1. Stellar Population Synthesis Including Planetary Nebulae Paola Marigo Astronomy Department, Padova University, Italy Lèo Girardi Trieste Observatory, INAF, Italy

2. Why population synthesis of PNe?  Understand basic properties of PNe and their nuclei e.g. M-R relation, line ratios, optical thickness/thinness, transition time, nuclear regime (H-burn. or He-burn.)  Analyse PNLFs in different galaxies e.g. depedence of the bright cut-off on SFR, IMF, Z(t)  Constrain progenitors’ AGB evolution e.g. superwind phase, Mi-Mf relation, nucleosynthesis and dredge-up

3. Basic requirements: extended grids of PN models  Kahn (1983,1989)  Kahn & West (1985)  Volk & Kwok (1985)  Stasińska (1989)  Ciardullo et al. (1989)  Jacoby (1989)  Kahn & Breitschwerdt (1990)  Dopita et al. (1992)  Mendez et al. (1993)  Stanghellini (1995)  Mendez & Soffner (1997)  Stasińska et al. (1998)  Stanghellini & Renzini (2000)  Marigo et al. (2001; 2004) Simplified approach still necessary. Various degrees of approximation: AGB evolution, nebular dynamics; photoionisation Recent improvements of hydrodynamical calculations: large sets now becoming available  Perinotto et al. 2004  Schoenberner et al. 2005

4.  central star mass (Mi, Z) [p][p]  AGB wind  density and chemical comp. of the ejecta (r, t) POST-AGB EVOLUTION  logL-logTeff tracks (H-burn./He burn.) [p][p]  fast wind DYNAMICAL EVOLUTION OF THE NEBULA IONISATION AND NEBULAR EMISSION LINES  photoionisation code [p] or other[p] semi-empirical recipe [p] [p]  (M neb, V exp ) parametrisation .interacting-winds model [p][p] Synthetic PN evolution: basic ingredients AGB EVOLUTION

5. Mi=1.7 M  ; M CS = 0.6 M  ; Z=0.019 Output of a synthetic PN model Time evolution of: Ionised mass nebular radius expansion velocity optical configurations emission line luminosities

6. Synthetic Samples of PNe MONTE CARLO TECHNIQUE SCHEME A) (Jacoby, Mendez, Stasinska, Stanghellini)  Randomly generate a synthetic PN sample obeying a given central-star mass N(Mc) distribution   Mi an age is randomly assigned in the [0,  t PN ] interval  Stellar and nebular parameters ( L, T eff, V exp, M ion, R ion, F ) from grid-interpolations

7. Synthetic Samples of PNe N ( M i, Z )   ( M i )  ( t –  H )  t PN   H (M i,Z) Main Sequence lifetime   t PN PN lifetime «  H   ( M i ) Initial mass function   ( t –  H ) Star formation rate  Z (t) Age-metallicity relation SCHEME B) (Marigo et al. 2004)  Randomly generate a synthetic PN sample obeying a given initial mass N(Mi,Z) distribution   Mi an age is randomly assigned in the [0,  t PN ] interval  Stellar and nebular parameters ( L, T eff, V exp, M ion, R ion, F ) from grid-interpolations N(M i ) MiMi MONTE CARLO TECHNIQUE

8. Different synthetic schemes Author Jacoby 89 Stasinska91 Mendez97 Stanghellini00 Marigo04 ———————————————————————————————————————————————— CS masses gaussian gaussian exponential+cut-off pop-synthesis pop-synthesis PAGB tracks S83+WF86 S83 S83+B95 VW94 VW94 Dynamics (M neb,V neb ) (M neb,V neb )   interacting winds Line fluxes phot. model phot. model analytic recipe  phot. model SFR   constant +cut-off constant various choices

9. Properties of PNe and their Central Stars M ion -R ion relation N el -R ion relation Line ratios Optical thickness/thinness Transition time Nuclear burning regime

10. How to explain the observed invariance of the bright cut-off ? I.Jacoby (1996): narrow CSPN mass distribution (0.58 ± 0.02 M  ) over the age range (3-10 Gyr), i.e. initial mass range (1-2 M  ) II.Ciardullo & Jacoby (1999) : circumstellar extinction always estinguishes the overluminous and massive-progenitor PNe below the cut-off. III.Marigo et al. (2004): still open problem, difficult to recover for Ellipticals IV. Ciardullo (2005): Possible contribution of PNe in binary systems SO FAR NOT ROBUST THEORETICAL EXPLANATION

11. WHICH PNe FORM THE CUT-OFF? 1.  OIII  5007 LUMINOSITIES AS A FUNCTION OF AGE Jacoby 1989 Stasińska et al. 1998 Marigo et al. 2004

12. WHICH PNe FORM THE CUT-OFF? 2. CENTRAL MASS DISTRIBUTION AS A FUNCTION OF LIMITING MAGNITUDE Marigo et al. 2004 M CSPN  0.70-0.75 M  ; M i  2-3 M  ; age  0.5-1.0 Gyr

