving the level population equation in the hydrogenic approximation and including low temperature dielectronic recombination effects. Our results in the hydrogenic approximation agree well with those of previous works. When comparing our results including dielectronic recombination we find differences which we ascribe to updates in the atomic physics (e.g., collision rates) and to the approximate solution method of the statistical equilibrium equations adopted in previous studies. A comparison with observations is discussed in an accompanying article, as radiative transfer effects need to be considered.
In the second paper of the series, we have modeled low frequency carbon radio recombination lines (CRRL) from the interstellar medium. Anticipating the LOw Frequency ARray (LOFAR) survey of Galactic CRRLs, we focus our study on the physical conditions of the diffuse cold neutral medium (CNM). We have used the improved departure coefficients computed in the first paper of the series to calculate line-to-continuum ratios. The results show that the line width and integrated optical depths of CRRL are sensitive probes of the electron density, gas temperature, and the emission measure of the cloud. Furthermore, the ratio of CRRL to the [CII] at 158 $mu$m line is a strong function of the temperature and density of diffuse clouds. Guided by our calculations, we analyze CRRL observations and illustrate their use with data from the literature.
We have introduced a new method of estimating the electron temperature and density of H II regions by using single dish observations. In this method, multiple hydrogen radio recombination lines of different bands are computed under the assumption of low optical depth. We use evolutionary hydrodynamical models of H II regions to model hydrogen recombination line emission from a variety of H II regions and assess the reliability of the method. According to the simulated results, the error of the estimated temperature is commonly < 13%, and that of the estimated density is < 25% for a < 1% uncertainty of the observed line fluxes. A reasonable estimated value of electron density can be achieved if the uncertainty of the line fluxes are lower than 3%. In addition, the estimated values are more representative of the properties in the relatively high-density region if the gas density gradient is present in the H II region. Our method can be independent of the radio continuum observations. But the accuracy will be improved if a line-to-continuum ratio at millimeter wavelengths is added to the estimation. Our method provides a way to measure the temperature and density in ionized regions without interferometers.
Solving the recombination equation has been a long-standing challenge of emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of emph{stochastic} models of population genetics, into the deterministic setting. With the help of an ancestral partitioning process, which is obtained by letting population size tend to infinity (without rescaling parameters or time) in an ancestral recombination graph, we obtain the solution to the recombination equation in a transparent form.
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