Stellar Population Synthesis Including Planetary Nebulae Paola Marigo

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

Why population synthesis of PNe? q 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. ) q Analyse PNLFs in different galaxies e. g. depedence of the bright cut-off on SFR, IMF, Z(t) q Constrain progenitors’ AGB evolution e. g. superwind phase, Mi-Mf relation, nucleosynthesis and dredge-up

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

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

Output of a synthetic PN model Mi=1. 7 M ; MCS= 0. 6 M ; Z=0. 019 Time evolution of: • Ionised mass • nebular radius • expansion velocity • optical configurations • emission line luminosities

Synthetic Samples of PNe MONTE CARLO TECHNIQUE SCHEME A) (Jacoby, Mendez, Stasinska, Stanghellini) ØRandomly generate a synthetic PN sample obeying a given central-star mass N(Mc) distribution Ø Mi an age is randomly assigned in the [0, t. PN] interval ØStellar and nebular parameters (L, Teff, Vexp, Mion, Rion, F ) from grid-interpolations

Synthetic Samples of PNe N(Mi, Z) (Mi) (t – H) t. PN MONTE CARLO TECHNIQUE SCHEME B) (Marigo et al. 2004) ØRandomly generate a synthetic PN sample obeying a given initial mass N(Mi, Z) distribution H(Mi, Z) Main Sequence lifetime § N(M ) § t. PN PN lifetime « H § (Mi) Initial mass function § (t – H) Star formation rate M i i Ø Mi an age is randomly assigned in the [0, t. PN] Z(t) Age-metallicity relation interval § ØStellar and nebular parameters (L, Teff, Vexp, Mion, Rion, F ) from grid-interpolations

Different synthetic schemes Author Jacoby 89 Stasinska 91 Mendez 97 Stanghellini 00 Marigo 04 ———————————————————————— CS masses gaussian exponential+cut-off pop-synthesis PAGB tracks Dynamics Line fluxes SFR S 83+WF 86 (Mneb, Vneb) phot. model S 83+B 95 VW 94 interacting winds analytic recipe phot. model constant +cut-off constant various choices

Properties of PNe and their Central Stars Mion-Rion relation Nel-Rion relation Line ratios Optical thickness/thinness Transition time Nuclear burning regime

How to explain the observed invariance of the bright cut-off ? I. III. 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. III. Ciardullo & Jacoby (1999) : circumstellar extinction always estinguishes the overluminous and massive-progenitor PNe below the cut-off. IV. V. VI. III. IV. V. VI. 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

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

WHICH PNe FORM THE CUT-OFF? 2. CENTRAL MASS DISTRIBUTION AS A FUNCTION OF LIMITING MAGNITUDE MCSPN 0. 70 -0. 75 M ; Mi 2 -3 M ; age 0. 5 -1. 0 Gyr Marigo et al. 2004

DEPENDENCE ON THE AGE OF THE LAST EPISODE OF STAR FORMATION Jacoby 1989 Stanghellini 1995 0. 77 0. 695 0. 68 Mendez & Soffner 1997 Marigo et al. 2004 Mmax=0. 63 Mmax=0. 70 Mmax=1. 19 1. 15 0. 74 0. 68 0. 65 0. 61

A FEW CONCLUDING REMARKS 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/He. II 4686 anticorrel. , Te distribution; [OIII] 5007/H distribution; optical thickness/thinness; H-/He-burners, transition time; Mi-Mf relation; distribution of chemical abundances 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.

TRANSITION TIME MOSTLY UNKNOWN PARAMETER: dependence on Menv, pulse phase, MLR, Mcs, etc. Stanghellini & Renzini 2000

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

DEPENDENCE OF THE PNLF ON H-/He-BURNING TRACKS Jacoby 1989 Marigo 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 )

Synthetic AGB evolution: observational constraints C-star LF Mi-Mf relation WD mass distr. Renzini & Voli 1981 Marigo 1999 Van der Hoek & Groenewegen 1997 Marigo 2001

Post-AGB evolutionary tracks Mostly used sets: H-burning central stars 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): He-burning central stars loops less luminous longer evolutionary timescales Frankovsky (2003) CS masses : 0. 56 – 0. 94 M Metallicities: Z= 0. 016, 0. 004

PN DYNAMICS Simple scheme Combination of constant parameters (Mneb, Vexp, R/R) Interacting-winds model (Kahn 1983; Volk & Kwok 1985; Breitschwerdt & Kahn 1990)

NEBULAR FLUXES: photoionisation codes Jacoby, Ciardullo et al. Stasinska et al. Marigo et al. INPUT • Nebular geometry • Rin, Rout • density N(H) • Elemental abundances (H, He, C, N, O, etc. ) • L and Teff of the CSPN OUTPUT • Te (volume average) • ionisation fractions • line fluxes Example: CLOUDY (Ferland 2001) Mi=2. 0 M ; MCSPN=0. 685 M ; Z=0. 008; H-burn. ; Mion=0. 091 M ; t. PN=3000 yr

OPTICAL PROPERTIES OF THE NEBULA ABSORBED IONISING PHOTONS ABSORBING FACTOR (MKCJ 93) EMITTED IONISING PHOTONS q Mendez et al. : randomly assigned as. Simulated a function. PN of sample: Teff, following results of model atmospheres applied Galactic CSPN. M 5007 < 1; Ntot to = 500 In particular, on heating tracks with T>40000 K tatr=500 yr SFR=const. ; Z=0. 019; H-burn. random uniform distribution 0. 05 and He-burn. max tracks optically thick ; optically thin q Jacoby et al. Stasinska et al. Marigo et al. derives from the coupling between nebular dynamics and photoionisation

Ionised mass-radius relation Simulated PN sample: M 5007 < 1; Ntot = 500 SFR=const. ; Z=0. 019; ttr=500 yr H-burn. and He-burn. tracks optically thick ; optically thin Observed data from Zhang (1995), Boffi & Stanghellini (1994)

Electron density-radius relation Simulated PN sample: M 5007 < 1; Ntot = 500 SFR=const. ; Z=0. 019; ttr=500 yr H-burn. and He-burn. tracks optically thick ; optically thin Observed data from Phillips (1998)

Line ratios Stasinska 1989

NEBULAR FLUXES: a semi-empirical recipe q 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

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