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Collision strengths for FIR and UV transitions in P iii and the phosphorus abundance

Collision strengths for FIR and UV transitions in P iii and the phosphorus abundance Collision strengths for FIR and UV transtions in P iii and the phosphorus abundance 1 1 1,2,3 Rahla Naghma , Sultana N. Nahar , Anil K. Pradhan 1 2 3 Department of Astronomy, Chemical Physics Program, Biophysics Graduate Program, The Ohio State University, Columbus, OH 43210, USA. Accepted xxxxxx Received xxxxxx; in original form xxxxxx ABSTRACT Phosphorus abundance is crucial for DNA-based extraterrestrial life in exoplanets. Atomic data for observed spectral lines of P-ions are needed for its accurate determi- nation. We present the first calculations for collision strengths for the forbidden [P iii] 2 2 o fine structure transition 3s 3p( P ) within the ground state at 17.9 μm , as well 1/2−3/2 2 2 o 2 2 2 2 as allowed UV transitions in the 3s 3p( P ) → 3s3p ( D , S , P ) 3/2,5/2 1/2 1/2,3/2 1/2,3/2 multiplets between 915-1345 A. Collision strengths are computed using the Breit-Pauli R-Matrix method including the first 18 levels, and they exhibit extensive auto-ionizing resonance structures. In particular, the Maxwellian averaged effective collision strength for the FIR 17.9 μm transition shows a factor 3 temperature variation broadly peaking at typical nebular temperatures. Its theoretical emissivity with solar phosphorus abun- dance is computed relative to Hβ and found to be similar to observed intensties from planetary nebulae; the abundances derived in earlier works are 3-5 times sub-solar. The results pertain to the reported paucity of phosphorus from preferred production sites in supernovae, and abundances in planetary nebulae and supernova remnants. Key words: ISM: atoms ¡ Interstellar Medium (ISM), Nebulae, ISM: supernova rem- nants, Physical Data and Processes ¡ atomic processes, astrobiology, infrared: general 1 INTRODUCTION using singly ionized P ii lines found up to 100 times the P/Fe ratio in the young core-collapse SNR Cassiopeia A than the Phosporus abundance is of considerable interest in the Milky Way average (Koo et al. 2013). Phosphorus is chemi- search for life forms in exoplanets. It is the backbone element cally very reactive, so its low gas phase abundance may also in the DNA molecule, enabling chemical bonds among myr- be difficult to determine due to dust and grain formation. iad nucleotides that constitute the complex double-helical structure. However, ascertaining nucleosynthesis pathways Despite its astrophysical and increasing astrobiological and determining the actual abundance of phosphorus (Z importance, theoretical spectral analysis is hampered by the = 15) is challenging because it is much lower than low-Z paucity of radiative and collisional atomic data for phos- α-elements, and orders of magnitude lower than the other phorus ions. It is surprising that very little data for the five most common elements of the six that constitute the important low ionization stages of P-ions in stellar and neb- CHONPS-based life organisms on the Earth. The photo- ular sources are available, relative to nearly all other first spheric solar abundances numerically relative to hydrogen and second row elements (viz. Pradhan and Nahar 2011). −4 −5 are (Asplund et al. 2009): C (2.7 ×10 ), N (6.8 ×10 ) O Electron impact excitation cross sections for P i have been −4 −7 −5 (4.9 ×10 ), P (2.6 ×10 ) and S (1.3 ×10 ). calculated in the Born approximation for excitations from Phosphorus abundances have been measured from the the ground 3p up to several nℓ sub-orbitals (Ganas 1998). mid-infrared [P iii] 17.9 µ m observations of late stages of Elaborate Dirac R-Matrix calculations for photoionization stellar remnants such as planetary nebulae (Pottsch et al. of low-lying ground and metastable levels of P iii have been 2008, Pottasch and Bernard-Salas 2008, Otsuka et al. 2011) done over a small photon energy range, with good agree- and from ground based observations of FGK dwarf stars ment with experimental measurements (Wang et al. 2016). (Maas et al. 2017). Whereas phosphorus, with an odd atomic Recently, sophistcated Breit-Pauli R-Matrix (BPRM) cal- number Z=15, can be synthesized during the AGB phase of culations have been carried out for photoionization of a low-mass stars, it is thought to be mainly produced in evo- large number of P ii levels using an 18-level coupled chan- lutionary stages of massive stars, before and during super- nel wavefunction expansion for P iii (Nahar et al. 2017a,b,c); novae explosion by neutron capture with silicon. An analysis very good agreement was found with the experimental P ii Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 photoionization cross sections measured at the Berkeley Ad- expression gives the emissivity in terms of only the electron vanced Light Source, particularly for the detailed resonance impact excitation rate coefficient and transition energy hν, structures in the near-threshold region. These earlier works 2 o 2 o 2 o 2 o ǫ( P − P ) = N N q( P − P )hν/4π. (3) e ion 3/2 1/2 3/2 1/2 forms the basis for the calculations reported in this Letter. There are no other previous calculations for collisional Eq. (3) implicitly assumes that all excitations to the up- 2 o excitation of low ionization stages of P-ions. We also develop per level P would be followed by downward decay to 3/2 an atomic physics framework for astrophysical spectral di- 2 o the ground state P , leaving the temperature-dependent 1/2 agnostics in nebular environments as function of tempera- electron impact excitation rate coefficient q as the only im- ture, density and ionization equilibrium, potentially leading portant quantity to be calculated. That, in turn, is related to to more accurate abundance determination. the Maxwellian averaged effective collision strength Υij(Te) as −6 g 8.63 × 10 j −E /kT ij q (T ) = q e = Υ(T ), (4) ij e ji e 1/2 2 PHOSPHORUS ABUNDANCE ANALYSIS g g T i i Previous works are based on observational analysis of rela- and tive intensities of phosphorus lines compared to other ele- Υ (T ) = Ω (E) exp(−E/kT )d(E/kT ), (5) ments. For example, nebular abundances