1. Abundance determinations in photoionized nebulae Grazyna Stasinska Observatoire de Meudon Mexico october 2006

2. Why care ? 1- abundances in HII regions probe the present-day abundances in galaxies 2- abundances of some elements in planetary nebulae probe nucleosynthesis in intermediate-mass stars Good news 1- observations of emission lines are easy, even for distant objects 2 - the methods for abundance derivations are easy

3. Contents 1- theory of photoionized nebulae in a nutshell 2- abundance determination through photoionization modelling 3- abundance determination with empirical methods 4 - the temperature fluctuation problem 5 - abundances from recombination lines

4. physical processes in ionized nebulae Ionization Ionic fractions Recombination Heating Electron temperature Cooling Photoionization Collisions Charge exchange Radiative recombination Dielectronic recombination Charge exchange Photoionization Collisional ionization Free-free radiation Free-bound radiation Bound-bound radiation

5. What drives the electron temperature The energy gain of the electrons are: G =  i, j  n i j  i j where the  i j are due to photoionization and collisional ionization The energy losses of the electrons are: L =  i, j  n i j  i j where the  i j are due to recombination and collisional excitation followed by photon emission The net energy gain is: dE / dt = G - L If thermal equilibrium is achieved, the temperature is determined by: G = L

6. Why is the gas temperature roughly uniform in photoionized nebulae Energy gained by photoionization of H at a distance r from the source G = n(H°)  4  J  /(h ) a (h -13.6eV) d  erg cm -3 s -1 ] Ionization equilibrium equation of H at distance r =f R S n(H°)  4  J  /(h )a d  = n(H + ) n e  B (H) Substituting: G = n(H + ) n e  B (H) with =  4  J  /(h ) a (h -h °) d   4  J  /(h )a d  ≈ A T*  Energy gains due to photoionization of H are independent of distance to the star proportional to the star temperature

7. comments on energy losses The most important cooling process is collisionally excited line radiation For a given ion in a two-level approximation, the cooling rate is given by L coll = n 2 A 21 h 21  erg cm -3 s -1 ] where n 2 results from the equilibrium equation of levels 1 and 2 : n 1 n e q 12 = n 2 (A 21 + n e q 21 ) In the limit of small n e one has L coll = n 1 n e q 12 h 21 = (n 1 /n H ) n H n e 8.629 10 -6  (1,2) /  1 T e -0.5 exp (-E 12 /kT e ) h 21 For « normal abundances » the most important cooling ion is O ++ (H and He, the most abundant elements, have too high excitation potentials to be significantly excited at “normal temperatures”) Cooling by collisional line excitation is important in the case of abundant ions lines corresponding to large  levels that can be easily attained at the temperature of the medium

8. Other comments on the gas temperature Dependence of T e with distance to the ionizing source no dependence to first order Spatial variations of Te are mostly determined by the mean energy of the absorbed photons the populations of the main cooling ions are generally small except at high metallicities in the O ++ zone cooling is very efficient through emission of [OIII]52, 88  lines which have very low excitation potentials while in the O + zone the cooling efficiency is smaller (O + has no low-lying levels ) General dependence of Te with the defining properties of the nebulae for a given T*, T e is lower for higher metallicity for a given metallicity, T e is lower for lower T* for given T*, ionization state and metallicity T e is higher if n > n crit

9. The T e structure in ionized nebulae Photoionization models from Stasinska 1978 effect of metallicity ---- Z subsolar __ Z over solar Strong T e gradients are present at high metallicities due to important O ++ cooling

10. comments on line intensities Most nebular lines are optically thin exception: resonance lines H Ly , CIV 1550A, Si IV 1391A, NV 1240A Optically thin lines are powerful tools for abundance determinations Ratios of collisionally excited IR lines are almost independent of T e Recombination line intensities are inversely proportional to T e Ratios of recombination lines are almost independent of T e The ratios of a collisionally excited optical line and a recombination line strongly depend on T e

11. The various methods for abundance determinations Photoionization model fitting Empirical methods Individual (or Te-based) methods Statistical (or strong line) methods

