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Buzzoni, A., Arnaboldi, M., Corradi, R.L.M.:
"Planetary nebulae as tracers of galaxy stellar populations",
2006, MNRAS, 368, 877.

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We address the general problem of the luminosity-specific planetary nebula (PN) number, better known as the "α" ratio, given by α = NPN/Lgal, and its relationship with age and metallicity of the parent stellar population. Our analysis relies on population synthesis models, that account for simple stellar populations (SSPs), and more elaborated galaxy models covering the full star-formation range of the different Hubble morphological types. This theoretical framework is compared with the updated census of the PN population in Local Group galaxies and external ellipticals in the Leo group, and the Virgo and Fornax clusters. The main conclusions of our study can be summarized as follows:
i) according to the Post-AGB stellar core mass, PN lifetime in a SSP is constrained by three relevant regimes, driven by the nuclear (Mcore &ge 0.57 Msun), dynamical (0.57 Msun ≥ Mcore  ≥ 0.55 Msun) and transition (0.55 Msun &ge Mcore ≥  0.52 Msun) timescales. The lower limit for Mcore also sets the minimum mass for stars to reach the AGB thermal-pulsing phase and experience the PN event;
ii) mass loss is the crucial mechanism to constrain the value of α, through the definition of the initial-to-final mass relation (IFMR). The Reimers mass-loss parameterization, calibrated on Pop II stars of Galactic globular clusters, poorly reproduces the observed value of α in late-type galaxies, while a better fit is obtained using the empirical IFMR derived from white-dwarf observations in the Galaxy open clusters;
iii) the inferred PN lifetime for Local Group spirals and irregulars exceeds 10000 yr, which suggests that Mcore  ≤ 0.65 Msun cores dominate, throughout;
iv) the relative PN deficiency in elliptical galaxies, and the observed trend of α with galaxy optical colors support the presence of a prevailing fraction of low-mass cores (Mcore ≥ 0.55 Msun) in the PN distribution, and a reduced visibility timescale for the nebulae as a consequence of the increased AGB transition time. The stellar component with Mcore ≤ 0.52 Msun, which overrides the PN phase, could provide an enhanced contribution to hotter HB and Post-HB evolution, as directly observed in M 32 and the bulge of M 31. This implies that the most UV-enhanced ellipticals should also display the lowest values of α, as confirmed by the Virgo cluster early-type galaxy population;
v) any blue-straggler population, invoked as progenitor of the Mcore ≥ 0.7 Msun PNe in order to preserve the constancy of the bright luminosity-function cut-off magnitude in ellipticals, must be confined to a small fraction (few percents at most) of the whole galaxy PN population.