have been deter- ij e ij e e mined in planetary nebulae (PNe) NGC 3242 and NGC 6369 from mid-IR observations of [P iii] forbidden 17.9 µ m line us- where E is the energy difference and Ω is the collision ij ij ing the Infrared Spectrograph aboard the Spitzer Space Tele- strength for the transition i → j. The exponentially decay- scope and the Short Wavelength Spectrograph on the Infrared ing Maxwellian factor implies that at low temperatures only Space Observatory (Pottasch and Bernard-Salas 2008) and the very low energy Ω (E)) would determine the Υ(T ). ij e NGC 2392 (Pottasch et al. 2008). A comparison of abun- Furthermore, the detailed Ω(E) is generally a highly energy- dances for NGC 3242 shows phosphorus underabundance in dependent function due to autoionizing resonances, which a number of PNe, by a factor of 5 relative to solar, and more leads to temperature sensitivity in the rate coefficient q(T ) than a factor of 3 in NGC 6369. The large discrepancies are via Υ(T ) as in Eqs. (4-5). attributed to dust formation (Pottasch and Bernard-Salas 2008). However, the results are model dependent since they entail atomic parameters and ionization fractions not known 3 THEORY AND COMPUTATIONS to high precision. For a single observed line the ion abundance may be de- A brief theoretical description of the calculations is given. rived from the measured intensity ratio under certain con- In particular, we describe relatvistic effects and the repre- ditions. Relative to recombination line Hβ, we may write sentation of the (e + ion) system. (Pottasch and Beintema 1999) I N λ A N ion ion Hβ ji j 3.1 Relativistic fine structure = N (1) I N λ α (Hβ) N Hβ p+ ji R ion The relativistic Hamiltonian (Rydberg units) in the Breit- where N is the ionic abundance, N is the upper level pop- ion j Pauli R-matrix (BPRM) approximation is given by ulation, A i is the Einstein decay rate between levels j → i, BP and α is the Hβ-recombination coefficient. The present case H = N+1 n o P P N+1 N+1 (6) 2 mass Dar so of [P iii] is similar to the well-known C ii 157 µ m line emit- 2Z 2 −∇ − + + H + H + H . i N+1 N+1 N+1 i=1 r r 2 2 o j>i i ij ted via the 2s 2p P transition (Blum and Pradhan 1/2−3/2 1991). Theoretically, we write line emissivity for the [P iii] where the last three terms are one-body relativistic correc- FIR transition formed with a given phosphorus abundance tions of the Breit interaction, respectively: as (Pradhan and Nahar 2011) mass α 4 the mass correction term, H = − p , 4 i Dar Zα 2 1 2 o 2 o 2 o the Darwin term, H = ∇ ( ), (7) 4 i r hνA( P − P ) N( P ) i 3/2 1/2 n(P III) 3/2 so 2 1 ǫ(17.9m µ ) = × × the spin − orbit interaction term, H = Zα l .s . 3 i i i r 4π N ((P III) n(P ) i n(P ) × × n(H) ergs/cm /sec. (2) 3.2 Wavefunction representation and calculations n(H) Based on the coupled channel approximaton, the R-matrix The sum in the denominator on the RHS of Eq. (2) refers to method (Burke 2011) entails a wavefunction expansion of all levels included in the atomic model. Calculating the level the (e + ion) system in terms of the eigenfuctions for the populations requires rate coefficients for contributing atomic target ion. In the present case we are interested in low-lying processes that may be due to recombination-cascades, elec- FIR transition within the ground configuration 3s 3p and tron impact excitation and fluorescent excitation from an the next excited configuration 3s3p . Therefore we confine external radiation field. In addition, Eq. (2) also depends on ourselves to an accurate wavefunction representation for the ionization balance for existing states in the plasma, as well first 18 levels dominated by the spectroscopic configurations as the elemental abundance itself – the quantity to be de- 2 2 6 2 2 o 2 4 2 2 [1s , 2s , 2p ]3s 3p( P ), 3s3p ( P , D , S , termined. However, if the two closely-spaced levels are effec- 1/2,3/2,5/2 3/2,5/2 1/2 1/2,3/2) 2 2 2 2 2 2 2 o tively de-coupled from other levels in the ion then a simple P ), 3s 3d( D ), 3s 4s( S ), 3s 4p( P ), 1/2,3/2 3/2,5/2 1/2 1/2,3/2 Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 4 RESULTS We describe the two main sets of results for the FIR and the UV transitions, as well as the diagnostic lines. Collision strengths have been computed for all 153 transitions among the 18 P iii levels. Selected results are presented below; no previous data are available for comparison. 4.1 The forbidden 17.9 µ m transition The calculated fine structure collision strength is shown in Fig. 2a, that exhibits considerable autoionizing resonance structures and energy dependence throughout the range up to the highest level of the P iii ion included in the BPRM Figure 1. Energy diagram of P iii showing the ground 3s 3p and 3 2 o wavefunction expansion, E(3p P ) = 1.45 Ry. The fall- 3/2 the first excited configuration 3s3p levels. The energy separation off for E > 1.0 Ry indicates that the collision strength is 2 o of the ground state fine structure P transition at 17.9 1/2,3/2 much lower at higher energies, and has converged for this μm is 0.0051 Ry, and well separated from the dipole allowed UV forbidden transtion. 2 o 2 2 2 transitions of the P − D, S, P multiplets between 915− 1/2,3/2 One particularly noteworthy feature is that the 17.9 µ m 1345A with E > 0.68 Ry. FIR transition is very strong, with large collision strengths and resonances just above the excitation threshold at E ≈ 0.1 Ry. That yields a maximum effective collision strength 3 4 Υ(T ) > 2.0 between 10 − 10 K; by comparison the strong 3 4 o 2 o 2 o 3p ( S , D , P ). The atomic structure calcu- 3/2 3/2,5/2 1/2,3/2 157 micron transition in C II has a value of ∼1.6 (Blum and lations using the code SUPERSTRUCTURE (Eissner et al. Pradhan 1991). Consequently, the exciation rate coefficient 1974), and the BPRM calculations are described in Nahar and emissivity (Eqs. 3, 4) would indicate strong observable et al. (2017a). The calculated and experimentally observed intensity relative to other FIR lines from other elements (viz. energies generally agree to within 5% for all levels; the Pottasch and Bernard-Salas). In addition, the energy depen- relatively small and sensitive fine structure splitting differs dence of Ω(E) in