Fluorescence and recombination in IC418

Excitation of emission lines by fluorescence and recombination in IC418

V. Escalante, C. Morisset11footnotemark: 1 and L. Georgiev11footnotemark: 1
Centro de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, Ap. Postal 72–3, C. P. 58091,
Morelia, Michoacán, México
Instituto de Astronomía, Universidad Nacional Autónoma de México, Ap. Postal 70–264, C. P. 04510, México, DF, México
Instituto de Astrofísica de Canarias, C/ Vía Láctea, S/N, 38205 San Cristóbal de la Laguna (Tenerife), España
E–mails: v.escalante@crya.unam.mx; chris.morisset@gmail.com; georgiev@astro.unam.mx
Abstract

We compare calculated intensities of lines of C ii, N i, N ii  O i and O ii with a published deep spectroscopic survey of IC 418. Our calculations use a self–consistent nebular model and a synthetic spectrum of the central star atmosphere to take into account line excitation by continuum fluorescence and electron recombination. We found that the N ii spectrum of s, p and most d states is excited by fluorescence due to the low excitation conditions of the nebula. Many C ii and O ii lines have significant amounts of excitation by fluorescence. Recombination excites all the lines from f and g states and most O ii lines. In the neutral–ionized boundary the N i quartet and O i triplet dipole allowed lines are excited by fluorescence, while the quintet O i lines are excited by recombination. Electron excitation produces the forbidden optical lines of O i  and continuum fluorescence enhances the N i forbidden line intensities. Lines excited by fluorescence of light below the Lyman limit thus suggest a new diagnostic to explore the inner boundary of the photodissociation region of the nebula.

keywords:
atomic processes– planetary nebulae: individual: IC 418
pagerange: Excitation of emission lines by fluorescence and recombination in IC418References

1 Introduction

With an apparent simple geometry the low excitation planetary nebula IC 418 lends itself to simpler models with fewer assumptions on its structure and kinematics than are generally necessary to reproduce observations of planetary nebulae (PNe). A recent deep spectroscopic survey of this object by Sharpee et al. (2003) (hereafter SWBH) identified several hundred lines in IC 418 from which Sharpee, Baldwin & Williams (2004) (hereafter SBW) derived ionic abundances for CNONe ions relative to H. Many dipole–allowed line intensities from those ions in that survey cannot be explained by the recombination theory with the same abundances derived from collisionally excited lines (CELs). The intensities of recombination lines are often used to measure ionic abundances because they depend more weakly on temperature and density than CELs. Abundances derived from recombination lines, however, are usually higher than those derived from CELs in the Orion nebula (Esteban et al., 1998; Baldwin et al., 2000; Esteban et al., 2004; Mesa–Delgado, Esteban, & García–Rojas, 2008), many H ii regions (García–Rojas & Esteban, 2007), and planetary nebulæ (Liu et al., 1995, 2001b; Luo, Liu & Barlow, 2001; Liu et al., 2006; Tsamis et al., 2008; García–Rojas, Peña M. & Peimbert, 2009; Otsuka et al., 2009). Williams et al. (2008) showed that CELs probably give the correct abundances because the values derived from CELs are consistent with those derived from UV absorption lines in a sample of four PNe. The discrepancies of less than a factor of 2 found by SBW in IC 418 between abundances from CELs and dipole–allowed lines are smaller than in other objects. Nevertheless it is important to ensure that the intensities of the dipole–allowed lines are not enhanced by additional excitation mechanisms besides recombination whenever they are used in temperature or density diagnostics (Fang, Storey & Liu, 2011) (hereafter FSL) or abundance determinations.

The usual procedure to determine a species X abundance directly from optical line intensities is to measure the ratio of the intensity of a line emitted by the species with respect to the  intensity and assume that the ratio of column densities producing the lines is equal to the abundance. Specifically, the abundance X/H is taken from the equation

(1)

where is the ratio of intensities corrected for reddening, and are the emissivities of a line emitted by X and of  respectively, both are integrated over some volume fraction of the nebula covered by the aperture, and means some kind of average of the emissivities over that volume fraction. Averaged emissivities over the volume within the solid angle of the aperture imply the adoption of average values for the temperature, density and filling factors.

An alternative procedure to determine chemical abundances in a nebula is to propose mutually consistent models of the nebula and the atmosphere of the exciting star or stars. The stellar parameters, chemical abundances and density profile of the nebula are inputs to a photoionization model, and their values are fixed by matching the predicted line intensities to the observations. The variation of stellar and nebular parameters of the model can be constrained by direct observations of the star and nebula to reduce the degeneracy of different parameters giving similar matches to the observed line intensities. Morisset & Georgiev (2009) (hereafter MG) showed that a consistent stellar energy distribution (SED) of the central star of IC 418 and a photoionization model give an impressive agreement of predictions and measured intensities of CELs and many recombination lines within observational errors. However most dipole–allowed lines in the SWBH survey were not included in the model by MG, and some of the ones that were included show observed intensities much larger than their predicted values because the MG calculations did not include fluorescence excitation.

