Abundance determinations  in photoionized  nebulae
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Abundance determinations in photoionized nebulae. Grazyna Stasinska. Observatoire de Meudon Mexico october 2006. Why care ?. 1- abundances in HII regions probe the present-day abundances in galaxies

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Abundance determinations in photoionized nebulae

Abundance determinations in photoionized nebulae

Grazyna Stasinska

Observatoire de Meudon

Mexico october 2006


Why care

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


Contents

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


Physical processes in ionized nebulae

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


What drives the electron temperature

What drives the electron temperature

  • The energy gain of the electrons are:

  • G = S i, jni j Gi j

  • where the Gi j are due to photoionization and collisional ionization

  • The energy losses of the electrons are:

  • L = S i, jni j Li j

    where the Li 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


Why is the gas temperature roughly uniform in photoionized nebulae

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°) 4pJn/(hn) an (hn-13.6eV) dn erg cm-3 s-1]

  • Ionization equilibrium equation of H at distance r =f RS

  • n(H°) 4pJn/(hn)an dn= n(H+)neaB(H)

  • Substituting:

  • G =n(H+)neaB(H)< E >

  • with < E > = 4pJn/(hn) an (hn-hn°) dn 4pJn/(hn)an dn ≈ A T*

  • Energy gains due to photoionization of H are

  • independent of distance to the star

  • proportional to the star temperature


Comments on energy losses

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

    Lcoll = n2 A21 hn21erg cm-3 s-1]

    where n2 results from the equilibrium equation of levels 1 and 2 :

    n1 ne q12 = n2 (A21 + ne q21)

  • In the limit of small ne one has

    Lcoll= n1 ne q12 hn21 = (n1 /nH) nHne 8.629 10-6W (1,2) /w1Te-0.5exp (-E12/kTe)hn21

  • 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 W

    • levels that can be easily attained at the temperature of the medium


    Other comments on the gas temperature

    Other comments on the gas temperature

    • Dependence of Te 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 m 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*, Te is lower for higher metallicity

      • for a given metallicity, Te is lower for lower T*

      • for given T* , ionization state and metallicity Te is higher if n > ncrit


    The t e structure in ionized nebulae

    The Te structure in ionized nebulae

    Photoionization models from Stasinska 1978

    effect of metallicity

    ---- Z subsolar

    __ Z over solar

    Strong Te gradients are present at high metallicities due to important O++ cooling


    Comments on line intensities

    comments on line intensities

    • Most nebular lines are optically thin

      exception: resonance lines H Lya, 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 Te

    • Recombination line intensities are inversely proportional to Te

    • Ratios of recombination lines are almost independent of Te

    • The ratios of a collisionally excited optical line and a recombination line strongly depend on Te


    The various methods for abundance determinations

    The various methods for abundance determinations

    • Photoionization model fitting

    • Empirical methods

      • Individual (or Te-based) methods

      • Statistical (or strong line) methods


    The process of model fitting

    the process of model-fitting

    Model

    Must

    Match

    Observations


    Abundance derivation by model fitting

    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 Hb flux

      • The SHb distribution (and the angular size of the Hb zone)

      • The visual magnitude of the ionizing source

      • The line intensities

    • 4) Go back to 1 and iterate until observations are reproduced


    For a good quality model fitting

    for a good quality model fitting

    • use as many observational constraints as possible

      • not only line intensity ratios

        2) keep in mind that some constraints are very important

      • eg: HeII/Hb, [OIII]4363/5007

        3) some constraints are not independant

      • eg if [OIII]5007/Hb is fitted => [OIII]4959/Hb 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/Hb 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 c2 = Si [(Imodi-Iobsi ) / si ]2minimization criterion

      • better use ∀i, [(Imodi-Iobsi ) / si ] 2<1


    Possible conclusions from model fitting

    possible conclusions from model fitting

    • 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


    An example of photoionization modelling with insufficient constraints

    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 2.40-41.00-3 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


    An example of photoionization modelling without a satisfactory solution

    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


    Empirical abundance determinations

    Empirical abundance determinations

    • Individual (or Te-based) methods

      1) Te and ne are obtained from plasma diagnostics

    Energy level diagrams

    Plasma diagnostic diagram for NGC 7027


    Empirical abundance determinations1

    Empirical abundance determinations

    • Individual (or Te-based) methods

      2) Ionic abundance ratios are determined from line intensity ratios

      eg:O++/H+ = ([OIII]5007/Hb) / (e[OIII]5007(Te)/eHb(Te))

    • 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)


    A note on ionization correction factors

    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 Te (UV lines or transauroral lines)


