Stellar Population SynthesisIncluding Planetary Nebulae

Paola Marigo Astronomy Department, Padova University, Italy

Lèo Girardi Trieste Observatory, INAF, Italy

Why population synthesis of PNe?

Understand basic properties of PNe and their nucleie.g. M-R relation, line ratios, optical thickness/thinness,transition time, nuclear regime (H-burn. or He-burn.)

Analyse PNLFs in different galaxiese.g. depedence of the bright cut-off on SFR, IMF, Z(t)

Constrain progenitors’ AGB evolutione.g. superwind phase, Mi-Mf relation, nucleosynthesisand dredge-up

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

central star mass (Mi, Z) [p] AGB wind density and chemical comp. of the ejecta (r, t)

POST-AGB EVOLUTION logL-logTeff tracks (H-burn./He burn.) [p] fast wind

DYNAMICAL EVOLUTION OF THE NEBULA

IONISATION AND NEBULAR EMISSION LINES

photoionisation code [p] or other semi-empirical recipe [p]

(Mneb, Vexp) parametrisation .interacting-winds model [p]

Synthetic PN evolution:basic ingredients

AGB EVOLUTION

Mi=1.7 M; MCS= 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

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, tPN] interval

Stellar and nebular parameters (L, Teff, Vexp, Mion, Rion, F) from grid-interpolations

Synthetic Samples of PNe

N(Mi,Z) (Mi) (t – H) tPN

H(Mi,Z) Main Sequence lifetime

tPN PN lifetime «H

(Mi) 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, tPN] interval

Stellar and nebular parameters (L, Teff, Vexp, Mion, Rion, F) from grid-interpolations

N(Mi)

Mi

MONTE CARLO TECHNIQUE

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 (Mneb,Vneb) (Mneb,Vneb) interacting winds

Line fluxes phot. model phot. model analytic recipe phot. model

SFR 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. 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

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

Marigo et al. 2004

MCSPN 0.70-0.75 M; Mi 2-3 M; age 0.5-1.0 Gyr

DEPENDENCE ON THE AGE OF THE LAST EPISODE OF STAR FORMATION

Mmax=0.63Mmax=0.70Mmax=1.19

0.680.6950.77

Jacoby 1989

Mendez & Soffner 1997

Stanghellini 1995

Marigo et al. 2004

0.610.650.680.741.15

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

TRANSITION TIME

MOSTLY UNKNOWN PARAMETER: dependence on Menv, pulse phase, MLR, Mcs, etc.

Stanghellini & Renzini 2000

DEPENDENCE OF THE PNLF ON TRANSITION TIME

(continued)

Stanghellini 1995 Marigo et al. 2004

Differences in the bright cut-off due to different ttr show up for larger Mmax, or equivalently for younger ages

Solid line: constat ttr; dashed line: mass -dependent ttr

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-burningCS (0.65 M) compared to He-burning CS (0.61 M)

C-star LF Mi-Mf relation WD mass distr.

Renzini & Voli 1981

Marigo 1999

Van der Hoek & Groenewegen 1997

Synthetic AGB evolution: observational constraints

Marigo 2001

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

PN DYNAMICS

(Kahn 1983; Volk & Kwok 1985; Breitschwerdt & Kahn 1990)

Interacting-winds model

Simple scheme Combination of constant parameters (Mneb, Vexp, R/R)

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; MCSPN=0.685 M; Z=0.008; H-burn.; Mion=0.091 M; tPN=3000 yr

OUTPUT• Te (volume average)• ionisation fractions• line fluxes

Jacoby, Ciardullo et al.Stasinska et al.Marigo et al.

OPTICAL PROPERTIES OF THE NEBULA

ABSORBING FACTOR (MKCJ93)

ABSORBED IONISING PHOTONS EMITTED IONISING PHOTONS

Mendez et al. : randomly assigned as a function of Teff, 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:

M5007 < 1; Ntot = 500SFR=const.; Z=0.019; ttr=500 yrH-burn. and He-burn. tracks optically thick ; optically thin

Ionised mass-radius relation

Observed data from Zhang (1995), Boffi & Stanghellini (1994)

Simulated PN sample:

M5007 < 1; Ntot = 500SFR=const.; Z=0.019; ttr=500 yrH-burn. and He-burn. tracks optically thick ; optically thin

Electron density-radius relation

Observed data from Phillips (1998)

Simulated PN sample:

M5007 < 1; Ntot = 500SFR=const.; Z=0.019; ttr=500 yrH-burn. and He-burn. tracks optically thick ; optically thin

Line ratios

Stasinska 1989

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) HOIII 5007 fluxes

I([OIII]5007)/I(H) DISTRIBUTION of GALACTIC PNe

Observed (McKenna et al. 1996)

Predicted (He-burning tracks)

Predicted (He-burning tracks)