12. the process of model-fitting Model Must Match Observations

13. abundance derivation by model fitting 1) Define the input parameters The characteristics of the ionizing radiation field The density distribution of the nebular gas The chemical composition of the nebular gas The distance 2) Use a photoionization code (e.g. CLOUDY) that solves The system of ionization equations for each species The energy balance equation The transfer of the ionizing radiation 3) Compare model output with observations (corrected for extinction) The total observed H  flux The SH  distribution (and the angular size of the H  zone) The visual magnitude of the ionizing source The line intensities 4) Go back to 1 and iterate until observations are reproduced

14. for a good quality model fitting 1)use as many observational constraints as possible not only line intensity ratios 2) keep in mind that some constraints are very important eg: HeII/H , [OIII]4363/5007 3) some constraints are not independant eg if [OIII]5007/H  is fitted => [OIII]4959/H  should be fitted as well because [OIII]5007/4959 is fixed by atomic physics if it is not, this may indicate an observational problem, eg that the strong [OIII]5007 line is saturated so [OIII]4959/H  should not be used as a test of the model but of the observations 4) chose a good estimator for your goodness of fit eg avoid using a  2 =   (I mod i -I obs i ) /  i ] 2 minimization criterion better use ∀  i, [(I mod i -I obs i ) /  i ] 2 <1

15. possible conclusions from model fitting 1) If all the observations are well fitted within the error bars this may imply that the model abundances are the true abundances (within error bars not easy to determine) If the constraints are not sufficient, the model abundances may be very different from the true ones 2) If some observations cannot be fitted either the observations are not as good as thought or the model does not represent the object well i.e. some assumptions are incorrect, eg the nebular geometry (eg not spherical) the assumed stellar radiation field some important process is missing (eg heating by an additional mechanism) => the chemical composition is not known to the desired accuracy

16. an example of photoionization modelling with insufficient constraints obs Ratag B1 B2 B3 T* 37500K 39000K 37000K 39000K r* (cm) 5.00+10 5.75+10 4.90+10 Rin 0.062 pc 0.050 pc 0.065 pc Rout 0.10 pc 0.087 pc 0.081 pc 0.085 pc F(Hbeta) 3.9-12 3.92-12 3.90-12 3.88-12 ne (cm-3) 2050 1800 1700 1800 He 0.117 0.117 0.180 0.100 C 1.50-3 1.00-3 1.20-3 N 4.80-4 2.50-4 5.50-4 6.00-4 O 2.20-4 2.40-4 1.00-3 1.20-3 Ne 5.00-5 2.00-4 2.40-4 S 2.30-5 3.00-6 6.00-6 7.00-6 [OII] 3727 0.596 a) 0.587 0.613 0.604 [NeIII] 3869 0.014 0.0084 0.0096 [OIII] 4363 <0.0013 0.0006 0.0002 0.0001 HeII 4686 0.0004 0.0003 0.0003 HI 4861 1.00 1.00 1.00 1.00 [OIII] 5007 0.283 0.304 0.281 0.275 [NI] 5200 0.0149 0.0043 0.0093 0.0087 [NII] 5755 0.0071: 0.0151 0.0069 0.0060 HeI 5876 0.128 0.126 0.124 0.128 [OI] 6300 0.0054 0.0106 0.0116 [NII] 6584 2.85 2.79 2.87 2.81 [SII] 6717 0.0565 0.053 0.0602 0.0558 [SII] 6731 0.084 0.077 0.0868 0.0826 [OII] 7325 0.0091: 0.0126 0.0070 0.0063 T(NII) 6734 5422 5426 T(OIII) 7319 5876 5394 Is the PN M 2-5 O-poor or O-rich ? Ratag 1992 claimed it to be O-poor Stasinska, Malkov, Golovatyj 1995 found that both O-poor (B1) and O-rich (B2 abd B3) models can fit all the available data factor 5 uncertainty in O/H

17. an example of photoionization modelling without a satisfactory solution Detailed modelling of the giant HII region NGC 588 in M33 Jamet et al 2005 many observational constraints narrow band imaging long slit optical spectra infrared data from ISO full characterization of the ionizing stars failure of the models the observed [OIII]4363/5007 and [OIII]88m/5007 cannot be explained at the same time this implies an uncertainty of at least a factor 2 in the oxygen abundance

