Galactic Planetary Nebulae as Probes of Radial Metallicity Gradients and Other Abundance Patterns

As described in SH10, Type I PNe are those with log(N/H) + 12 > 8.4 and log(He/H)+12 > 11.1; Type II and Type III PNe are defined as non-Type I PNe with (absolute) peculiar velocities respectively smaller (Type II) or larger (Type III) than 60 km s⁻¹. Type I PNe are probably evolving from AGB stars with mass M > 2–3 M_⊙ (Peimbert & Serrano 1980; Kaler et al. 1990). Stars of these masses represent a young stellar population at all metallicities. Type II are disk PNe, the progeny of the 1.2 M_⊙ ≤ M ≤ 2 M_⊙ stars at solar metallicity. Type III PNe are those evolving from stars of M ≤ 1.2 M_⊙ (Perinotto et al. 2004). All of these mass limits are very approximate, and they are valid only for Galactic PNe.

In Figure 1, we show the stellar age vs turnoff mass relation from Maraston (1998)'s fuel consumption theorem. The progenitor age ranges are 0 Gyr ≤ t_⋆ < 1 Gyr for Type I PNe, 1 Gyr ≤ t_⋆ < 5 Gyr for Type II PNe, and t ≥ 5 Gyr for Type III PNe, from their (very approximate) turnoff mass. In the figure, we mark the separations corresponding to the assumed limiting ages of the progenitors of Type I, II, and III PNe. The stellar progenitors of Type III PNe are old, but a sizable fraction of Type II PNe may be old as well; thus, it is difficult to sort Type II and Type III PNe into clear age groups. The state of the art is that these PN Types do not offer a quantitative indication of their progenitor ages, and this is the reason why, in this paper, we are developing a more quantitative way to date PN progenitors.

The extensive stellar data that have been flourishing in recent years can give us more insight on the PN progenitor dating problem. Ramírez et al. (2013) analyzed hundreds of nearby FGK field stars and derived their ages, masses, and several atomic abundances, including oxygen and iron. We selected a subsample of their large stellar data set (>800 stars) to build an O/H versus t_⋆ relation that we can use to date PN progenitors. We started by studying their [O/Fe]-versus-[Fe/H] relation, then scaled it with their [O/Fe]-versus-t_⋆ relation. We have only used stars with 5600 K < T_eff < 5900 K to only keep stars with the best determined atmospheric parameters. We also selected stars with [O/Fe] > (−0.48[Fe/H] + 0.04), in order to discard metal-poor thin disk stars, which are mainly objects of the outer disk seen in the solar vicinity but have a chemical evolution different from stars in the population that we want to compare to PN progenitors.

The resulting sample is populated by 181 stars. We plot their ages and masses given in Ramírez et al. (2013) in Figure 1. From the comparison of these data with the age–mass relation for old stars, it is clear that Type I and Type II PN classes do not discriminate the progenitors' ages very well.

In Figure 2, we plot log(O/H) + 12, derived by us as described above, versus stellar age. Clearly, stars with log(O/H) + 12 > 8.7 have an almost equal chance to be younger or older than 7.5 Gyr. On the other hand, stars with log(O/H) + 12 < 8.7 are almost invariably older than 7.5 Gyr. Conversely, if we assume that oxygen is not produced or processed by PN progenitors, and if we select PNe whose log(O/H) + 12 < 8.7, we are selecting a very old disk population of PNe with progenitors older than ∼7.5 Gyr. This selection method works well to exclude young progenitors from PN samples whose oxygen abundance is known. By working with oxygen gradients, we want to characterize the complete population of PNe with old progenitors; i.e., we like to include those PNe whose oxygen abundance is larger than 8.7 and whose progenitors have ages >7.5 Gyr (i.e., the ones that represent the progeny of the stars in the upper right corner of Figure 2). In order to do so, we need to look into AGB evolutionary yields, as described in the next section.