Fig. 3(a) leads to variation of more than by 15% (Nahar 2017a). a factor of 3 in Υ(Te) in Fig. 3b. Therefore, the intensity of Fig. 1 presents the Grotrian energy level diagram of the line is a sensitive indicator of temperature in the typical 2 2 o 2 5 P iii. As noted above, the ground state 3s 3p P fine nebular range of 10 − 10 K, encompassing spectral forma- 1/2,3/2 structure is well separated by about 0.6 Ry or 7 eV from tion in important sources such as PNe and SNRs. the next excited 3s3p configuration terms and levels (Na- har et al. 2017a; see Pradhan and Nahar (2011) for a general description of atomic processes and calculations). By com- 4.2 Allowed UV transitions parison, in C ii it is less than 0.4 Ry, and approximation in There are a number of intercombination and dipole al- Eq. (4) has been utilized assuming that the Boltzmann fac- lowed E1 transitions between the odd parity ground state tor exp(−Eij/kT ) effectively de-couples the electron impact 2 2 o fine structure levels 3s 3p( P ) and the even parity excitation of the forbidden FIR transition from higher lev- 1/2−3/2 4 2 4 2 2 2 els of the ion (Eq. 4). For example, at T = 10 K we have e 3s3p ( P , D , S , P ) levels. How- 1/2,3/2,5/2 3/2,5/2 1/2 1/2,3/2 exp(-E/kT) ≈ exp(-16E) and the value of q(T ) for allowed e ever, laboratory and theoretical radiative data for measured UV transitions is orders of magnitude lower compared to the wavelengths and Einstein A-values available from the Na- FIR transition. Even though the observed and experimental tional Institute of Standards and Technology show only 2 o 2 values are close, a small difference in resonance positions rel- the three transitions in the P − D . Fig. 3a 3/2,5/2 1/2,3/2 ative to threshold can introduce a significant uncertainty in presents sample collision strengths for fine struture compo- the effective collision strengths. The observed energies were nents of dipole transitions in the three allowed multiplets. substituted for theoretical ones in order to reproduce the The BPRM calculations again show resonance structures be- threshold energies more accurately. This is of particular im- low the highest target ion threshold at 1.45 Ry due to low-ℓ portance for excitation at low temperatures dominated by partial waves included in the calculations with ℓ ≈ 10. As near-threshold resonances. these are E1 transitions, the collision strengths rise with in- The BPRM collision strengths were computed up to 5 creasing energy owing to divergent higher partial wave con- times the energy of the highest level in the atomic calcula- tributions ℓ > ℓ . The general form in the high energy re- 3 4 o tions, 3p ( S ) at 1.45 Ry. Particular care is taken to test gion may be approximated by the Bethe formula Ω ∼ alnE, 3/2 and ensure convergence of collision strengths with respect to where a is related to the dipole oscillator strength, assuming partial waves and energy resolution. Total (e + ion) symme- high-ℓ collisions as radiatively induced (Pradhan and Nahar tries up to (LS)Jπ with J 6 19.5 were included in the calcu- 2011). We therefore, match the BPRM collision strengths lations, though it was found that the collision strengths for at 1.45 Ry to the Bethe expression. While there may be forbidden transitions converged for J 6 7. An energy mesh of some uncertainty in the vicinity of this energy region, the −5 ΔE ∼ 10 Rydbergs was used to resolve the near-thresold overall behaviour of the collision strengths in Fig. 3a ap- resonances. The resonances were delineated in detail prior pears to be correct (c.f. Blum and Pradhan (1991) for C II to averaging over the Maxwellian distribution. collision strengths for similar transitions). The effective col- Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 30.0 2 2 o 2 2 6.0 2 2 o 2 2 o 3s 3p P -3s3p D 3s 3p P -3s 3p P 1/2 3/2 1/2 3/2 4.0 25.0 2.0 20.0 0.0 8.0 2 2 o 2 2 3s 3p P -3s3p S 1/2 1/2 6.0 15.0 4.0 2.0 10.0 0.0 6.0 2 2 o 2 2 3s 3p P -3s3p P 1/2 5/2 5.0 4.0 2.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 E (Ryd) E (Ryd) 2.5 1 2 2 o 2 2 2 2 o 2 2 o 3s 3p P -3s3p D 3s 3p P - 3s 3p P 1/2 3/2 1/2 3/2 0.1 2.0 0.01 1E-3 2 2 o 2 2 3s 3p P -3s3p S 1.5 1/2 1/2 0.1 0.01 1.0 1E-3 2 2 o 2 2 3s 3p P -3s3p P 1/2 3/2 0.5 0.1 0.01 0.0 1E-3 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 LogT (K) logT (K) Figure 2. (a) Collision strength for the 17.9 μm [P iii] IR fine Figure 3. (a) Collision strengths Ω(E) for sample UV 2 o 2 structure transition. High resolution at near-threshold energies is fine structure transitions from the ground level P → 1/2 necessary for accuracy in rate coefficients at low temperatures. 2 2 D , S , P For E > 1.5 Ry the Coulomb-Bethe form 3/2 1/2 3/2 (b) Maxwellian averaged effective collision strengths Υ(T ) (Eq. Ω(E) ∼ lnE is employed, typical of dipole allowed transitions 5). There is a factor of 3 or more variation broadly peaking at at high energies and partial waves. (b) Maxwellian averaged ef- typical nebular temperatures Te > 10 K. structures. fective collision strengths Υ(T ) for the transitions transitions in (a). lision strengths Υ(T ) in Fig. 3b show the expected rising behaviour with temperature, typical of allowed transitions. transitions with a practically complete 18-level collisional- radiative atomic model. The FIR and UV lines can not be observed with the same spectrometer and their spectral for- 4.3 Maxwellian averaged collision strengths mation may be governed by different physical conditions, as well as subject to extinction that is highly wavelength depen- In Table 1 we present the effective collision strengths (Eq. dent and would differntially attenuate line intensities. Some 3) for the four FIR and UV transitions reported herein. The temperature dependence may be deduced from the energy tabulation is carried out at a range of temperatures typi- behaviour inherent in the collision strengths data presented, 2 5 cal of nebular environments 10 − 10 K. It is striking how and derived line emissivities. Based on extensive benchmark- much stronger the forbidden FIR 17.9 µ m is relative to the ing of R-matrix data with experiments, we estimate the ac- allowed UV transitions, and dominates collisional excitation curacy of the effective collision strengths between 10-20%. to all other levels by up to two orders of magnitude for tem- We may calculate nebular phosphorus abundance as peratures between 100-10,000 K, although the values be- outlined in Section 2 Eqs. 1-5, based on the [P iii] 17.9 come comparable towards higher temperatures as shown in µ m line intensity ratio relative to Hβ. We assume a tem- Fig. 3b. That further numerically supports the approxima- 4 4 −3 perature 10 K, density 10 cm , transtion energy hν = tion that the FIR line intensity may be little affected by 0.069 eV, solar P-abundance, and ionic ratio P III/P = excitation to higher levels. 