18. Empirical abundance determinations Individual (or Te-based) methods 1) T e and n e are obtained from plasma diagnostics Plasma diagnostic diagram for NGC 7027Energy level diagrams

19. Empirical abundance determinations Individual (or Te-based) methods 2) Ionic abundance ratios are determined from line intensity ratios eg: O ++ /H + = ([OIII]5007/H  ) / (  [OIII]5007 (T e )/  H  (T e )) 3) Elemental abundance ratios are obtained either by adding all the observed ions eg: O/H = O + /H + + O ++ /H + + O +++ /H + + … or by using ionization correction factors (icfs)

20. a note on ionization correction factors Ionization correction factors based on ionization potentials a first approximation promoted by M. and S. Peimbert but risky: eg (O +++ +..)/O ≠ He ++ /He there is nothing which empedes O ++ ions to be present in the He ++ zone Ionization correction factors based on model grids may be risky too observations often pertain only to a small fraction of the object there is no robust formula to correct for He° Cases when no icf is needed when all the expected ionization stages are observed however in this case beware of errors in determining ionic abundances from different spectral ranges from lines extremely sensitive to T e (UV lines or transauroral lines)

21. a rough evaluation of T e -based methods the methods are easy to implement they depend on a very limited amount of assumptions error bars are relatively easy to estimate the abundances of the most important elements are expected to be correct (within error bars) they are very close to abundances obtained from successfull tailored photoionization modelling

22. abundances from optical lines 1.many telescopes, large collectors 2.all lines available in same spectrum 3.spectra affected by extinction 4.lines optically thin 5.intensities depend on T e, emitted in regions of T e >4000K 6.recombination affects forbidden lines at low T e 7.no icf needed for O in HII regions 8.icfs needed for N, Ne, S, Ar 9.main available diagnostic lines [NII] 6584 [OII] 3727, [OIII] 5007 [NeIII 3869], [NeV]3426 [SII] 6720, [SIII] 9532, [Ar III] 7751, [Ar IV]4740, [ArV]6435 T e :[ OIII] 4363/5007, [NII]5755/6884 n e : [SII]6731/6717, [ArIV]4740/4711 abundances from FIR lines 1.few telescopes, small collectors 2.beamsize and calibration problems 3.FIR lines probe obscured regions 4.lines may be optically thick 5.intensities of CE lines independent of T e 6. 7.icf needed for O 8.no icf for N, small for Ne, S, Ar 9.main available lines [NII] 121.7, [NIII]57.3m, [OIII] 51.8mu, [OIV] 25mu, [NeII] 12.8, [NeIII] 15.5, [NeV] 14.3 [SIII] 18.6, [SIV ]10.5 [ArII] 6.9, [ArIII] 9.0, [ArV], [ArVI] n e :[OIII]52/88,[SIII]18/33,[NeIII]15/36, [ArIII] 9/21,[NeV]14/24

23. a case of failure of T e -based abundances metal rich giant HII regions (Stasinska 2005) with VLTs [OIII]4363/5007, [NII]5755/6584, [SIII]6312/9532 become measurable even at high metallicity (eg Bresolin et al 2005) the problem at Z > Z  strong T e gradients are predicted T e sensitive ratios strongly overestimate T e in the emitting zones depending on what line is measured and what relation is adopted between T(O+) and T(O++) O/H is strongly biased !

24. a further problem at high metallicity contamination of collisionally excited lines by recombination at low temperatures, collisionally excited lines such as [OII]7330 or [NII]5755 may be dominated by recombination this effect, very strong in the case of [OII]7330 is wrongly corrected in the literature

25. Empirical abundance determinations statistical (or strong line) methods In many cases, the weak [OIII] 4363 or [NII]5755 lines are not available because the temperature is too low the spectra are of low signal-to-noise the data consist of narrow band images in the strongest lines only It is possible, under certain conditions, to estimate the metallicity (i.e. O/H) using only “strong lines” Strong line methods are statistical have to be calibrated Best known strong line methods: the ones based on oxygen lines Pagel et al 1979 used ([OII]+[OIII])/H  as an indicator of O/H this method, la          , has been calibrated many times Mc Gaugh 1994 refined the method to account for the ionization parameter U Pilyugin (2000, 2001..., 2005) proposed the most sophisticated approach