In this work we add fluorescence excitation of permitted lines to a photoionization model and a SED similar to the ones used by MG, and compare the results with all lines observed by SWBH that have probable identifications as dipole–allowed lines of C ii, N i, N ii, O i, and O ii and optical forbidden lines of N i and O i. Continuum fluorescence of starlight was suggested as a mechanism to excite permitted lines in ionized nebulae by Seaton (1968) and Grandi (1975, 1976). Escalante and Morisset (2005) (hereafter EM) showed that fluorescence in Orion dominates the intensities of N ii permitted lines. The low excitation level of IC 418 and the resemblance of its ionization degree to that of the Orion nebula noted by Torres–Peimbert, Peimbert & Daltabuit (1980) suggest that a similar fluorescence mechanism may occur in both objects.

2 Line emissivities

In our previous work (EM) we found that the rate of continuum fluorescence excitation typically depends on the absorption of photons in several resonant transitions, also called pumping transitions, to quantum states of moderate excitation. Excitation by recombination on the other hand involves the capture of free electrons into a much larger number of excited states. In the fluorescence and recombination mechanisms subsequent transitions to lower states produce the optical lines observed in ionized regions although many lines in the UV and IR are also emitted.

Our calculation of quantum state populations is based on the cascade matrix formalism described in detail by EM. In that formalism excited states are populated by recombinations and by transitions from the ground and metastable states. The contribution of recombinations to the population of a state is given by the effective recombination coefficient of the state, . The effective fluorescence coefficient defined by EM, , gives the contribution of pumping transitions from the ground and metastable states to excited states that produce decays ending in state . Both coefficients can be calculated in terms of the cascade matrix of Seaton (1959). The emissivity of a line for a transition from state to with a branching ratio and frequency at a point in the nebula is

(2)

where is the electron density, is the density of the ion before recombination, and is the population density of the ground or metastable state of the recombined ion or atom. The branching ratio , where is the Einstein coefficient for transition from states to , and is the total decay rate of the upper state . The line effective recombination coefficient is defined as:

(3)

It is assumed that the ion density can be calculated from the ionization balance condition, and the ground and metastable state populations can be calculated from the balance of collisional and radiative transitions with the aid of a nebular photoionization model.

The cascade matrix formalism assumes that every transition from the continuum or from the ground or metastable state to a higher–energy state is followed by transitions to lower–energy states, and that metastable states are not significantly affected by those transitions. Those are valid assumptions at the temperatures and densities of a photoionized nebula because collisional excitation and deexcitation with electrons control the population of metastable states, but fluorescence can compete with collisions with electrons and atoms in the colder interface of the neutral and ionized part of a nebula. Bautista (1999) proposed that the forbidden lines of atomic N are excited by fluorescence and collisions with electrons and atoms in Orion. Because the collisional excitation of metastable states violates the assumption of downward transitions in the calculation of the cascade matrix, the population densities of the metastable and ground states, and , must be solved for from equations of the type:

(4)

where if state is energetically higher than , and is the collisional excitation or deexcitation rate from states to . The summations comprise all the metastable and ground states, except state . The system of equations (4) is non–linear because the effective fluorescence rates depend on the optical depth of transitions from the ground and metastable states to excited states (see equations [2] through [7] of EM). We found that the system (4) can be solved iteratively by updating the optical depths across the nebula, and then using matrix inversion to solve for the populations at each point in the nebula in each iteration. The five–state inversion formulae by Kafatos & Lynch (1990) can be easily modified to include the fluorescence rates in equation (4). The emissivity of a forbidden line is then

(5)

Effective recombination coefficients depend on temperature and more weakly on density. They have been tabulated with their radiative and dielectronic parts for spectroscopic terms of astrophysically important ions in the literature. We assume that  for an individual fine structure state of a given term is proportional to the relative weight of the state . This is a good approximation for direct recombinations from the continuum. Nevertheless it is worth noticing that  adds the contribution of a large number of cascading bound–bound transitions after the free-bound transition, and probabilities of fine structure transitions are not proportional to relative weights. To date only the calculation of effective recombination coefficients of  by FSL has considered the fine structure splitting of quantum states.

In the calculation of  we split quantum states in their fine structure components either assuming the LS or LK angular momentum coupling schemes as appropriate or using published intermediate coupling calculations when available. The fine structure of states can be important in fluorescence calculations because quantum selection rules can selectively pump certain states.

The calculation of  involves a large number of quantum states that can be reached by downward transitions following an absorption from the ground or a metastable state. Metastable states and some core–excited states of the form can build up a significant population under low density conditions because of their low transition probabilities to the ground state. The population densities, , in equation (2) include all the fine structure states of the ground and metastable terms. Optical lines involving core–excited configurations have often been attributed to low temperature dielectronic recombination (Nussbaumer & Storey, 1981), but radiative recombination or fluorescence followed by two–electron transitions can also produce excited–core configurations. EM found that it is important to take into account spin forbidden transitions and core excited configurations in the calculation of .

3 Atomic data

We used the compilation in the NIST Atomic Spectra Database (Ralchenko, Kramida & Reader, 2008) to classify quantum states and store the observed energies and probabilities for some transitions. However we relied substantially on more recent and complete calculations of probabilities from other authors. Systematic variations among different atomic databases have small effects in the cascade matrix in most cases because the calculation depends on branching ratios.