0.33. Using Υ(10 K) from Table 1, the rate coefficient −8 3 q = 7.77×10 cm /sec and (4π/N N )ǫ(17.9m µ ) = 7.33× p e −28 3 10 ergs/cm /sec. Nebular recombination Hβ line inten- 4.4 Discussion −26 sities (4π/N N )j(Hβ) are: 8.3×10 (Case A) and 1.24× p e −25 3 The results reported herein should enable spectral diagnos- 10 ergs cm sec (Case B). Therefore, ǫ(17.9m µ )/Hβ = −3 −3 tics of both the [P iii] forbidden 17.9 µ m line as well as UV 8.8 × 10 (Case A) and 5.9 × 10 (Case B) respectively. Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 C o llisio n S tren g th E ffectiv e C o llisio n S tren g th E ffeciv e C o llisio n S ren g th C o llisio n S tren g th Table 1. Effective Maxwellian averaged collision strengths for FIR and UV transitons in P iii 2 o 2 o 2 2 o 2 2 o 2 2 o 2 o 2 2 o 2 2 o 2 LogT (K) P P − D P − S P − P LogT (K) P P − D P − S P − P J-J’ 1/2-3/2 1/2-3/2 1/2-1/2 1/2-3/2 J-J’ 1/2-3/2 1/2-3/2 1/2-1/2 1/2-3/2 ˚ ˚ ˚ ˚ ˚ ˚ λ 17.9 μm 1334.8 A 998.6 A 914.5 A λ 17.9 μm 1334.8 A 998.6 A 914.5 A 2.0 7.73(-1) 1.20(-3) 1.18(-3) 1.13(-3) 3.6 2.19 4.76(-2) 4.68(-2) 4.51(-2) 2.1 9.45(-1) 1.50(-3) 1.48(-3) 1.43(-3) 3.7 2.16 5.99(-2) 5.89(-2) 5.67(-2) 2.2 1.13 1.90(-3) 1.86(-3) 1.79(-3) 3.8 2.10 7.54(-2) 7.41(-2) 7.14(-2) 2.3 1.33 2.39(-3) 2.34(-3) 2.26(-3) 3.9 2.04 9.50(-2) 9.33(-2) 8.99(-2) 2.4 1.52 3.00(-3) 2.95(-3) 2.84(-3) 4.0 1.97 1.20(-1) 1.18(-1) 1.13(-1) 2.5 1.70 3.78(-3) 3.72(-3) 3.58(-3) 4.1 1.90 1.51(-1) 1.48(-1) 1.43(-1) 2.6 1.85 4.76(-3) 4.68(-3) 4.51(-3) 4.2 1.83 1.90(-1) 1.86(-1) 1.79(-1) 2.7 1.98 5.99(-3) 5.89(-3) 5.67(-3) 4.3 1.77 2.39(-1) 2.34(-1) 2.26(-1) 2.8 2.08 7.54(-3) 7.41(-3) 7.14(-3) 4.4 1.73 3.00(-1) 2.93(-1) 2.84(-1) 2.9 2.16 9.50(-3) 9.33(-3) 8.99(-3) 4.5 1.69 3.75(-1) 3.63(-1) 3.56(-1) 3.0 2.20 1.20(-2) 1.18(-2) 1.13(-2) 4.6 1.65 4.63(-1) 4.43(-1) 4.45(-1) 3.1 2.23 1.51(-2) 1.48(-2) 1.43(-2) 4.7 1.60 5.62(-1) 5.32(-1) 5.55(-1) 3.2 2.24 1.90(-2) 1.86(-2) 1.79(-2) 4.8 1.55 6.70(-1) 6.32(-1) 6.91(-1) 3.3 2.25 2.39(-2) 2.34(-2) 2.26(-2) 4.9 1.47 7.87(-1) 7.45(-1) 8.64(-1) 3.4 2.24 3.00(-2) 2.95(-2) 2.84(-2) 5.0 1.39 9.19(-1) 8.82(-1) 1.09 3.5 2.22 3.78(-2) 3.72(-2) 3.58(-2) These ǫ(17.9m µ )/Hβ line ratios lie in the range observed in RAD at: www.astronomy.ohio-state.edu∼nahar, and TIP- several PNe, but the P-abundances heretofore derived are TOPBase at the Opacity Project/Iron Project webpage: factor of 3-4 lower than solar (viz. Pottasch and Bernard- http://cdsweb.u-strasbg.fr/OP.htx. Salas 2008); present work may yield higher abundances. Further refinements can be made by considering addi- tional atomic processes such as level-specific (e + P IV) ACKNOWLEDGMENTS → P iii recombination-cascades, and flourescent excitation The computational work was carried out at the Ohio Super- from an external radiation field such as in PNe central computer Center in Columbus Ohio. This work was partially stars with T ≈ 80, 000 − 120, 000K. A more elaborate rad supported by the Astronomy Division of the U.S. National calculation can be done using Eq. (2) that would combine Science Foundation (SNN and AKP), and from the Indo-US the collisional-radiative model with a photoionization model Science and Technology Forum and Science and Engineering that describes P-ionization states more accurately than, say, Research Board, Government of India (RN). the P iii/P value of 0.33 assumed above. However, these im- provement would require extensive new atomic calculations for photoionization and (e + ion) recombination (e.g. Nahar REFERENCES et al. 2017). An interesting possibility is that of laser action in the Asplund, M., Grevesse, N., Jacques Sauval, A. and Scott, 17.9 µ m line, similar to that explored for the C ii 157 mi- P., 2009, Ann. Rev. Astron. Astrophys. 209, 47 cron transition (Peng and Pradhan 1994). Population inver- Blum, R. D. and Pradhan, A. K., 1991, Phys. Rev. A 44, sion may occur owing to the extremely small magnetic dipole 2 o 2 o −3 (M1) radiative decay rate A( P − P ) = 1.57×10 /sec 3/2 1/2 Burke, P.G., R-Matrix Theory of Atomic Collisions, 2011, (NIST Atomic Spectral Database: www.nist.gov). Equating Springer 4 −3 N q = A, we obtain N = 2.0 ×10 cm . Therefore, at elec- e e Ganas, P. S., 1998, Eur. Phys. J. D-1, 165 4 −3 tron densities N > 10 cm , electron impact excitation ex- Maas, Z. G., Pilachowski, C. A. and Cescutti, G., 2017, As- ceeds spontaneous decay, and population inversion and laser trophys. J. 841, 108 emission may occur in higher density SNRs or other sources. Nahar, S. N., et al. , 2017a, New Ast. 50, 19; 2017b, JQSRT 187, 215; 2017c, MNRAS 469, 3225 Otsuka, M., Mexner, M., Riebel, D., Hyung, S., Tajitsu, A. 4.5 Conclusion and Izumiura, H., 2011, Astrophys. J. 729, 39 Peng, J. and Pradhan, A. K., 1994, Astrophys. J. Lett. 432, Accurate collision strengths including fine structure with rel- L123 ativistic effects are computed for diagnostics of the [P iii] Pottasch, S. R. and Beintema, D. A., 1999, Astron. Astro- forbidden FIR and allowed UV lines to enable a more pre- phys. 347, 975 cise re-examination of phosphorus abundance. The results Pottasch, S. R., Bernard-Salas, J. and Roelig, T. L., 2008, show signficant temperature dependence that should pro- Astron. Astrophys. 481, 393 vide additional information on the physical environment Pottasch, S. R. and Bernard-Salas, J., 2008, Astron. Astro- and spectral formation. In particular, this work suggests phys. 490, 715 searches for the [P iii] FIR line using Spitzer IRS data Pradhan, A. K. and Nahar, S. N., 2011, Atomic Astro- and abundance determination. Further work is in progress physics and Spectroscopy, Cambridge University Press on photoionization and collisional excitation of P-ions rel- Wang, H., Jiang, G. and Duan, J., 2016, Eur. Phys. J. D evant to this investigation. All data are available from 70, 122 the authors and archived in S. N. Nahar’s database NO- Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society Letters Oxford University Press