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   Browse the jpeg tables and figures (click on the thumbnails)
Table 1 - Luminosity-specific PN number for Salpeter SSPs(ASCII)     (Jpeg)
Table 2 - The luminosity-specific PN number for template galaxy models(ASCII)     (Jpeg)
Table 3 - The PN Luminosity Functions(ASCII)     (Jpeg)
Table 4 - The PN census in the Local Group galaxies(ASCII)     (Jpeg)
Table 5 - Recent additions to PN census in early-type galaxies(ASCII)     (Jpeg)
Table 6 - The updated PN sample for local and distant early-type galaxies(ASCII)     (Jpeg)
Figure 1 -
Specific evolutionary flux B, from eq. (4), for Buzzoni (1989) SSP models. Different metallicity sets (between Z~1/20 and 2 Zsun) are overplotted. In addition to the Salpeter case (s = 2.35), other IMF power-law coefficients are explored, as labeled on the plot. The value of B is given in units of (Lsunyr)-1.
Figure 2 -
Theoretical fuel consumption for stars along the PAGB evolution according to different model sets: Paczynski (1971; pentagon markers), Schönberner (1981, 1983; squares and rhombs), Vassilias & Wood (1994; dots and triangles). The different markers for the same model source refer to the prevailing case of a H or He thermal pulse terminating the AGB evolution, as labeled. Fuel is expressed in Hydrogen-equivalent solar mass, i.e. 1g of H-equivalent mass = 6x1018 ergs (cf. Renzini & Buzzoni 1986), and a solar metallicity is assumed in the models. A smooth analytical relation matching the data, according to eq. (5) is plotted as a solid curve.
Figure 3 -
Time evolution of the stellar mass at some tipping points across the H-R diagram for SSPs of different metallicity Z, about the solar value, as labeled in each panel. Upper strips in each panel are the theoretical loci for stellar mass at the tip of the RGB evolution, (MRGB) according to a Reimers mass loss parameter in the range 0.3 ≤ η ≤ 0.5, as labeled in the middle panel, for general reference. Lower strips mark the locus for stellar mass at the onset of PAGB evolution (MPAGB), again for the same reported range of the mass loss parameter η. The minimum mass for stars to reach the AGB thermal pulsing phase (and eventually produce a PN) is marked by the dashed line, according to Dorman et al. (1993) and Blöcker (1995).
Figure 4 -
The initial-to-final mass relation according to different calibrations. The solid strip is the theoretical relation of Iben & Renzini (1983) for a standard mass loss parameter η in the range between 0.3 and 0.5, as labeled on the plot. Small dots report the individual values as from the Buzzoni (1989) SSP models of Table 1 and the same Reimers parameters. Short- and long-dashed curves are the theoretical loci for stars to set on the AGB thermal pulsing phase (MTP), according to Iben & Renzini (1983) and Wagenuber & Weiss (1994) (WW94). Finally, big dots and solid curve report the Weidemann (2000) empirical relation based on the mass estimate of white dwarfs in Galactic open cluster.
Figure 5 -
The luminosity-specific PN number for SSP models of Table 1 (both for η = 0.3 and 0.5 and different metallicity, as reported top left) compared to the PAGB stellar core mass. Overplotted are also the expected calibration assuming the theoretical IFMR of Iben & Renzini (1983) and the empirical one from Weidemann (2000), as labeled. Note the clean relationship in place, with Mcore being the leading parameter to constrain α.
Figure 6 -
Theoretical time evolution of the luminosity-specific PN number for SSP models of Table 1 (both for  = 0.3 and 0.5 and the different metallicity values, as labeled top left on the plot) compared to the expected calibrations assuming the theoretical initial-to-final mass relation of Iben & Renzini (1983) and the empirical one from Weidemann (2000).
Figure 7 -
Theoretical time evolution of the luminosity specific PN density (α) for the Buzzoni (2005) template galaxy models along the whole E-Sa-Sb-Sc-Sd-Im Hubble morphological sequence. Models in left panel assume an IFMR as from the standard mass loss parameter η = 0.3, while those in the right panel rely on the empirical relation from Weidemann (2000). Note, in the latter case, the much shallower evolution of α. In the two panels, bulge-dominated spirals tend to approach the evolution of ellipticals at early epochs due to the increasing bulge contribution to the global galaxy luminosity.
Figure 8 -
Upper panel: the cumulative fraction of PNe in the different magnitude bins with respect to the luminosity-function bright cut-off (M*) for the double-exponential fit of the PNLF, as in eq. (18) (solid curve) and for the empirical SMC luminosity function according to Jacoby (2005) (dashed curve). Lower panel: completeness factor (CF = Ntot/N(M-M*)) for the same calibrations as in the upper panel. Also reported are the Ciardullo et al. (1989) data for M 31 (star markers), and the relevant correction factor for the α2.5 parameter. For better convenience, data are also listed in Table 3.
Figure 9 -
The expected bolometric correction for theoretical template galaxy models according to Buzzoni (2005). The models for different morphological type span the age range from 1 to 15 Gyr (the latter limit being marked by the solid dot on each curve). Bolometric correction refers to the V (upper panel) and B band (lower panel). A value of (Bol &minus V) = BCV = −0.85 mag can be taken as a representative correction for the whole galaxy types within a 10% uncertainty, as shown by the arrow on the upper plot. This also translates into BCB =−0.85− (B−V)gal for the B-band correction, as displayed by the dashed line in the lower panel.
Figure 10 -
A comprehensive overview of the luminosity-specific PN number in Local Group galaxies (star markers) and external ellipticals from Table 5 (solid triangles) and Table 6 (open triangles). PN data for local galaxies are from Table 4, and are based on the "Local Group Census Project" of Corradi et al. (2005). Also superposed on the plot, there are the Buzzoni (2005) template galaxy models, as summarized in Table 2. Galaxy evolution is tracked by models along the whole E-Sa-Sb-Sc-Sd-Im Hubble morphological sequence from 5 to 15 Gyr, with the latter limit marked by the big solid dots. Two model sequences are reported on the plot assuming an IFMR as from the standard case of a Reimers mass loss parameter η = 0.3 (lower sequence), and from the empirical relation of Weidemann (2000) (upper sequence). For the Widemann (2000) models, the relevant data of Table 2 have been corrected by Δ(B-V) = −0.02 mag and log α = log αW+0.04, according to the arguments of footnote (5). An indicative estimate of the mean representative PN lifetime (in years) is sketched on the right scale, according to eq. (22).
Figure 11 -
The observed distribution of the elliptical galaxy sample of Table 6 (plus M 32 and the bulge of M 31, as labeled on the plot) versus Lick spectrophotometric index Mg2. Note the relative lack of PNe (per unit galaxy luminosity) in more metal rich ellipticals. The relevant case of the merger galaxy NGC 1316 is singled out, while the active star forming elliptical NGC 205 is out of range with Mg2≤ 0.1 and not shown. See text for a discussion.
Figure 12 -
Same as Fig. 11, but for the galaxy velocity dispersion σ in km s-1. It is evident a lower value of α in high-σ (roughly more massive) galaxies. See text for further details.
Figure 13 -
The luminosity-specific PN number versus ultraviolet color (1550−V), as originally defined by Burstein et al. (1988), for the elliptical galaxy sample of Table 6 (plus the Andromeda satellites and the bulge of M 31). Some relevant cases, like NGC 205 (star forming), NGC 1316 and NGC 5128 (merger ellipticals) are singled out on the plot. Note the tight relationship between "quiescent" ellipticals and α, with UV-bright galaxies to be also PN-poor. See text for a full discussion of this important effect.
Figure 14 -
The blue shift of the integrated B−V color of old open clusters in the Galaxy caused by the BS stellar population, from Xin & Deng (2005). The BS component (NBS) is normalised in terms of its ratio to the number of MS stars down to 2 mag below the TO luminosity (N2). Solid dots are for the oldest (t ≥5 Gyr) clusters, while star markers include clusters with 1 ≤ t < 5 Gyr. Symbol size is proportional to cluster statistical richness.
Figure 15 -
A representation of the envisaged PN evolution versus core mass of PAGB stars. The effect of different parameters, like metallicity, mass loss and age is outlined. In particular three evolutionary regimes are singled out, with PN visibility lifetime τPN (and correspondingly α) constrained respectively by the nuclear timescale (τPAGB), shell dynamics (τdyn), and transition time (τtt). PN visibility drastically reduces for Mcore ≤ 0.55 Msun until reaching a critical limit for PN formation about Mcore ~ 0.52 Msun. See text for full discussion.

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