3.1

This ion has the simplest structure. The ground core term produces a doublet manifold of excited states . Consequently free–bound transitions tend to concentrate in fewer states, and give rise to more intense lines from states with higher quantum numbers. The excited cores , and produce quartet and doublet manifolds. We used the populations of the fine structure states of terms and as the variables in equation (2) for this ion. Some excited core configurations, like and , were also detected in IC 418 by SWBH.

We used term–averaged transition probabilities calculated by Nahar (1995) with the R–matrix approach supplemented with spin forbidden transitions from the NIST database. The latter compiles the Opacity Project calculations by Yan, Taylor & Seaton (1987), and some intermediate coupling calculations by Nussbaumer & Storey (1981). We split transition probabilities among fine structure components assuming pure LS coupling (Allen, 1973) since no significant departures from that coupling have been reported (Wiese, Fuhr & Deters, 1988). We used the effective recombination coefficients calculated by Dayal, Storey & Kisielius (2000).

3.2

The ground–core term of this ion produces singlet and triplet manifolds of excited states. The fine–structure populations of the terms , and , were used as the populations in equation (2). Terms with the excited cores and were detected in IC 418 by SWBH. Those cores produce singlet, triplet and quintet manifolds. The quintets are not reachable by transitions from the continuum if LS coupling selection rules prevail. Therefore the lines observed by SWBH between 5526.2 and 5551.9, which are probably identified with the N ii multiplet , may be produced by dielectronic recombination out of LS coupling followed by stabilizing transitions to the term. Recombination coefficients for those transitions have not been calculated yet to our knowledge.

The atomic data to calculate this spectrum was described in detail by EM. Different calculations of transition probabilities —with due account of the fine structure splitting and breakdown of the LS coupling scheme in 4f and 5g states— generally agree (Lavín, Olalla & Martín, 2000).

Transition (Å)
(1) (2) (3) (3) (4) (5) (6) (7)
5006 0.942 21 238.00
5005.15 1.000 9 77.20 105.00 108.28 1.246
5025.66 0.092 7 8.69 7.92 7.78 0.118 0.107
5001.47 0.907 7 85.60 78.00 76.36 1.050
5016.30 0.140 5 9.60 7.43 8.42 0.186 0.162
5001.13 0.844 5 58.20 45.00 50.75 0.976
4433 0.416 20 27.20
4433.48* 0.461 3 4.52 1.300 1.070
4442.02 0.258 5 5.17 5.35 4.22 0.695 0.824 0.578
4432.74* 0.830 7 18.40 19.00 18.98 1.790 1.926
4690 0.129 20 8.46
4678.14* 0.317 5 5.19 1.030 0.717
4694.64 0.481 5 6.18 6.40 7.88 0.607 0.753 1.076
4174 0.182 28 18.30
4171.60 0.508 7 16.50 12.10 12.76 0.448 0.544 1.181
4176.16* 0.380 7 13.20 9.18 9.54 1.130 1.280 0.886
4242 0.554 28 55.60
4236.93* 0.747 5 21.00 15.00 13.39 1.850 1.758
4246.86? 0.004 5 0.07 0.007 0.009
4241.76* 0.456 7 20.60 14.40 11.43 0.728 0.886
4241.79* 0.889 9 36.10 26.80 28.69 1.960 2.090
4237.05? 0.343 9 38.58 6.29 8.60 0.986 0.797
4089 0.069 28 6.92
4095.90 0.104 9 2.77 2.05 3.35 0.144 0.244
4096.57 0.004 7 0.103 0.075 0.10 0.009
4082.27 0.007 9 6.86 5.08 0.22 0.335 0.485 0.016
4082.89 0.043 7 0.41 0.30 1.08 0.011 0.100
4073.05 0.004 7 7.90 5.81 0.096 0.499 0.631 0.0089
4543 0.234 32 28.30
4530.41* 0.535 9 15.30 19.90 18.18 1.450 1.490 1.242
4552.52* 0.424 9 9.10 8.53 14.41 0.611 0.650 0.993
4039 0.765 32 92.40
4026.08 0.436 9 7.15 9.34 14.81 0.672 0.794 1.013
4041.31* 0.999 11 28.60 37.90 41.48 2.080 2.780 2.430
4043.53* 0.540 9 18.00 16.90 18.34 1.250 1.130 1.266
4035.08* 0.917 7 19.10 17.90 24.24 1.300 1.650 2.232
4058.16? 0.0012 7 0.080 0.074 0.033 0.0031

The notation in LK coupling is 4f .

* Observed in IC 418.

? Uncertain identification in IC 418.

averaged over values.

Table 1: Comparison of effective recombination coefficients and values for selected N ii lines at . (1) Branching ratio of the line or multiplet from EV, (2) statistical weight of term or state, (3) FSL, (4) EV, (5) Mar et al. (2000), (6) Shen et al. (2010), (7) Victor & Escalante (1988).

Most calculations of effective recombination coefficients give rates for terms in some coupling scheme, usually LS coupling. Escalante & Victor (1990) (hereafter EV) calculated  for the f states assuming an LK coupling scheme. In that scheme, the core total spin, is added to the total angular momentum to produce an intermediate angular momentum with values 3/2, 5/2, 7/2 and 9/2 for the f states. The valence electron spin is added to to give a doublet of total angular momentum for each LK term. Victor & Escalante (1988) and EV give transition probabilities and  averaged over the states of each term. To get the transition probability to a given term, the –averaged probability of the transition must be multiplied by the relative weight of the term. The probability of the inverse transition is the same for all the states of the term. We split the multiplets into fine structure components with formulae given by Escalante & Góngora–T. (1990). Effective recombination coefficients of LK terms were multiplied by the relative weight, , to get the fine structure . All of the above calculations to obtain the recombination and transition rates to individual fine structure states assume that the radial part of the dipole transition element of an LS or LK term does not change significantly among different states of a term.