Collision strengths for FIR and UV transitions in P iii and the phosphorus abundance

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Collision strengths for FIR and UV transtions in P iii and the phosphorus abundance 1 1 1,2,3 Rahla Naghma , Sultana N. Nahar , Anil K. Pradhan 1 2 3 Department of Astronomy, Chemical Physics Program, Biophysics Graduate Program, The Ohio State University, Columbus, OH 43210, USA. Accepted xxxxxx Received xxxxxx; in original form xxxxxx ABSTRACT Phosphorus abundance is crucial for DNA-based extraterrestrial life in exoplanets. Atomic data for observed spectral lines of P-ions are needed for its accurate determi- nation. We present the first calculations for collision strengths for the forbidden [P iii] 2 2 o fine structure transition 3s 3p( P ) within the ground state at 17.9 μm , as well 1/2−3/2 2 2 o 2 2 2 2 as allowed UV transitions in the 3s 3p( P ) → 3s3p ( D , S , P ) 3/2,5/2 1/2 1/2,3/2 1/2,3/2 multiplets between 915-1345 A. Collision strengths are computed using the Breit-Pauli R-Matrix method including the first 18 levels, and they exhibit extensive auto-ionizing resonance structures. In particular, the Maxwellian averaged effective collision strength for the FIR 17.9 μm transition shows a factor 3 temperature variation broadly peaking at typical nebular temperatures. Its theoretical emissivity with solar phosphorus abun- dance is computed relative to Hβ and found to be similar to observed intensties from planetary nebulae; the abundances derived in earlier works are 3-5 times sub-solar. The results pertain to the reported paucity of phosphorus from preferred production sites in supernovae, and abundances in planetary nebulae and supernova remnants. Key words: ISM: atoms ¡ Interstellar Medium (ISM), Nebulae, ISM: supernova rem- nants, Physical Data and Processes ¡ atomic processes, astrobiology, infrared: general 1 INTRODUCTION using singly ionized P ii lines found up to 100 times the P/Fe ratio in the young core-collapse SNR Cassiopeia A than the Phosporus abundance is of considerable interest in the Milky Way average (Koo et al. 2013). Phosphorus is chemi- search for life forms in exoplanets. It is the backbone element cally very reactive, so its low gas phase abundance may also in the DNA molecule, enabling chemical bonds among myr- be difficult to determine due to dust and grain formation. iad nucleotides that constitute the complex double-helical structure. However, ascertaining nucleosynthesis pathways Despite its astrophysical and increasing astrobiological and determining the actual abundance of phosphorus (Z importance, theoretical spectral analysis is hampered by the = 15) is challenging because it is much lower than low-Z paucity of radiative and collisional atomic data for phos- α-elements, and orders of magnitude lower than the other phorus ions. It is surprising that very little data for the five most common elements of the six that constitute the important low ionization stages of P-ions in stellar and neb- CHONPS-based life organisms on the Earth. The photo- ular sources are available, relative to nearly all other first spheric solar abundances numerically relative to hydrogen and second row elements (viz. Pradhan and Nahar 2011). −4 −5 are (Asplund et al. 2009): C (2.7 ×10 ), N (6.8 ×10 ) O Electron impact excitation cross sections for P i have been −4 −7 −5 (4.9 ×10 ), P (2.6 ×10 ) and S (1.3 ×10 ). calculated in the Born approximation for excitations from Phosphorus abundances have been measured from the the ground 3p up to several nℓ sub-orbitals (Ganas 1998). mid-infrared [P iii] 17.9 µ m observations of late stages of Elaborate Dirac R-Matrix calculations for photoionization stellar remnants such as planetary nebulae (Pottsch et al. of low-lying ground and metastable levels of P iii have been 2008, Pottasch and Bernard-Salas 2008, Otsuka et al. 2011) done over a small photon energy range, with good agree- and from ground based observations of FGK dwarf stars ment with experimental measurements (Wang et al. 2016). (Maas et al. 2017). Whereas phosphorus, with an odd atomic Recently, sophistcated Breit-Pauli R-Matrix (BPRM) cal- number Z=15, can be synthesized during the AGB phase of culations have been carried out for photoionization of a low-mass stars, it is thought to be mainly produced in evo- large number of P ii levels using an 18-level coupled chan- lutionary stages of massive stars, before and during super- nel wavefunction expansion for P iii (Nahar et al. 2017a,b,c); novae explosion by neutron capture with silicon. An analysis very good agreement was found with the experimental P ii Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 photoionization cross sections measured at the Berkeley Ad- expression gives the emissivity in terms of only the electron vanced Light Source, particularly for the detailed resonance impact excitation rate coefficient and transition energy hν, structures in the near-threshold region. These earlier works 2 o 2 o 2 o 2 o ǫ( P − P ) = N N q( P − P )hν/4π. (3) e ion 3/2 1/2 3/2 1/2 forms the basis for the calculations reported in this Letter. There are no other previous calculations for collisional Eq. (3) implicitly assumes that all excitations to the up- 2 o excitation of low ionization stages of P-ions. We also develop per level P would be followed by downward decay to 3/2 an atomic physics framework for astrophysical spectral di- 2 o the ground state P , leaving the temperature-dependent 1/2 agnostics in nebular environments as function of tempera- electron impact excitation rate coefficient q as the only im- ture, density and ionization equilibrium, potentially leading portant quantity to be calculated. That, in turn, is related to to more accurate abundance determination. the Maxwellian averaged effective collision strength Υij(Te) as −6 g 8.63 × 10 j −E /kT ij q (T ) = q e = Υ(T ), (4) ij e ji e 1/2 2 PHOSPHORUS ABUNDANCE ANALYSIS g g T i i Previous works are based on observational analysis of rela- and tive intensities of phosphorus lines compared to other ele- Υ (T ) = Ω (E) exp(−E/kT )d(E/kT ), (5) ments. For example, nebular abundances have been deter- ij e ij e e mined in planetary nebulae (PNe) NGC 3242 and NGC 6369 from mid-IR observations of [P iii] forbidden 17.9 µ m line us- where E is the energy difference and Ω is the collision ij ij ing the Infrared Spectrograph aboard the Spitzer Space Tele- strength for the transition i → j. The exponentially decay- scope and the Short Wavelength Spectrograph on the Infrared ing Maxwellian factor implies that at low temperatures only Space Observatory (Pottasch and Bernard-Salas 2008) and the very low energy Ω (E)) would determine the Υ(T ). ij e NGC 2392 (Pottasch et al. 2008). A comparison of abun- Furthermore, the detailed Ω(E) is generally a highly energy- dances for NGC 3242 shows phosphorus underabundance in dependent function due to autoionizing resonances, which a number of PNe, by a factor of 5 relative to solar, and more leads to temperature sensitivity in the rate coefficient q(T ) than a factor of 3 in NGC 6369. The large discrepancies are via Υ(T ) as in Eqs. (4-5). attributed to dust formation (Pottasch and Bernard-Salas 2008). However, the results are model dependent since they entail atomic parameters and ionization fractions not known 3 THEORY AND COMPUTATIONS to high precision. For a single observed line the ion abundance may be de- A brief theoretical description of the calculations is given. rived from the measured intensity ratio under certain con- In particular, we describe relatvistic effects and the repre- ditions. Relative to recombination line Hβ, we may write sentation of the (e + ion) system. (Pottasch and Beintema 1999) I N λ A N ion ion Hβ ji j 3.1 Relativistic fine structure = N (1) I N λ α (Hβ) N Hβ p+ ji R ion The relativistic Hamiltonian (Rydberg units) in the Breit- where N is the ionic abundance, N is the upper level pop- ion j Pauli R-matrix (BPRM) approximation is given by ulation, A i is the Einstein decay rate between levels j → i, BP and α is the Hβ-recombination coefficient. The present case H = N+1 n o P P N+1 N+1 (6) 2 mass Dar so of [P iii] is similar to the well-known C ii 157 µ m line emit- 2Z 2 −∇ − + + H + H + H . i N+1 N+1 N+1 i=1 r r 2 2 o j>i i ij ted via the 2s 2p P transition (Blum and Pradhan 1/2−3/2 1991). Theoretically, we write line emissivity for the [P iii] where the last three terms are one-body relativistic correc- FIR transition formed with a given phosphorus abundance tions of the Breit interaction, respectively: as (Pradhan and Nahar 2011) mass α 4 the mass correction term, H = − p , 4 i Dar Zα 2 1 2 o 2 o 2 o the Darwin term, H = ∇ ( ), (7) 4 i r hνA( P − P ) N( P ) i 3/2 1/2 n(P III) 3/2 so 2 1 ǫ(17.9m µ ) = × × the spin − orbit interaction term, H = Zα l .s . 3 i i i r 4π N ((P III) n(P ) i n(P ) × × n(H) ergs/cm /sec. (2) 3.2 Wavefunction representation and calculations n(H) Based on the coupled channel approximaton, the R-matrix The sum in the denominator on the RHS of Eq. (2) refers to method (Burke 2011) entails a wavefunction expansion of all levels included in the atomic model. Calculating the level the (e + ion) system in terms of the eigenfuctions for the populations requires rate coefficients for contributing atomic target ion. In the present case we are interested in low-lying processes that may be due to recombination-cascades, elec- FIR transition within the ground configuration 3s 3p and tron impact excitation and fluorescent excitation from an the next excited configuration 3s3p . Therefore we confine external radiation field. In addition, Eq. (2) also depends on ourselves to an accurate wavefunction representation for the ionization balance for existing states in the plasma, as well first 18 levels dominated by the spectroscopic configurations as the elemental abundance itself – the quantity to be de- 2 2 6 2 2 o 2 4 2 2 [1s , 2s , 2p ]3s 3p( P ), 3s3p ( P , D , S , termined. However, if the two closely-spaced levels are effec- 1/2,3/2,5/2 3/2,5/2 1/2 1/2,3/2) 2 2 2 2 2 2 2 o tively de-coupled from other levels in the ion then a simple P ), 3s 3d( D ), 3s 4s( S ), 3s 4p( P ), 1/2,3/2 3/2,5/2 1/2 1/2,3/2 Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 4 RESULTS We describe the two main sets of results for the FIR and the UV transitions, as well as the diagnostic lines. Collision strengths have been computed for all 153 transitions among the 18 P iii levels. Selected results are presented below; no previous data are available for comparison. 4.1 The forbidden 17.9 µ m transition The calculated fine structure collision strength is shown in Fig. 2a, that exhibits considerable autoionizing resonance structures and energy dependence throughout the range up to the highest level of the P iii ion included in the BPRM Figure 1. Energy diagram of P iii showing the ground 3s 3p and 3 2 o wavefunction expansion, E(3p P ) = 1.45 Ry. The fall- 3/2 the first excited configuration 3s3p levels. The energy separation off for E > 1.0 Ry indicates that the collision strength is 2 o of the ground state fine structure P transition at 17.9 1/2,3/2 much lower at higher energies, and has converged for this μm is 0.0051 Ry, and well separated from the dipole allowed UV forbidden transtion. 