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During the AGB, the chemistry of the outer layers of the star changes due to nucleosynthesis. These outer layers, once ejected and ionized, become the PN; thus, abundance analysis of PNe can be directly compared to the final yields of AGB evolution, and from this comparison one can derive a sound assessment of the progenitor's mass and metallicity. The key elements for comparison between theoretical yields and observed abundances are carbon and nitrogen, largely processed in AGB stars, while oxygen and other α-elements are almost invariant in this phase of stellar evolution and are needed to frame the initial conditions of the models. Nitrogen is highly enhanced at the expense of carbon in high-mass progenitors; thus, PNe with enriched nitrogen have progenitor masses at least as high as the minimum critical mass for HBB processing.

While it is impossible to model the evolution of the progenitor of every single observed PN, in the last few years new models of AGB evolution have become available spanning a larger mass and metallicity domain. Ventura et al. (2016) showed the final C/H, N/H, and O/H yields for a broad range of metallicities and for turnoff masses 1.5 M_⊙ < M_TO < 8 M_⊙. We use their N/H versus C/H and N/H versus O/H theoretical planes (Ventura et al. 2016, their Figure 2) to determine zones where PNe are bound to have either old or young progenitors.

Old and young PN progenitors on the N/H versus C/H plane occupy markedly different loci; thus, carbon abundances, in combination with nitrogen abundances, are the most useful to date PN progenitors. From Ventura et al. (2016, Figure 2, right panel), we infer that if C/H > N/H, the AGB star has gone through the carbon star phase. Thus, if we observe a PN with C/H > N/H, we can be reasonably sure that it has a low-mass progenitor. On the other hand, if log(N/H) + 12 is above the 0.57 × [log(C/H) + 12] + 3.67 line (obtained by a linear fit on the plot), the AGB star has gone through the HBB; thus, it has M > 3 M_⊙ and t_⋆ < 0.5–1 Gyr, depending on metallicity.

Direct carbon abundances in PNe are based on the observation of the bright carbon emission line in the UV; thus, they are difficult to observe and need space-based data. Nitrogen and oxygen abundances are measured from optical spectra. To enlarge the sample of PNe for which we can determine the progenitor age, we also use the N/H-versus-O/H diagnostics. Following the plot by Ventura et al. (2016, their Figure 2, left panel), we determine that PNe with nitrogen below the [log(N/H) + 12] = 0.8 × [log(O/H) + 12] + 1.4 line (fitted on the plot) are those that may descend from carbon stars. On the other hand, nitrogen abundances above the [log(N/H) + 12] = 0.6 × [log(O/H) + 12] + 3.3 line are the clear signature of the HBB occurrence, which indicates masses above ∼3 M_⊙ and thus t_⋆ < 1 Gyr.

We define PNe with old progenitors (or OPPNe) as those PNe with C/H > N/H or [log(N/H) + 12] < 0.8 × [log(O/H) + 12] + 1.4. We define PNe with young progenitors (or YPPNe) as those PNe whose abundances comply with the equations C/H < N/H or [log(N/H) + 12] > 0.6 × [log(O/H) + 12] + 3.3.

Tables 1–3 give the data used to calculate radial metallicity gradients and other abundance patterns in this paper. In Table 1, we give the PN G number, heliocentric and Galactocentric distances (in kpc), angular radius (in arcsec), main morphology, and PN progenitor type (OPPNe or YPPNe), if available, of the PNe in our study.

In Table 2, we give the elemental abundances of He, C, N, O, Ne, and Ar, selected by us from the references above (S method).

In Table 3, we give the average abundances (A method) and their ranges, for all PNe with more than one abundance measurement of at least one of the elements He, C, N, O, Ne, and Ar. All abundances are from the above references. Those PNe with no or just one abundance measurement of each element in the reference above are not listed in Table 3.

Tables 1– 3 are published in their entirety only electronically.