Recently FSL calculated effective recombination coefficients of N ii fine structure states in intermediate coupling and including the effects of dielectronic recombination. Their rates of certain lines show a hitherto unknown strong dependence on electron density due to the variation of the populations of the parent ion ground states with density. Table 1 shows a comparison of effective recombination coefficients at and two electron densities for some of the most intense lines excited by recombination at that temperature.

There is general agreement between the new effective recombination coefficients of FSL and those of EV at the electron densities of and , but there are significant differences in some transitions, most notably in multiplet . Since there is agreement between the two calculations in some transitions of that term, the differences in the other transitions with the same upper state appear to arise from the branching ratio of the transition, , or more specifically from the transition probability. For the transitions with the largest disagreements in , the probabilities of Victor & Escalante (1988) are much smaller than the experimental measurements by Mar et al. (2000) and relativistic calculations by Shen, Yuan & Liu (2010). Those discrepancies may point to important relativistic effects in some transitions that were not taken into account in the term–averaged values of Victor & Escalante (1988) and the way in which we split the probabilities among the fine structure components. Unfortunately those transitions were not detected in IC 418 by SWBH, although they should be just below their detection limit if the larger branching ratios are correct.

3.3

This ion has a ground configuration . The populations of the fine–structure states of its terms ,  and  were used in equation (2) as the variables. Those terms are connected to quartet and doublet manifolds of excited states with several cores. SWBH possibly identified 85 transitions with the ground core, 32 transitions with the excited core, 12 transitions involving both cores, and a few lines with the excited core.

We used the transition probabilities of Nahar (2009) supplemented with the intermediate coupling calculations for the array by Liu et al. (1995), who found significant effects of LS coupling breakdown in 4f and some 3d terms. Terms with are better described in LK coupling (Wenåker, 1990). Effective recombination coefficients were taken from Liu et al. (1995) for the 3d and 4f terms, and from Storey (1994) for other states. The effective recombination coefficients of Nussbaumer & Storey (1984) for terms with the core involve only the dielectronic contribution. Transitions between states with the core and states with the core, some observed with non–negligible intensity in IC 418, may add a contribution of radiative recombination to the terms with the core at lower temperatures.

3.4 N and O

For nitrogen we used the NIST compilation of transition probabilities mentioned at the beginning of this section. For oxygen we used the model potential calculations of Escalante & Victor (1994) complemented with the NIST compilation for spin forbidden and two–electron transitions. Since these atoms are abundant in the neutral zone, the main transitions pumping the lines by fluorescence will be below the Lyman limit. Effective recombination coefficients were taken from Escalante & Victor (1992) and Péquignot, Petitjean & Boisson (1991). Effective collision strengths for excitation of O metastable states were taken from Berrington & Burke (1981) and Bell, Berrington & Thomas (1998) for electron collisions and Krems, Jamieson & Dalgarno (2006) and Abrahamsson, Krems & Dalgarno (2007) for collisions with H atoms. Effective collision strengths for excitation of N metastable states by electrons were taken from Tayal (2006). Transition probabilities for the N and O metastable states were taken from Froese Fischer & Tachiev (2004).

Atomic N has the same atomic configurations as  and the populations of the five states of the metastable terms , and were found from equation (4). Atomic O has a ground configuration with terms , and , and its excited states in the ground core configuration form quintet and triplet manifolds. There is a singlet manifold with a excited core. SWBH detected 10 possible lines with that core, but there are no calculations of effective recombination coefficients for them. Recombination from the ground states of  or fluorescence from the states can affect the populations of the metastable singlet states and through spin–forbidden transitions from the excited triplet states. Those transitions will be important in the cascade only if the stronger resonant transitions of the triplets are optically thick, the so called case B (Escalante & Victor, 1992), and the temperature is low enough to prevent collisions with electrons and H atoms from dominating the populations of the O metastable states.

4 Model calculations

The efficiency of fluorescence to enhance dipole–allowed lines depends on the transfer of starlight, the intensity of the diffuse field and the ion distribution throughout the nebula. Therefore a detailed SED and model of the nebula are required to predict adequately the intensity of permitted lines.

4.1 Stellar energy distribution

Ions Levels Superlevels
H i 30 20
He i 69 45
He ii 30 30
C ii 92 40
C iii 243 99
C iv 64 59
N ii 85 45
N iii 70 34
N iv 76 44
N v 67 45
O ii 123 54
O iii 170 88
O iv 78 38
O v 152 75
O vi 13 13
Si iii 34 20
Si iv 33 22
P iv 178 36
P v 62 16
S iii 28 13
S iv 142 51
S v 98 31
S vi 58 28
Ne ii 48 14
Ne iii 71 23
Ne iv 52 17
Ar iii 36 10
Ar iv 105 31
Ar v 99 38
Fe iii 1433 104
Fe iv 1000 100
Fe v 1000 139
Fe vi 433 44
Fe vii 153 29
Table 2: Ions used in the stellar model
Figure 1: Continuum–normalized SED with identifications of stellar lines. Unlabelled lower vertical lines (blue) show the wavelengths of the transitions in N ii multiplet 533.51–533.88, and N ii line 582.156 in the rest frame of the photosphere.