2 o 2 2 2 transitions of the P − D, S, P multiplets between 915− 1/2,3/2 One particularly noteworthy feature is that the 17.9 µ m 1345A with E > 0.68 Ry. FIR transition is very strong, with large collision strengths and resonances just above the excitation threshold at E ≈ 0.1 Ry. That yields a maximum effective collision strength 3 4 Υ(T ) > 2.0 between 10 − 10 K; by comparison the strong 3 4 o 2 o 2 o 3p ( S , D , P ). The atomic structure calcu- 3/2 3/2,5/2 1/2,3/2 157 micron transition in C II has a value of ∼1.6 (Blum and lations using the code SUPERSTRUCTURE (Eissner et al. Pradhan 1991). Consequently, the exciation rate coefficient 1974), and the BPRM calculations are described in Nahar and emissivity (Eqs. 3, 4) would indicate strong observable et al. (2017a). The calculated and experimentally observed intensity relative to other FIR lines from other elements (viz. energies generally agree to within 5% for all levels; the Pottasch and Bernard-Salas). In addition, the energy depen- relatively small and sensitive fine structure splitting differs dence of Ω(E) in Fig. 3(a) leads to variation of more than by 15% (Nahar 2017a). a factor of 3 in Υ(Te) in Fig. 3b. Therefore, the intensity of Fig. 1 presents the Grotrian energy level diagram of the line is a sensitive indicator of temperature in the typical 2 2 o 2 5 P iii. As noted above, the ground state 3s 3p P fine nebular range of 10 − 10 K, encompassing spectral forma- 1/2,3/2 structure is well separated by about 0.6 Ry or 7 eV from tion in important sources such as PNe and SNRs. the next excited 3s3p configuration terms and levels (Na- har et al. 2017a; see Pradhan and Nahar (2011) for a general description of atomic processes and calculations). By com- 4.2 Allowed UV transitions parison, in C ii it is less than 0.4 Ry, and approximation in There are a number of intercombination and dipole al- Eq. (4) has been utilized assuming that the Boltzmann fac- lowed E1 transitions between the odd parity ground state tor exp(−Eij/kT ) effectively de-couples the electron impact 2 2 o fine structure levels 3s 3p( P ) and the even parity excitation of the forbidden FIR transition from higher lev- 1/2−3/2 4 2 4 2 2 2 els of the ion (Eq. 4). For example, at T = 10 K we have e 3s3p ( P , D , S , P ) levels. How- 1/2,3/2,5/2 3/2,5/2 1/2 1/2,3/2 exp(-E/kT) ≈ exp(-16E) and the value of q(T ) for allowed e ever, laboratory and theoretical radiative data for measured UV transitions is orders of magnitude lower compared to the wavelengths and Einstein A-values available from the Na- FIR transition. Even though the observed and experimental tional Institute of Standards and Technology show only 2 o 2 values are close, a small difference in resonance positions rel- the three transitions in the P − D . Fig. 3a 3/2,5/2 1/2,3/2 ative to threshold can introduce a significant uncertainty in presents sample collision strengths for fine struture compo- the effective collision strengths. The observed energies were nents of dipole transitions in the three allowed multiplets. substituted for theoretical ones in order to reproduce the The BPRM calculations again show resonance structures be- threshold energies more accurately. This is of particular im- low the highest target ion threshold at 1.45 Ry due to low-ℓ portance for excitation at low temperatures dominated by partial waves included in the calculations with ℓ ≈ 10. As near-threshold resonances. these are E1 transitions, the collision strengths rise with in- The BPRM collision strengths were computed up to 5 creasing energy owing to divergent higher partial wave con- times the energy of the highest level in the atomic calcula- tributions ℓ > ℓ . The general form in the high energy re- 3 4 o tions, 3p ( S ) at 1.45 Ry. Particular care is taken to test gion may be approximated by the Bethe formula Ω ∼ alnE, 3/2 and ensure convergence of collision strengths with respect to where a is related to the dipole oscillator strength, assuming partial waves and energy resolution. Total (e + ion) symme- high-ℓ collisions as radiatively induced (Pradhan and Nahar tries up to (LS)Jπ with J 6 19.5 were included in the calcu- 2011). We therefore, match the BPRM collision strengths lations, though it was found that the collision strengths for at 1.45 Ry to the Bethe expression. While there may be forbidden transitions converged for J 6 7. An energy mesh of some uncertainty in the vicinity of this energy region, the −5 ΔE ∼ 10 Rydbergs was used to resolve the near-thresold overall behaviour of the collision strengths in Fig. 3a ap- resonances. The resonances were delineated in detail prior pears to be correct (c.f. Blum and Pradhan (1991) for C II to averaging over the Maxwellian distribution. collision strengths for similar transitions). The effective col- Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 30.0 2 2 o 2 2 6.0 2 2 o 2 2 o 3s 3p P -3s3p D 3s 3p P -3s 3p P 1/2 3/2 1/2 3/2 4.0 25.0 2.0 20.0 0.0 8.0 2 2 o 2 2 3s 3p P -3s3p S 1/2 1/2 6.0 15.0 4.0 2.0 10.0 0.0 6.0 2 2 o 2 2 3s 3p P -3s3p P 1/2 5/2 5.0 4.0 2.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 E (Ryd) E (Ryd) 2.5 1 2 2 o 2 2 2 2 o 2 2 o 3s 3p P -3s3p D 3s 3p P - 3s 3p P 1/2 3/2 1/2 3/2 0.1 2.0 0.01 1E-3 2 2 o 2 2 3s 3p P -3s3p S 1.5 1/2 1/2 0.1 0.01 1.0 1E-3 2 2 o 2 2 3s 3p P -3s3p P 1/2 3/2 0.5 0.1 0.01 0.0 1E-3 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 LogT (K) logT (K) Figure 2. (a) Collision strength for the 17.9 μm [P iii] IR fine Figure 3. (a) Collision strengths Ω(E) for sample UV 2 o 2 structure transition. High resolution at near-threshold energies is fine structure transitions from the ground level P → 1/2 necessary for accuracy in rate coefficients at low temperatures. 2 2 D , S , P For E > 1.5 Ry the Coulomb-Bethe form 3/2 1/2 3/2 (b) Maxwellian averaged effective collision strengths Υ(T ) (Eq. Ω(E) ∼ lnE is employed, typical of dipole allowed transitions 5). There is a factor of 3 or more variation broadly peaking at at high energies and partial waves. (b) Maxwellian averaged ef- typical nebular temperatures Te > 10 K. structures. fective collision strengths Υ(T ) for the transitions transitions in (a). lision strengths Υ(T ) in Fig. 3b show the expected rising behaviour with temperature, typical of allowed transitions. transitions with a practically complete 18-level collisional- radiative atomic model. The FIR and UV lines can not be observed with the same spectrometer and their spectral for- 4.3 Maxwellian averaged collision strengths mation may be governed by different physical conditions, as well as subject to extinction that is highly wavelength depen- In Table 1 we present the effective collision strengths (Eq. dent and would differntially attenuate line intensities. Some 3) for the four FIR and UV transitions reported herein. The temperature dependence may be deduced from the energy tabulation is carried out at a range of temperatures typi- behaviour inherent in the collision strengths data presented, 2 5 cal of nebular environments 10 − 10 K. It is striking how and derived line emissivities. Based on extensive benchmark- much stronger the forbidden FIR 17.9 µ m is relative to the ing of R-matrix data with experiments, we estimate the ac- allowed UV transitions, and dominates collisional excitation curacy of the effective collision strengths between 10-20%. to all other levels by up to two orders of magnitude for tem- We may calculate nebular phosphorus abundance as peratures between 100-10,000 K, although the values be- outlined in Section 2 Eqs. 1-5, based on the [P iii] 17.9 come comparable towards higher temperatures as shown in µ m line intensity ratio relative to Hβ. We assume a tem- Fig. 3b. That further numerically supports the approxima- 4 4 −3 perature 10 K, density 10 cm , transtion energy hν = tion that the FIR line intensity may be little affected by 0.069 eV, solar P-abundance, and ionic ratio P III/P = excitation to higher levels. 