In Figure 4, we show the radial oxygen gradients derived for YPPNe (top) and OPPNe (bottom). In this plot, we use S abundances, excluding those with known uncertainties larger than 0.5 dex. Gradient slopes, obtained from a simple linear fit, are −0.015 and −0.027 for the OPPNe and YPPNe populations, respectively (see Table 4). Linear fits can also be obtained using the fitexy routine, which takes into account uncertainties in both axes (Press et al. 1992). A fit that includes the data of Figure 4 with uncertainties either measured or assumed to be 0.2 dex for all abundances gives a χ² fit probability of q > 0.9 for both OPPNe and YPPNe, Δlog(O/H)/ΔR_G (OPPNe) = −0.0013 ± 0.005 dex kpc⁻¹ and Δlog(O/H)/ΔR_G (YPPNe) = −0.023 ± 0.008 dex kpc⁻¹, consistent with basic linear fits. The calculated uncertainties on the slopes, 0.005 and 0.008 dex kpc⁻¹, respectively, for OPPNe and YPPNe, are smaller than the slope difference between the two populations. We thus conclude that the OPPN radial oxygen gradient is significantly flatter than the YPPN one, indicating steepening of the gradient slope since Galaxy formation.

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If we (attempt to) exclude bulge and halo PNe from the sample by the same approach used in SH10, we obtain a gradient slope for the old population of Δlog(O/H)/ΔR_G(OPPNe) = −0.019, and for the young population of Δlog(O/H)/ΔR_G(YPPNe) = −0.026. In general, by eliminating bulge and halo PNe from a sample, its metallicity gradient does not vary in a significant way.

By using OPPNe and YPPNe and measuring the radial oxygen gradients with Galactocentric distances based on a different distance scale, for example, the brightness temperature distance scale (van de Steene & Zijlstra 1995), we obtain Δlog(O/H)/ΔR_G (OPPNe) = −0.0103 and Δlog(O/H)/ΔR_G(YPPNe) = −0.024. Using another distance calibration, such as the surface brightness–to–physical radius correlation (e.g., Frew et al. 2016), does not change the gradients significantly either.

All gradient plots shown so far are characterized by high scatter. More information can be derived by binning these plots in the Galactocentric distance direction, as shown in Figure 5. Here the data of Figure 4 have been binned in Galactocentric distance bins of 1, 3, and 9 kpc (top to bottom). The slopes of the YPPNe are always steeper than the slopes of the OPPNe with the same binning, and intercepts are always larger for the young populations. The gradient slopes of Figure 5 are Δlog(O/H)/ΔR_G (YPPNe) = −0.034, −0.035, and −0.023 and Δlog(O/H)/ΔR_G (OPPNe) = −0.015, −0.012, and −0.012 for the 1, 3, and 9 kpc binning, respectively. In the figure, it is clear that the gradients of the old and young populations are similar in the inner Galactic disk, and they diverge for large Galactocentric distances.

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The comparison with other published gradients must take into account the radial extent and age range of the probes. For example, oxygen gradients have been measured by the APOGEE team using Galactic open clusters (Cunha et al. 2016). Most of the clusters have ages within 1–2 Gyr; thus, they compare well with our YPPNe. Cunha et al. (2016) found an oxygen gradient of −0.032 ± 0.007 dex kpc⁻¹, which agrees with the YPPNe gradient slope within the uncertainties.

By applying a standard correction from O/H to Fe/H abundance gradients, the iron gradient from YPPNe would be about −0.06 dex kpc⁻¹ (2 × −0.03 dex kpc⁻¹), to compare with gradients measured on open clusters and field stars around ∼−0.1 dex kpc⁻¹. The reason why the PN gradient is shallower than other gradients might be the distance range taken into account. The PN sample extends from the Galactic center to R > 20 kpc, while open cluster is essentially observed at R > 6 kpc. When the PN gradient is measured on a more restricted interval (see Section 6.2), the gradient is much steeper and compatible with other tracers. The PN data are, however, too sparse to be able to measure the variation of the local gradient on the sample of YPPNe, making it difficult to know if the gradient has flattened or steepened over the distance range 6–10 kpc, as seems to be the case for open clusters.