    A rough evaluation of t e based methods

    a rough evaluation of Te-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


    Abundance determinations in photoionized nebulae

    • abundances from optical lines

      • many telescopes, large collectors

      • all lines available in same spectrum

      • spectra affected by extinction

      • lines optically thin

      • intensities depend on Te, emitted in regions of Te>4000K

      • recombination affects forbidden lines at low Te

      • no icf needed for O in HII regions

      • icfs needed for N, Ne, S, Ar

      • 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

        Te:[ OIII] 4363/5007, [NII]5755/6884

        ne: [SII]6731/6717, [ArIV]4740/4711

    • abundances from FIR lines

      • few telescopes, small collectors

      • beamsize and calibration problems

      • FIR lines probe obscured regions

      • lines may be optically thick

      • intensities of CE lines independent of Te

      • icf needed for O

      • no icf for N, small for Ne, S, Ar

      • 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]

        ne:[OIII]52/88,[SIII]18/33,[NeIII]15/36, [ArIII] 9/21,[NeV]14/24


    A case of failure of t e based abundances

    a case of failure of Te-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 Te gradients are predicted

      • Te sensitive ratios strongly overestimate Te 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 !


    A further problem at high metallicity

    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


    Empirical abundance determinations statistical or strong line methods

    Empirical abundance determinationsstatistical (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 1979used ([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


    Rationale of mc gaugh s method

    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 , <T*>, U, O/H, N/O

    • underlying hypothesis of the method

      • <T*> 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])/Hb, 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)


    Mcgaugh diagrams for the o 23 method

    McGaugh diagrams for the O23+ method

    N/ersu/

     versus /


    What lies behind the behaviour of oiii 5007 h b vs o h

    what lies behind the behaviour of [OIII]5007/Hb vs O/H

    • Intensity ratio: [OIII]5007/Hb = A n(O++) / n(H+) Te0.5 exp (-28800/Te)

    • Thermal balance equation: n(H+) ne T* ≈ B ni jne Te-0.5 exp (- Eexc/Te)

    • For 12 + log O/H < 8.2

    • cooling is due to H Ly a,

    • Te is independent of O/H

    • [OIII]5007/Hb ≈ C T* O/H

    • For 12 + log O/H > 9

    • cooling is essentially

    • due to [OIII]52,88m

    • [OIII]5007/Hb ≈ C T* f(Te)

    • wheref(Te) = Te exp (- 28800/Te)

    • which decreases

    • with increasing O/H


    An evaluation of strong line methods

    An evaluation of strong line methods

    • Perez-Montero & Diaz 2005

    • uses a data base of 367 objects with measured Te

    • including some giant HII regions in the inner parts of galaxies (expected to be metal rich)

    • but ignores the strong bias due to low Te evidenced by Stasinska 05


    The strong line method recalibrated

    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 Te evidenced by Stasinska 05

        => the last word on abundances from strong line methods is not said


    Other problems and uncertainties in abundance determinations

    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


    Aperture correction

    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


    Relevance of elemental abundances in case of depletion

    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


    Correction for dust extinction

    Correction for dust extinction

    • The method:

      • The “logarithmic extinction at Hb”, C, is derived from the observed Ha/Hb ratio by comparing it to the theoretical one for case B recombination (at the Te corresponding to the nebula) using an extinction law f(l)

        C = [ log (FHa / FHb)B - log (FHa/ FHb)obs ] / (fa- fb)

      • Emission line ratios are then dereddened using the formula

        log (Fl1 / Fl2)corrB = log (Fl1 / Fl2)obs + C (fl1- fl2)

    • Problems:

      • The “extinction law” is not universal

      • The intrinsic Ha/Hb 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


    The extinction law is not universal

    the “extinction law” is not universal

    • the canonical extinction law corresponds to RV=AV / E(B-V) =3.2

    • in Orion RV = 5.5

    • towards the Galactic bulge, RV ~ 2.5 (Stasinska et al 94)

    • larger values of RV are found for lines of sight crossing molecular clouds where dust grains are expected to be larger

    Extinction laws corresponding to various RV=AV / E(B-V)

    .1989

    Histogram of RV for 95 galactic O stars Patriarchi et al 2001


    Checks on the reddening correction

    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 , Hg / Hb is close to the case B recombination value

        • If not, [OIII]4363/5007 is likely to be in error by the same amount as Hg/Hb 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


    Temperature fluctuations

    Temperature fluctuations

    • Were postulated by Peimbert (1967) to explain discrepancies betwen Tefrom various diagnostics

  • Peimbert’s formalism

    • Do temperature fluctuations exist?