0.33. Using Υ(10 K) from Table 1, the rate coefficient −8 3 q = 7.77×10 cm /sec and (4π/N N )ǫ(17.9m µ ) = 7.33× p e −28 3 10 ergs/cm /sec. Nebular recombination Hβ line inten- 4.4 Discussion −26 sities (4π/N N )j(Hβ) are: 8.3×10 (Case A) and 1.24× p e −25 3 The results reported herein should enable spectral diagnos- 10 ergs cm sec (Case B). Therefore, ǫ(17.9m µ )/Hβ = −3 −3 tics of both the [P iii] forbidden 17.9 µ m line as well as UV 8.8 × 10 (Case A) and 5.9 × 10 (Case B) respectively. Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018 C o llisio n S tren g th E ffectiv e C o llisio n S tren g th E ffeciv e C o llisio n S ren g th C o llisio n S tren g th Table 1. Effective Maxwellian averaged collision strengths for FIR and UV transitons in P iii 2 o 2 o 2 2 o 2 2 o 2 2 o 2 o 2 2 o 2 2 o 2 LogT (K) P P − D P − S P − P LogT (K) P P − D P − S P − P J-J’ 1/2-3/2 1/2-3/2 1/2-1/2 1/2-3/2 J-J’ 1/2-3/2 1/2-3/2 1/2-1/2 1/2-3/2 ˚ ˚ ˚ ˚ ˚ ˚ λ 17.9 μm 1334.8 A 998.6 A 914.5 A λ 17.9 μm 1334.8 A 998.6 A 914.5 A 2.0 7.73(-1) 1.20(-3) 1.18(-3) 1.13(-3) 3.6 2.19 4.76(-2) 4.68(-2) 4.51(-2) 2.1 9.45(-1) 1.50(-3) 1.48(-3) 1.43(-3) 3.7 2.16 5.99(-2) 5.89(-2) 5.67(-2) 2.2 1.13 1.90(-3) 1.86(-3) 1.79(-3) 3.8 2.10 7.54(-2) 7.41(-2) 7.14(-2) 2.3 1.33 2.39(-3) 2.34(-3) 2.26(-3) 3.9 2.04 9.50(-2) 9.33(-2) 8.99(-2) 2.4 1.52 3.00(-3) 2.95(-3) 2.84(-3) 4.0 1.97 1.20(-1) 1.18(-1) 1.13(-1) 2.5 1.70 3.78(-3) 3.72(-3) 3.58(-3) 4.1 1.90 1.51(-1) 1.48(-1) 1.43(-1) 2.6 1.85 4.76(-3) 4.68(-3) 4.51(-3) 4.2 1.83 1.90(-1) 1.86(-1) 1.79(-1) 2.7 1.98 5.99(-3) 5.89(-3) 5.67(-3) 4.3 1.77 2.39(-1) 2.34(-1) 2.26(-1) 2.8 2.08 7.54(-3) 7.41(-3) 7.14(-3) 4.4 1.73 3.00(-1) 2.93(-1) 2.84(-1) 2.9 2.16 9.50(-3) 9.33(-3) 8.99(-3) 4.5 1.69 3.75(-1) 3.63(-1) 3.56(-1) 3.0 2.20 1.20(-2) 1.18(-2) 1.13(-2) 4.6 1.65 4.63(-1) 4.43(-1) 4.45(-1) 3.1 2.23 1.51(-2) 1.48(-2) 1.43(-2) 4.7 1.60 5.62(-1) 5.32(-1) 5.55(-1) 3.2 2.24 1.90(-2) 1.86(-2) 1.79(-2) 4.8 1.55 6.70(-1) 6.32(-1) 6.91(-1) 3.3 2.25 2.39(-2) 2.34(-2) 2.26(-2) 4.9 1.47 7.87(-1) 7.45(-1) 8.64(-1) 3.4 2.24 3.00(-2) 2.95(-2) 2.84(-2) 5.0 1.39 9.19(-1) 8.82(-1) 1.09 3.5 2.22 3.78(-2) 3.72(-2) 3.58(-2) These ǫ(17.9m µ )/Hβ line ratios lie in the range observed in RAD at: www.astronomy.ohio-state.edu∼nahar, and TIP- several PNe, but the P-abundances heretofore derived are TOPBase at the Opacity Project/Iron Project webpage: factor of 3-4 lower than solar (viz. Pottasch and Bernard- http://cdsweb.u-strasbg.fr/OP.htx. Salas 2008); present work may yield higher abundances. Further refinements can be made by considering addi- tional atomic processes such as level-specific (e + P IV) ACKNOWLEDGMENTS → P iii recombination-cascades, and flourescent excitation The computational work was carried out at the Ohio Super- from an external radiation field such as in PNe central computer Center in Columbus Ohio. This work was partially stars with T ≈ 80, 000 − 120, 000K. A more elaborate rad supported by the Astronomy Division of the U.S. National calculation can be done using Eq. (2) that would combine Science Foundation (SNN and AKP), and from the Indo-US the collisional-radiative model with a photoionization model Science and Technology Forum and Science and Engineering that describes P-ionization states more accurately than, say, Research Board, Government of India (RN). the P iii/P value of 0.33 assumed above. However, these im- provement would require extensive new atomic calculations for photoionization and (e + ion) recombination (e.g. Nahar REFERENCES et al. 2017). An interesting possibility is that of laser action in the Asplund, M., Grevesse, N., Jacques Sauval, A. and Scott, 17.9 µ m line, similar to that explored for the C ii 157 mi- P., 2009, Ann. Rev. Astron. Astrophys. 209, 47 cron transition (Peng and Pradhan 1994). Population inver- Blum, R. D. and Pradhan, A. K., 1991, Phys. Rev. A 44, sion may occur owing to the extremely small magnetic dipole 2 o 2 o −3 (M1) radiative decay rate A( P − P ) = 1.57×10 /sec 3/2 1/2 Burke, P.G., R-Matrix Theory of Atomic Collisions, 2011, (NIST Atomic Spectral Database: www.nist.gov). Equating Springer 4 −3 N q = A, we obtain N = 2.0 ×10 cm . Therefore, at elec- e e Ganas, P. S., 1998, Eur. Phys. J. D-1, 165 4 −3 tron densities N > 10 cm , electron impact excitation ex- Maas, Z. G., Pilachowski, C. 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R. and Bernard-Salas, J., 2008, Astron. Astro- and spectral formation. In particular, this work suggests phys. 490, 715 searches for the [P iii] FIR line using Spitzer IRS data Pradhan, A. K. and Nahar, S. N., 2011, Atomic Astro- and abundance determination. Further work is in progress physics and Spectroscopy, Cambridge University Press on photoionization and collisional excitation of P-ions rel- Wang, H., Jiang, G. and Duan, J., 2016, Eur. Phys. J. D evant to this investigation. All data are available from 70, 122 the authors and archived in S. N. Nahar’s database NO- Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly095/5032944 by Ed 'DeepDyve' Gillespie user on 08 June 2018

Journal

Monthly Notices of the Royal Astronomical Society Letters – Oxford University Press

Published: Jun 5, 2018

Keywords: astrobiology; atomic processes; ISM: atoms; ISM: supernova remnants; ISM: nebulae; infrared: general

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