From the gradients studied in this section, we find a mild steepening of the gradient with time since Galaxy formation. The differences are small but persist in each experiment across assumptions on distance scale, bulge and halo PN inclusion, and independent of the abundance choices.

We explore the distance from the Galactic plane distribution of YPPNe and OPPNe, starting from the sample of Figure 4. While the scatter of the two populations is large, we find that the median distance from the Galactic plane of the OPPNe is twice that of the YPPNe, with $\langle | {\rm{z}}{| }_{\mathrm{YPPNe}}\rangle =265\pm 269$ pc, while $\langle | {\rm{z}}{| }_{\mathrm{OPPNe}}\rangle =484\pm 322$ pc (median values and standard deviations). Apparently, YPPNe do not populate the thick disk, in agreement with stellar studies.

The PN radial oxygen distributions shown so far may be best fitted with a step function rather than a continuous gradient. In the linear fits to the radial distributions based on old progenitors (Figure 4, OPPNe), the fitted gradients tend to be systematically below the observed points in the range 5 kpc < R_G < 11 kpc. In Figure 4, most of the points with R_G < 10 kpc have oxygen above log(O/H) + 12 = 8.5. The (few) points at R_G > 12–14 kpc are below the log(O/H) + 12 = 8.5 line, meaning that there is a kind of step function in the data. The distribution can be fitted by a flat gradient at R_G < 10 kpc and log(O/H) + 12 ∼ 8.6 (the slope is flat, with the fit giving a slope of 0.009 dex kpc⁻¹ in this region) and another flat gradient at R_G > 13.5, also with a flat slope (−0.006 dex kpc⁻¹) at log(O/H) + 12 ∼ 8.37, which, formally, represents a decrease of 0.065 dex kpc⁻¹ between 10 and 13.5 kpc. In Figure 6, we show the OPPNe panel of Figure 4, where we superimpose the gradients found by fitting the three regions, R_G < 10, 10 < R_G < 13.5, and R_G > 13.5 kpc, respectively.

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Preliminary results on the OPPNe oxygen gradient slope with Gaia parallax distances (L. Stanghellini et al. 2018, in preparation), available only for R_G < 10 kpc, agree with our result.

The step-like function seen in PNe is also observed in other tracers (although the distance scales for different probes may have relative biases). This is true in particular for open clusters, for which the gradient seems to be steep between about 7 and 10 kpc and then flattens (e.g., Lépine et al. 2011; Frinchaboy et al. 2013; Netopil et al. 2016; Reddy et al. 2016). The line between the two flat gradients of Figure 6 for OPPNe has a slope of roughly −0.033 dex kpc⁻¹, which, allowing for the standard factor of 2 for the conversion between O and Fe (see SH10 and references therein), would mean a gradient around −0.07 dex kpc⁻¹. Similar steep gradients have been found on field stars between 7 and 10 kpc (e.g., Bovy et al. 2014; −0.09 dex kpc⁻¹), while results from, for instance, the APOGEE survey from Hayden et al. (2015) found a gradient of about −0.05 dex kpc⁻¹ beyond R ∼ 6 kpc, with no indication of a flattening beyond 10 kpc. Figure 7 of Hayden et al. (2015) shows that the peak of the thin disk metallicity distribution function varies from +0.25 to −0.1 dex, or an ∼0.35 dex decrease in metallicity between 6 and 10 kpc, a value similar to that of Bovy et al. (2014). Although with fewer points, the distribution of YPPNe and OPPNe suggests the same behavior, with the mean oxygen abundance below 10 kpc being significantly higher than the distribution beyond this limit, as is found on other data.

Finally, it is interesting to note that OPPNe draw a homogeneous population with no significant gradient within 10 kpc, a characteristic that is also found in the thick disk population, which extends to the same limits and has no detected gradient (see Cheng et al. 2012).