To evaluate the amount of emitted energy better and increase the resolution of the SED near the wavelengths of the most important pumping transitions, we calculated a new model of the central star atmosphere using the cmfgen code (Hillier and Miller, 1998) with a more complex atomic structure than the one used in MG as shown in table 2. The increased number of lines in the far UV region of the spectrum changed the ionization balance of the nebula. Following the same procedure used by MG, we adjusted the stellar atmosphere model, increasing its temperature to 39000 and keeping the other parameters unchanged. The new self–consistent stellar and nebular models reproduce the intensities of the emission lines common to both models with a quality factor (see definition in equation (6) of MG) of the same order of magnitude as the one obtained with the previous SED. The new high–dispersion () SED was corrected for a stellar rotation velocity of 30 as derived in MG.

The Doppler shift of the resonant transition frequencies due to internal motions of the nebular gas must be taken into consideration with a SED of that resolution as discussed in section 5.6. We adopted a velocity field with a maximum velocity at the outer edge of the nebula. MG adopted a similar velocity law to reproduce the profiles of the , [N ii] and [O iii] lines (see appendix B of MG). The effects of other velocity fields and of turbulence on the calculated line intensities are discussed in section 5.6.

We did not find a systematic decrease of fluorescence excitation of the CNO lines in the SWBH survey with a higher–dispersion SED as reported for the Balmer lines by Luridiana et al. (2009). The probable reason is the fact that excited states in multielectron species have several resonant transitions distributed over a range of wavelengths. The fluorescence excitation to those states can increase or decrease with a high–dispersion SED depending on the coincidence of those resonant transitions with the emission peaks or absorption troughs of the stellar wind profile in the rest frame of the absorbing ion or atom. The resolution of the adopted SED is larger than the width of the pumping lines in the gas. Therefore we do not expect any remaining bias in the predicted intensities with the adopted SED.

Fluorescence excitation depends on a large number of resonant transitions, but there are a few transitions especially important in the populations of certain states. Fig. 1 shows two sections of the SED with examples of important transitions in the excitation of N ii lines by fluorescence. The low abundance of  in the stellar atmosphere produces little depression of the continuum at the N ii pumping transitions in the gas, but other species do produce important absorption features in the SED as shown in Fig. 1

4.2 Photoionization model

The photoionization model calculated by MG took into account the small ellipticity of IC 418 by using the pseudo–3D code cloudy_3D (Morisset, 2006), which allows the calculation of nebular models with complex geometries. The near spherical symmetry of IC 418 and the small angle of the aperture used by SBW allowed us to approximate the nebula with a 1D spherical model to speed up the calculation of thousands of transitions in this work. We extracted continuum opacities, ground and metastable state populations, ion and electron densities, and electron temperatures from version c08.00 of cloudy(Ferland et al., 1998) with the SED described above and a density distribution similar to the one used by MG. Emissivities calculated with equations (2) and (5) are then integrated along a beam across the nebula to simulate the size and position of the aperture used by SBW. Images of the slit position on the nebula are given in MG.

The stellar light is attenuated by geometrical dilution and continuum opacity as given by cloudy. The self–absorption within the resonant transition is taken into account with the ‘pumping probability’ defined by Ferland (1992). The calculation of  uses the escape probability formalism of Hummer & Storey (1992) to approximate the propagation of photons in the resonant transitions with an overlapping continuum in the nebula. This in effect takes into account the variation of optical depth in a medium partially thick in the resonant transitions, a situation named ‘case D’ by Luridiana et al. (2009). Additional details can be found in EM.

Although MG used some nebular lines to adjust the stellar atmosphere and nebular model parameters, most of their calculated and all of the calculated line intensities in the present work are ab initio predictions of the SED and nebular model. The abundances adjusted by MG with this procedure and used in this work are given in table 3. The density profile in this work is

where is the distance to the central star in cm. Table 4 gives the adopted values for parameters , , , , and . Parameters , have intermediate values between the long and short axes in the ellipsoidal model of MG. This density profile was chosen to match the HST images of the intense nebular lines as discussed in detail by MG (see their figure 5). With few exceptions, the predicted line intensities in our 1D model vary by less than 30 per cent when are varied simultaneously by 20 per cent or when and are varied simultaneously by 20 per cent.

Element
He
C
N
O
Ne
Mg
Si
S
Cl
Ar
Fe
Table 3: Element abundances in the nebular model
Parameter Unit Value
2850
5260
9500
20500
cm 16.06
cm 16.28
cm 17.02
cm 17.10
cm 15.96
cm 16.46
Table 4: Nebular density profile parameters

4.3 The photodissociation region

It has long been known that IC 418 has a PhotoDissociation Region (PDR) extending beyond the optical nebula (Cohen & Barlow, 1974; Taylor & Pottasch, 1987) with low ionization and atomic components (Monk, Barlow & Clegg, 1990; Taylor, Gussie & Goss, 1989; Meixner et al., 1996). Taylor et al. (1989) measured an H mass of M☉ over a radius arcsec from the center of the nebula. Thus far there have been no detections of molecular emission in IC 418 (Huggins et al., 1996; Dayal & Bieging, 1996; Hora et al., 1999). Liu et al. (2001a) obtained an average density for the PDR of from observations of the [C ii] 158–m and [O i] 63–m and 146–m lines. That density is much higher than the one needed to explain the radio observations and suggests the existence of a narrow dense shell just outside the ionization front or clumps in the PDR.