26. Rationale of Mc Gaugh’s method there are 4 independent strong line ratios H  H , [OII]/H , [OIII]/H , [NII] /H  there are 5 parameters determining them C(H ,, U, O/H, N/O underlying hypothesis of the method is related to O/H (this is expected statistically for giant HII regions) the procedure both O/H and U are derived simultaneously from ([OII]+[OIII])/H , and [OIII]/[OII] a problem ([OII]+[OIII])/H  vs. O/H is double valued a way out [NII]/[OII] indicates whether O/H is high or low (“astrophysical” argument)

27. McGaugh diagrams for the O 23 + method    versus     /     N  /    ersu      /  

28. what lies behind the behaviour of [OIII]5007/H  vs O/H Intensity ratio: [OIII]5007/H  = A n(O ++ ) / n(H + ) T e 0.5 exp (-28800/T e ) Thermal balance equation: n(H + ) n e T* ≈ B n i j n e T e -0.5 exp (- E exc /T e ) For 12 + log O/H < 8.2 cooling is due to H Ly , T e is independent of O/H [OIII]5007/H  ≈ C T* O/H For 12 + log O/H > 9 cooling is essentially due to [OIII]52,88  [OIII]5007/H  ≈ C T* f(T e ) where f(T e ) = T e exp (- 28800/T e ) which decreases with increasing O/H

29. An evaluation of strong line methods Perez-Montero & Diaz 2005 uses a data base of 367 objects with measured T e including some giant HII regions in the inner parts of galaxies (expected to be metal rich) but ignores the strong bias due to low T e evidenced by Stasinska 05

30. the strong line method recalibrated Pilyugin Thuan 2005 upper branch calibration (ie high O/H) lower branch calibration (ie low O/H) uses a data base of over 700 objects with measured Te including some giant HII regions in the inner parts of galaxies (expected to be metal rich) uses only Te-derived abundances but ignores the strong bias due to low T e evidenced by Stasinska 05 => the last word on abundances from strong line methods is not said

31. other problems and uncertainties in abundance determinations atomic data stellar fluxes aperture correction and complex nebular geometry reddening correction temperature and density inhomogeneities the mystery of optical recombination lines the role dust grains

32. Aperture correction When the studied objects are more extended than the observing beam aperture correction is needed if the observing beams are not the same for all wavelenghts. For example combining optical and UV spectra from IUE combining FIR measurements with optical measurements combining various line intensities from ISO Aperture correction can be made using line ratios that have a known intrinsic value (e.g. HeII 1640 / He II 4686) using ratios of beam solid angles Such procedures bear uncertainties they do not take into account the ionization stratification of the nebulae

33. relevance of elemental abundances in case of depletion Mg, Si, Fe, Ni, Ca these elements can be almost entirely in the form of grains their abundances in the gas phase cannot be easily used as indicators of chemical evolution of galaxies or nuclear processes in PN progenitors C can be heavily depleted by carbon-based grains (graphite, PAHs...) O can be slightly depleted (20% for Orion, estimated from depletion pattern of metals, Esteban et al 1998) He, Ne, Ar rare gases, do not combine into grains

34. Correction for dust extinction The method: The “logarithmic extinction at H  ”, C, is derived from the observed H  /H  ratio by comparing it to the theoretical one for case B recombination (at the T e corresponding to the nebula) using an extinction law f( ) C = [ log (F H  / F H  ) B - log (F H  / F H  ) obs ] / (f  - f  ) Emission line ratios are then dereddened using the formula log (F 1 / F 2 ) corrB = log (F 1 / F 2 ) obs + C (f 1 - f 2 ) Problems: The “extinction law” is not universal The intrinsic H  /H  ratio may be different from the theoretical case B (collisional excitation, case C) If some dust is mixed with the ionized gas and strongly contributes to the extinction, no “extinction law” applies

35. the “extinction law” is not universal the canonical extinction law corresponds to R V =A V / E(B-V) =3.2 in Orion R V = 5.5 towards the Galactic bulge, R V ~ 2.5 (Stasinska et al 94) Histogram of R V for 95 galactic O stars Patriarchi et al 2001 larger values of R V are found for lines of sight crossing molecular clouds where dust grains are expected to be larger Extinction laws corresponding to various R V =A V / E(B-V)     .1989