13. DEPENDENCE ON THE AGE OF THE LAST EPISODE OF STAR FORMATION Mmax=0.63 Mmax=0.70 Mmax=1.19 0.68 0.695 0.77 Jacoby 1989 Mendez & Soffner 1997 Stanghellini 1995 Marigo et al. 2004 0.610.650.680.741.15

14. A FEW CONCLUDING REMARKS Population-age dependence of the PNLF: difficulty to explain the observed invariance of the bright cut-off in galaxies from late to early types Still to be included: full hydrodynamics, non-sphericity, binary progenitors, etc. Population synthesis including PNe is a powerful — still not fully exploited — tool to get insight into several aspects of PNe and their central stars e.g. ionised mass-radius rel.; electron density-radius rel.; [OIII] 5007/HeII4686 anticorrel., Te distribution; [OIII] 5007/H  distribution; optical thickness/thinness; H-/He-burners, transition time; Mi-Mf relation; distribution of chemical abundances

15. TRANSITION TIME MOSTLY UNKNOWN PARAMETER: dependence on M env, pulse phase, MLR, M cs, etc. Stanghellini & Renzini 2000

16. DEPENDENCE OF THE PNLF ON TRANSITION TIME (continued) Stanghellini 1995 Marigo et al. 2004 Differences in the bright cut-off due to different t tr show up for larger M max, or equivalently for younger ages Solid line: constat t tr ; dashed line: mass -dependent t tr

17. DEPENDENCE OF THE PNLF ON H-/He-BURNING TRACKS Jacoby 1989Marigo et al. 2004 H-burn. He-burn. Differences in the bright cut-off due to different tracks show up for older ages The bright cut-off is reproduced by more massive H-burning CS (0.65 M  ) compared to He-burning CS (0.61 M  )

18. C-star LFMi-Mf relationWD mass distr. Renzini & Voli 1981 Marigo 1999 Van der Hoek & Groenewegen 1997 Synthetic AGB evolution: observational constraints Marigo 2001

19. Mostly used sets: Schoenberner (1983) + Bloecker (1995) CS masses: 0.53 – 0.94 M  Metallicities: Z=0.021 Vassiliadis & Wood (1994) CS masses: 0.59 – 0.94 M  Metallicities: Z= 0.016, 0.008, 0.004, 0.001 Recent sets (synthetic): Frankovsky (2003) CS masses : 0.56 – 0.94 M  Metallicities: Z= 0.016, 0.004 H-burning central stars He-burning central stars  loops  less luminous  longer evolutionary timescales Post-AGB evolutionary tracks

20. PN DYNAMICS (Kahn 1983; Volk & Kwok 1985; Breitschwerdt & Kahn 1990) Interacting-winds model Simple scheme Combination of constant parameters (M neb, V exp,  R/R)

21. NEBULAR FLUXES: photoionisation codes INPUT Nebular geometry Rin, Rout density N(H) Elemental abundances (H,He,C,N,O,etc.) L and Teff of the CSPN Example: CLOUDY (Ferland 2001) Mi=2.0 M  ; M CSPN =0.685 M  ; Z=0.008; H-burn.; Mion=0.091 M  ; t PN =3000 yr OUTPUT Te (volume average) ionisation fractions line fluxes Jacoby, Ciardullo et al. Stasinska et al. Marigo et al.

22. OPTICAL PROPERTIES OF THE NEBULA ABSORBING FACTOR    (MKCJ93)  ABSORBED IONISING PHOTONS  EMITTED IONISING PHOTONS  Mendez et al. :  randomly assigned as a function of T eff, following results of model atmospheres applied to Galactic CSPN. In particular, on heating tracks with T>40000 K a random uniform distribution 0.05     max  Jacoby et al. Stasinska et al.  derives from the coupling between nebular dynamics and photoionisation Marigo et al. Simulated PN sample: M 5007 < 1 ; N tot = 500 SFR=const.; Z=0.019; t tr =500 yr H-burn. and He-burn. tracks  optically thick ;  optically thin

23. Ionised mass-radius relation Observed data from Zhang (1995), Boffi & Stanghellini (1994) Simulated PN sample: M 5007 < 1 ; N tot = 500 SFR=const.; Z=0.019; t tr =500 yr H-burn. and He-burn. tracks  optically thick ;  optically thin

24. Electron density-radius relation Observed data from Phillips (1998) Simulated PN sample: M 5007 < 1 ; N tot = 500 SFR=const.; Z=0.019; t tr =500 yr H-burn. and He-burn. tracks  optically thick ;  optically thin

25. Line ratios Stasinska 1989

26. NEBULAR FLUXES: a semi-empirical recipe  Mendez et al. : Once specified (L,Teff) of the CSPN Recombination theory for optically thick case  H  fluxes Random  - factor correction  true H  fluxes Empirical distribution I ( 5007)  I (H  )  H  OIII  5007 fluxes

27. I([OIII] 5007)/I(H  ) DISTRIBUTION of GALACTIC PNe Observed (McKenna et al. 1996) Predicted (He-burning tracks)