The cloudy nebular model can be readily extended to the PDR by adding an outer neutral atomic envelope to the ionized region starting at a distance of the central star . We chose the following density profile for the PDR:

(7)

where is the electron temperature in kelvins, and and are given in table 4. This density profile is constrained by the observed fluxes of the FIR [C ii] and [O i] lines. The temperature dependence in Eq. (7) allows for a smooth transition between the ionized and neutral material by increasing the density as the temperature drops. The extent of the neutral region needed to match the observed intensities of the FIR O i and C ii lines is just a few percent of the radius of the ionized region. A more realistic model of the ionized and molecular interface needs a hydrodynamic model, which is beyond the scope of this paper.

5 Results

5.1 Selection of observations

Proper line identification of weak spectral lines is a fundamental problem in the analysis of deep nebular spectroscopy. SWBH presented the line identification code emili to automate and standarise an otherwise tedious labour of identifying several hundreds of spectral lines. SBW selected a subset of emission line intensities from the survey of SWBH based on the likelihood of a correct, unique identification as given by emili and the availability of published effective recombination coefficients to determine abundances. Some lines in SWBH were not taken into account by SBW because those lines were probably blended with other emission lines or emili gave more than one plausible identification for them.

We have reexamined the SWBH line list and added many measured lines of C ii, N i, N ii, O i and O ii to the selection of SBW in order to compare them with our calculations either because we could estimate their effective recombination coefficients reasonably well or because they were the most probable contributor to a blend. Some cases for individual species are discussed in the following sections.

Published calculations often tabulate the line effective recombination coefficient in equation (3) for the most intense lines only. Coefficients for weaker lines with the same upper state can be readily estimated by dividing by the branching ratio of the tabulated transition and multiplying by the corresponding of the desired line as in equation (2). In order to do this consistently, it is necessary that authors publish the transition probability data or at least the branching ratios used in their calculations (Nussbaumer & Storey, 1984; Escalante & Victor, 1990; Pequignot et al., 1991; Escalante & Victor, 1992; Liu et al., 1995).

The issue of multiple identifications is more complicated. A line with multiple identifications may be either a real blend or some of the proposed identifications may not be real. Our calculations show that in many cases a transition in a possible blend contributes insignificantly to the measured intensity. When a transition in a blend of two transitions of the same species contributes more than 10 per cent of the total intensity, we have added the calculated intensities of the transitions to compare them with the measurements by SWBH. Blends of emissions of the same species are thus compared with our computed spectra without the need to assume theoretical intensities to ‘deblend’ the observed lines. Blends of emissions of different species are compared directly with the predicted intensities.

5.2 Comparison with observed intensities

In Fig. 2 to 6 we compare predicted intensities with observed intensities in a scale of . Tables 5 to 14 give the predicted intensities of dipole–allowed lines with intensities higher than of the  strength, which is close to the lower limit of detection in SWBH. Tables 13 and 14 also include predicted intensities of the optical forbidden lines of N i and O i. Some of the wavelengths given in the second column of the table are calculated from energy levels and have limited accuracy. The fraction of calculated intensity due to recombination is given in the third column of the tables. The calculated and observed intensities in the fourth and fifth columns are normalized to . The bottom line in each table gives the average of the ratio of the intensity due to recombination to the total calculated intensity and the average of the ratio of the calculated intensity to the observed intensity for each species. We have found some undetected lines with calculated intensities above the detection limit in SWBH. Some of them are blended with intense nebular lines, and a few were measured, but apparently not identified by emili. The observed intensity of lines not selected by SBW are marked with ‘?’ in the sixth column of the tables.

The uncertainty of each line intensity depends on several factors like the signal–to–noise ratio (), its relative width with respect to the instrument resolution and whether the line may be blended with other lines. In order to make meaningful comparisons with observations, MG estimated a variable uncertainty of the line fluxes in SBW between 10 per cent for the brighter lines to 30 per cent for the weaker lines. SBW suggest an uncertainty of 20 per cent for lines with a . Most of the lines analysed in this work are weaker than 0.01 times the intensity of , and have a . Therefore we will adopt a minimum general uncertainty of 20 per cent for all dipole–allowed lines in the SWBH survey.

Our calculations tend to underestimate most of the lines with dubious identification according to emili. Rola & Pela (1994) and Wesson, Stock & Scicluna (2012) have shown that measured intensities of lines with are strongly biased upwardly. We only have two lines with an underestimated predicted intensity and a measured , which corresponds to a true between 6 and 8 at the 1– confidence level according to the calculations of Rola & Pela (1994). In most of our cases it is more likely that the underestimated predictions indicate incorrect identifications or blends with other lines rather than uncertainties in the measured values. We have not included in the tables and figures features with a dubious identification and a predicted intensity less than 0.1 of the measured value.