36. checks on the reddening correction Before dereddening check that conditions for case B are likely satisfied If not, consider building a photoionization model, and redden the resulting the emission lines to fit the observed Balmer decrement. If case B is relevant for the object under study check that, after reddening correction, H  / H  is close to the case B recombination value If not, [OIII]4363/5007 is likely to be in error by the same amount as H  /H  differs from the case B value If many Balmer lines are measured with good accuracy Rather than using an “extinction law”, fit the observed spectrum to the theoretical Balmer decrement for reddening. This method is valid (in first approximation) also if dust is mixed with the ionized gas

37. Temperature fluctuations Do temperature fluctuations exist? see reviews by Peimbert 1995, 2001, Mathis 1997, Stasinska 1998, Esteban 1998, 2001 Numerous studies point towards t 2 ~ 0.04 But little direct evidence is seen Were postulated by Peimbert (1967) to explain discrepancies betwen T e from various diagnostics Peimbert’s formalism

38. example of indirect evidence for t 2 ≠ 0 In planetary nebulae T e from Balmer discontinuity is smaller than T[OIII] 4363/5007 (Liu & Danziger 1993) t 2 ~ 0.04 is a representative value

39. If T e fluctuations exist they affect abundance determinations e.g. abundance derived in M8 (Peimbert et al 1993) using Taylor series expansion of the line emissivites for various values of t 2 t 2 =0t 2 =0.02t 2 =0.04t 2 =0.06 He11.0211.0111.0010.99 C8.218.318.488.77 N7.577.667.777.88 O8.508.608.718.84 Abundances derived from optical forbidden lines with respect to H are underestimated when ignoring t 2 Abundances derived from recombination or FIR lines are not affected Abundance ratios like N/O or C/O are less affected

40. visualizing the Peimbert formalism on a two-zone toy model f = N 2 n 2 V 2 / N 1 n 1 V 1 V1n1N1T1V1n1N1T1 V2n2N2T2V2n2N2T2 in this case the values of T 0 and t 2 are simply : variations of T 1 and T 2 with f for t 2 = 0.04 and fixed T 0 f >> 1 corresponds to a photoionized nebula with small shock-heated regions of very high T 1 f << 1 corresponds to a nebula with high metallicity clumps of somewhat lower T 2 volume electron density ionic density temperature

41. Is the Peimbert formalism adequate ? plots of log O ++ as a function of f for two values of T 0 left: T 0 = 8000K right: T 0 = 15000K O ++ is derived from [OIII]5007 using Te measured by [OIII]4363/5007 The amount by which O ++ 5007 is underestimated depends on T 0 and f Even in a simple two-zone model, the situation requires 3 parameters to be described (e.g. T 0, t 2 and f ) not 2 (T 0 and t 2 )

42. Visualisation of energy requirements The simplest example: for t 2 = 0.04 and T 0 = 10000K, f =1 implies T 1 = 12000K and T 2 = 8000K - : log of heating rate in arbitrary units - : log of cooling rate in the O + zone By shifting the heating curve up and down one understands how T e varies with energy input t 2 = 0.04 requires  log  = 0.3, ie a factor 2 difference in heating rates between regions 1 and 2 !

43. What fluctuates? Te ? Natural gradients in photoionized nebulae are small except at high metallicities (Stasinska 1980, Garnett 1992, Kingdon & Ferland 1995, Perez 1997) Ne ? In high density clumps collisional dexcitation increases T e with respect to the ambient medium Kholtygin 1998, Mathis et al. 1998 (this is not sufficient to explain t 2 ~ 0.04) densities above 10 5 cm -3 boost [OIII] 4363/5007 (Viegas & Clegg 1994) but there is no evidence of such high densities in the O ++ zones