      • see reviews by Peimbert 1995, 2001, Mathis 1997, Stasinska 1998, Esteban 1998, 2001

      • Numerous studies point towards t2 ~ 0.04

      • But little direct evidence is seen


    Example of indirect evidence for t 2 0

    example of indirect evidence for t2 ≠ 0

    In planetary nebulae Te from Balmer discontinuity is smaller than T[OIII] 4363/5007 (Liu & Danziger 1993)

    t2 ~ 0.04 is a representative value


    If t e fluctuations exist they affect abundance determinations

    If Te 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 t2

    Abundances derived from optical forbidden lines with respect to H are underestimated when ignoring t2

    Abundance ratios like N/O or C/O are less affected

    Abundances derived from recombination or FIR lines are not affected


    Visualizing the peimbert formalism on a two zone toy model

    visualizing the Peimbert formalism on a two-zone toy model

    V1n1 N1 T1

    V2n2 N2 T2

    volume

    electron density

    ionic density

    temperature

    f = N2n2V2 / N1n1V1

    in this case the values of T0 and t2 are simply :

    • variations of T1 and T2 with f for t2 = 0.04 and fixed T0

    • f >> 1 corresponds to a photoionized nebula with small shock-heated regions of very high T1

    • f << 1 corresponds to a nebula with high metallicity clumps of somewhat lower T2


    Is the peimbert formalism adequate

    Is the Peimbert formalism adequate ?

    • plots of log O++ as a function of f for two values of T0

    • left: T0 = 8000K

    • right: T0 = 15000K

    • O++ is derived from [OIII]5007 using Te measured by [OIII]4363/5007

    The amount by which O++ 5007 is underestimated depends on T0 and f

    • Even in a simple two-zone model, the situation requires

      • 3 parameters to be described (e.g. T0, t2 and f )

      • not 2 (T0 and t2)


    Visualisation of energy requirements

    Visualisation of energy requirements

    The simplest example:

    for t2 = 0.04 and T0 = 10000K, f =1 implies T1 = 12000K and T2 = 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 Te varies with energy input

    t2 = 0.04 requires D log G = 0.3, ie a factor 2 difference in heating rates between regions 1 and 2 !


    What fluctuates

    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 Te with respect to the ambient medium Kholtygin 1998, Mathis et al. 1998

        • (this is not sufficient to explain t2 ~ 0.04)

      • densities above 105cm-3 boost [OIII] 4363/5007 (Viegas & Clegg 1994)

        • but there is no evidence of such high densities in the O++ zones


    What fluctuates1

    What fluctuates?

    • Ni ?

      • Te 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 Te with respect to the ambient medium Kholtygin 1998, Mathis et al. 1998

        • (this is not sufficient to explain t2 ~ 0.04)

      • densities above 105cm-3 boost [OIII] 4363/5007 (Viegas & Clegg 1994)

        • but there is no evidence of such high densities in the O++ zones


    Is photoionization the only heating source in photoionized nebulae

    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)


  • The orl cel discrepancy

    the ORL /CEL discrepancy

    • Expected properties of optical recombination lines (ORLs)

      • their emissivity is roughly proportional to Te-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


    Orl versus cel abundances

    ORL versus CEL abundances

    • ionic abundances in the planetary nebula NGC 6153Liu et al 2000


    Invoked causes of orl cel discrepancy

    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 10-4Mathis& Liu 1999

    no (from echelle spectra )

    have been recomputed with the R-matrix method Storey 1994

    ORL abundances from numerous transitions are in agreement

    t2 explaining ORL-CEL discrepancy >> t2 explaining Te[OIII] -Te(BJ)

    IR-CEL abundances are consistent with optical -CEL abundances Liu 2000,2001

    no (high order Balmer lines) Liu 2000...


    Invoked causes of orl cel discrepancy1

    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 10-4Mathis& Liu 1999

    no (from echelle spectra )

    have been recomputed with the R-matrix method Storey 1994

    ORL abundances from numerous transitions are in agreement

    t2 explaining ORL-CEL discrepancy >> t2 explaining Te[OIII] -Te(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 104K

    Chemical inhomogeneities: they require super metal rich inclusions with solar C/N/O/Ne Liu 2000, Tsamis 2003


    Temperature of the orl zones tsamis et al 2004 liu et al 2004

    Temperature of the ORL zones Tsamis et al 2004, Liu et al 2004

    • In 4 PNe, it has been possible to derive Te from ratios of OII recombination lines that have a slightly different sensitivity to Te

    • 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


    A dual abundance photoionization model for 30 dor tsamis p quignot 2005

    a dual abundance photoionization model for 30 DorTsamis & Péquignot 2005


    The t 2 problem and the orl cel discrepancy are still a subject of debate

    The t2 problem and the ORL/CEL discrepancy are still a subject of debate


    Quiz 1

    quiz 1


    Quiz 11

    quiz 1

    Is HeII/H fitted?


    Quiz 2

    quiz 2


    Quiz 21

    quiz 2


    Abundance determinations in photoionized nebulae

    Quiz 3

    1rst lines: observations

    2nd lines: models


    Abundance determinations in photoionized nebulae

    Quiz 3

    1rst lines: observations

    2nd lines: models


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