The excitation mechanisms of a spectrum can be diagnosed by contrasting the intensities of lines yielded by different atomic configurations as done by Grandi (1975, 1976). Lines from s, p and most d states with the same spin multiplicity as that of the ground state are enhanced in varying degrees by fluorescence relative to recombination lines if the recombined ion concentration is sufficiently high. Transitions from d states that are not connected to the ground or a metastable state by a resonant transition and transitions from f and g states are excited mostly or totally by recombination.

SBW found that some dipole–allowed lines of a species have profiles similar to those of the forbidden lines of the next higher ionization stage of the species, (e.g. some O i line profiles are similar to [O ii] profiles), indicating that they are produced in the same part of the nebula by recombination of the more ionized stage. Likewise they found that other dipole–allowed lines of the same species have profiles similar to those of the forbidden lines of the same ionization stage, indicating that they are produced by fluorescence excitation of that species.

SBW also found a correlation between the line width of the species producing the line and the ionization potential of the species, which indicates a relationship between the line width and the ionization stratification in the nebula. Recombination lines of species with lower ionization potential generally have broader lines and their widths are similar to those of the forbidden lines of the next higher ionization stage, indicating again a common place of origin within the nebula.

SBW proposed that line profile and line width similarities can be used to discriminate the excitation mechanism of the lines. The contributions of fluorescence and recombination, however, are comparable in many lines and produce many exceptions to the discriminating criteria proposed by SBW as discussed for particular cases below. Therefore a more quantitative analysis is needed to determine the excitation mechanism of a line.

Figure 2: Comparison of C ii intensities observed by SBW with predicted intensities produced by recombination and fluorescence of lines from s states (black squares), p states (black triangles), d states (open red circles), and f and g states (filled blue circles). The dash at the bottom of the vertical lines marks the intensity produced by recombination excitation only. The broken horizontal line is the average value of . Note that the observed intensities are normalized to .
Figure 3: Same as in Fig. 2 for N ii lines.
Figure 4: Same as in Fig. 2 for O ii lines.

5.3 C ii

The agreement of predicted recombination intensities within 20 per cent of observed values in the SBW selection of 9 lines or blends of lines from f and g states supports the accuracy of the recombination rates for this ion. That remarkable consistency can be explained by three factors concerning the observed high angular momentum states: those states are less dependent on atomic calculation assumptions because of their reduced non–hydrogenic effects, their populations are free from optical depth effects, and their fine–structure components are often blended in spectroscopic terms. In those blends, the effective transition rate of the term is a weighted average of several fine structure transition probabilities so that the total intensity of the blend is the sum of intensities of those components. Quantum calculations with different assumptions tend to agree on the transition probabilities for the more intense components of a term. The average tends to cancel out differences in the calculated –values of the fine structure components while the summation gives more weight to the components with the larger intensities and lower observational errors. Measurement errors are also expected to decrease with the higher S/N of a blend of several lines belonging to the same term.

Recombinations produce more than half the intensity of most C ii lines, but we find an important fluorescence contribution to all the observed lines from s, p and d states. SBW did not find differences in the line profiles of those lines with profiles of recombination lines as should be indicated by their proposed criteria based on line profile differentiation. The fluorescence contribution is particularly important in multiplets 3918.97, 3920.68, 4637.63–4639.07, 5889.28–5891.60, 6257.18–6259.80, and 6578.05, 6582.88, and it is mostly due to absorptions from the ground state in the doublet 636.994, 636.251, and the triplets 560.239–560.439, 543.258–543.445, followed by decays to term . This fluorescence excitation explains the enhanced intensities of those multiplets relative to the recombination lines, and the seemingly high  abundances derived from their intensities by SBW using recombination rates alone.

We added 13 lines from the SWBH survey with excited–core upper terms and and two lines from the term using additional effective recombination coefficients of Davey et al. (2000) published on line at the CDS site. Term is mostly excited by fluorescence through absorptions in multiplet 549.320–549.570. The calculated intensities for decays from that term agree with the observations within our adopted uncertainty intervals except for the line 7508.89 apparently undetected by SWBH, and the line 5121.83 underestimated by a factor of 2.8. Lines from term on the other hand are underestimated by our calculations by 30 to 50 per cent. Lines from the state have a 70 per cent excitation by fluorescence while lines from the other state have a 40 per cent excitation by fluorescence mainly in absorptions in multiplet 530.275–530.474. The relatively intense line 3835.72 is probably blended with the Balmer H9 line. The two blended lines and at 7860.50 are the only f multiplet with a strong discrepancy with observations with an observed intensity 2.8 times larger than the predicted intensity. The discrepancy may be due to uncertainties in the measurement because the observed S/N of 28.7 in SWBH is lower than the other C ii blends of f and g states and the intensity of the other blend from the term is within the uncertainty interval of the observed value.