44. What fluctuates? Ni ? T e is lower in C-rich zones (Torres-Peimbert et al 1990) The O ++ discrepancy between collisional and optical lines requires the existence of O-rich zones (Stasinska 1998, Liu et al 2000, 2001, Péquignot 2001) Te ? Natural gradients in photoionized nebulae are small except at high metallicities (Stasinska 1980, Garnett 1992, Kingdon & Ferland 1995, Perez 1997) Ne ? In high density clumps collisional dexcitation increases T e with respect to the ambient medium Kholtygin 1998, Mathis et al. 1998 (this is not sufficient to explain t 2 ~ 0.04) densities above 10 5 cm -3 boost [OIII] 4363/5007 (Viegas & Clegg 1994) but there is no evidence of such high densities in the O ++ zones

45. Is photoionization the only heating source in photoionized nebulae? In a number of nebulae, classical photoionization models produce T[OIII] lower than observed Giant HII regions: Campbell 1990, Garcia-Vargas et al 1997, Stasinska & Schaerer 1999, Luridiana et al 1999, Luridiana & Peimbert 2001 PNe: Peña et al 1998 Additional energy sources have been proposed: Shocks (Peimbert et al 1991) Conduction fronts (Maciejewski et al 1996)

46. the ORL /CEL discrepancy Expected properties of optical recombination lines (ORLs) their emissivity is roughly proportional to T e -1 they should give correct abundances with respect to H even in presence of temperature fluctuations ORL abundances versus CEL (collisionally excited lines) abundances ORL abundances larger than CEL abundances by important factors Wyse 1947, Peimbert et al 1993, Liu et al 1995 (O), Kaler 1986 (C) Esteban et al 1998, Liu et al 2000, 2001 (C,N,O) C ++ 1909 / O ++ 5007 versus C ++ 4267 /O ++ 5007 in planetary nebulae Compilation Rola & Stasinska 1994

47. ORL versus CEL abundances ionic abundances in the planetary nebula NGC 6153 Liu et al 2000

48. invoked causes of ORL-CEL discrepancy Faintness of the ORLs biased measurements flux calibration is difficult over a large dynamical range they may suffer from blends Heavy element recombination coefficients are not reliable Temperature fluctuations Density condensations no (from high S/N spectroscopy) no: [OIII]4931/[ [OIII]4959 agrees with theory: 4 10 -4 Mathis& Liu 1999 no (from echelle spectra ) have been recomputed with the R-matrix method Storey 1994 ORL abundances from numerous transitions are in agreement t 2 explaining ORL-CEL discrepancy >> t 2 explaining T e [OIII] -T e (BJ) IR-CEL abundances are consistent with optical -CEL abundances Liu 2000,2001 no (high order Balmer lines) Liu 2000...

49. invoked causes of ORL-CEL discrepancy Faintness of the ORLs biased measurements flux calibration is difficult over a large dynamical range they may suffer from blends Heavy element recombination coefficients are not reliable Temperature fluctuations Density condensations no (from high S/N spectroscopy) no: [OIII]4931/[ [OIII]4959 agrees with theory: 4 10 -4 Mathis& Liu 1999 no (from echelle spectra ) have been recomputed with the R-matrix method Storey 1994 ORL abundances from numerous transitions are in agreement t 2 explaining ORL-CEL discrepancy >> t 2 explaining T e [OIII] -T e (BJ) IR-CEL abundances are consistent with optical -CEL abundances Liu 2000,2001 no (high order Balmer lines) Liu 2000... Recombination coefficients computed so far do not include dielectronic recombination for n > 10 which is likely to be efficient at Te > 2 10 4 K Chemical inhomogeneities: they require super metal rich inclusions with solar C/N/O/Ne Liu 2000, Tsamis 2003

50. Temperature of the ORL zones Tsamis et al 2004, Liu et al 2004 In 4 PNe, it has been possible to derive T e from ratios of OII recombination lines that have a slightly different sensitivity to T e The zones emitting the OII recombination lines are found to be ultracold This goes against the dust+rec coeff explanation, at least for these objects The ORL zones must havedifferent metallicity (very high) compared to the rest of the nebula

51. a dual abundance photoionization model for 30 Dor Tsamis & Péquignot 2005

52. The t 2 problem and the ORL/CEL discrepancy are still a subject of debate

53. quiz 1

54. Is HeII/H  fitted?

55. quiz 2

57. Quiz 3 1rst lines: observations 2nd lines: models

58. Quiz 3 1rst lines: observations 2nd lines: models