Lower–Upper (Å)
3831.7 0.512 2.10 3.00 ?
3835.7 0.226 2.51
3836.7 0.226 0.50
3919.0 0.102 8.87 10.68
3920.7 0.102 17.70 20.52
4267.3 0.989 59.20 57.12
§ 4292.2 1.000 0.81 0.79
4329.7 0.954 0.68 0.70
4491.1 1.000 1.18 1.09
4618.8 0.942 0.97 1.07
4637.6 0.492 0.56 0.56
4638.9 0.807 0.65
4639.1 0.492 0.11
4744.8 0.654 0.09
4801.9 1.000 1.82 1.83
5032.1 0.512 2.48 4.34 ?
5035.9 0.226 2.97 5.58 ?
5040.7 0.226 0.59
5120.1 0.077 0.19
5121.8 0.077 0.96 2.68 ?
5125.2 0.043 0.69 0.58 ?
5127.0 0.043 0.34 0.30 ?
5341.5 1.000 3.11 2.77
5889.3 0.506 0.30
5889.8 0.506 2.69
5891.6 0.406 1.86 1.81
6145.9 0.969 2.22 2.53
6257.2 0.270 0.67 0.52
6259.6 0.544 0.64 0.84
6259.8 0.270 0.13
6460.1 1.000 6.04 5.84
6578.1 0.654 42.90 53.74
6582.9 0.527 26.60
7231.3 0.632 26.60 16.92
7236.4 0.836 43.30 46.73
7237.2 0.632 5.30 4.89
7508.9 1.000 0.17
7508.9 1.000 0.23
7508.9 0.077 0.25
7519.5 0.077 1.23 1.03 ?
7519.9 0.043 0.89 0.92 ?
7530.6 0.043 0.44 0.38 ?
7860.2 0.943 0.09
7860.5* 0.962 0.13 0.36 ?
8139.6 1.000 0.24
8139.6 1.000 0.31
8867.6 0.923 0.11
8868.1 0.956 0.16

§ Terms with no subscript are blended transitions of several states of angular momentum .
3p’ is core excited configuration .
*7860.5 includes blend with .

Table 5: Predicted and observed line intensities of C ii. is the fraction of the calculated intensity due to recombination, is the predicted intensity, is the measured intensity with a 20 per cent minimum uncertainty. The ? marks measured intensities taken from SWBH, but not selected by SBW.
Lower–Upper (Å)
9221.1 1.000 0.45
9221.1 1.000 0.35
9238.3 0.512 0.14
9251.0 0.226 0.17 0.24 ?
Table 6: continued

5.4 N ii

Fluorescence is the main excitation mechanism for most N ii lines in IC 418, but to a lesser extent than in the Orion nebula. The main pumping mechanisms in this ion were discussed in detail by Escalante and Morisset (2005). The ground core offers several pumping channels to the and terms through multiplets 529.36–529.87, 533.51–533.88 and 508.48–509.01. The only 3d term with significant recombination excitation is , but its brightest components at 5001.13, 5001.13 and 5005.15 are blended with the [O iii]5006.84 nebular line. The singlet lines 4447.03 and 6610.56 listed by SBW are also excited mostly by fluorescence due to absorptions in the transitions 534.657 and 574.650 respectively. The first one is a spin–forbidden transition with the ground triplet term while the second demonstrates that a metastable state can also produce fluorescence excitation.

The disagreement of observed intensities with predicted intensities in lines excited by fluorescence is greater in this ion. There is a systematic underestimation of the calculated values of lines from 3d states of 30 to 70 per cent. The rest of the calculated intensities selected by SBW are within 40 per cent of the observed values.

The 4f states are populated by recombination. Direct recombinations and transitions from the 4f states produce between 30 and 60 per cent of the intensity of the lines from the and terms. EM showed that fluorescence cannot significantly populate f and higher angular momentum states in  because quantum probabilities strongly favour downward transitions with decreasing angular momentum. That is a well known trend of transition probabilities inferred from atomic data compilations and theoretical considerations (Khriplovich & Matvienko, 2007). Consequently d states have a greater probability of decaying to p states than to f states. Should fluorescence enhance an f state population by decays from a higher d state, lines from lower p states, like 4630.54, would show at least a 70 per cent enhancement in their predicted intensity (EM). In our present calculations that line is already overpredicted by 20 per cent above its observed value without any plausible fluorescence contribution to f states. The enhanced intensity of the 5679.56 line by fluorescence in IC 418 puts its ratio with the recombination line 4041.31 out of the and ranges in fig. 8 of FSL, and highlights the importance of determining the atomic processes that excite a line before it is used as a diagnostic tool.

We have added 15 lines from the SWBH survey that were omitted in the analysis of SBW. Some like 4241.76, and 4241.78 are blended, and 4237.05 is probably blended with the transition 4236.91 listed in the selection of SBW. There are four lines standing out from f states with predicted intensities significantly below the observed values: 4058.16, 4176.16, 4246.71, 4433.48, and 9794.05, which are discussed below.

Because there is only one more line from a 4f D term with a secure identification (4678.14) and an intensity 15 per cent above the predicted value, we cannot assert whether the effective recombination coefficient of the 4433.48 line is underestimated. The other line produced by a 4f D term listed in SWBH, 4432.74, may be blended with a [Fe II] line, but our calculations predict an intensity 30 per cent above the measured value. The effective recombination coefficients of FSL and EV at agree for the lines of multiplet 4432.74–4442.02.

Our calculations predict intensities 0.002 times and 0.006 times the observed intensities of the lines 4058.16 and 4246.71 respectively. The low S/N of 10.3 and 9.2 and the displacement between the tabulated and observed wavelength of and respectively reported by SWBH for those lines suggest that they may be misidentifications. Other lines of the term , like