It is worth recalling that the Galactic PN distances may be slightly overestimated, since the SSV scale gives higher distances when compared to parallactic distances (Smith 2015). Using a different statistical scale will not change the results considerably.

Unlike in SH10, the more complete data presented here allowed us to find evidence of a step function in the radial distribution of the oxygen abundance of old progenitor PNe versus R_G; see Section 6.2. Halle et al. (2015; see also Halle et al. 2018) proposed that the step feature observed on chemical abundances (metallicities of field stars or open clusters (OCs), oxygen abundances of PNe) is the effect of the presence of the outer Lindblad resonance (OLR) of the bar at about the same radius (7–10 kpc from the Galactic center; see Dehnen 2000; Pérez-Villegas et al. 2017). Here N-body simulations show that the bar allows stars in the disk to gain or lose angular momentum between resonances (hence to migrate by "churning"), but they are generally not allowed to cross the OLR of the bar when the bar is the main asymmetry. The migration by churning essentially stops at the OLR, and the stars cannot migrate further out by gaining angular momentum. In the Milky Way disk, the OLR is located near the solar orbit (7–10 kpc from the Galactic center), according to Dehnen (2000), setting a barrier that separates the inner (R_G < 7 kpc) and outer (R_G > 10 kpc) disk and that may be responsible for the dichotomy in the chemical properties of the inner and outer disk, which is visible in local data (Haywood et al. 2013) and most clearly in the in situ APOGEE data; see Hayden et al. (2015).

Observations show that bars in Milky Way–type galaxies are forming at epochs around z = 1–1.5 (Sheth et al. 2008; Melvin et al. 2014). If this is also the case for the Milky Way, it means that this dynamical separation between the inner and outer disk could have been in place at the end of the thick disk formation, already 9 Gyr ago (see Haywood et al. 2016 and M. Haywood et al. 2018, in preparation). A long-lived bar and its OLR would then guarantee that these two regions would remain essentially separated in the last 8–9 Gyr, explaining the observed dichotomy and the step function also reflected in the distribution of PNe in chemical abundances.

Radial metallicity gradients are key constraints for chemical evolution models. Gradients can be modified by various physical processes whose contribution we must try to assess. Within 10 kpc of the Galactic center, the data show that the oxygen gradient is essentially flat for OPPNe. While it is not clear how much the OPPN sample represents the thick disk, this is reminiscent of the flat gradient that has been found for this population with the SEGUE data (Cheng et al. 2012). It has been argued that even if there had been a gradient in the thick disk, mixing of stars (by either blurring or churning) would have erased it. It must be remembered that this is not the case, for several reasons discussed in Haywood et al. (2015). A metallicity gradient at a given epoch means that, at the corresponding age, in the thick disk, stars of different metallicities and α-elements are formed. Yet it is observed that at any given age in the thick disk, metallicities and α-elements have a very small dispersion (Haywood et al. 2015, 2016), implying an absence of gradient and hence an absence of inside-out process in this population. We comment further on this result in the next section.

In nearby external spirals, the evolution of metallicity gradients has been inferred by comparing those from the populations of H ii regions and PNe. Even if they belong to different stellar evolutionary paths, these emission-line probes are observed and analyzed identically, often within the same multi-object observed frame; thus, the contrast between the resulting gradients is very credible. The PNe and H ii regions have been observed directly to derive radial oxygen gradients in a small sample of galaxies. All galaxies where PNe and H ii regions have been studied with direct abundances (M33: Magrini et al. 2009, 2010; M81: Stanghellini et al. 2010, 2014; NGC 300: Stasińska et al. 2013) showed moderate (or null) steepening of the radial oxygen gradient with time. Are gradients indeed steepening, or are they flattening, with time evolution? The local galaxies all seem to indicate that most likely gradients are not highly variable in the times probed by the observations.

In Figure 7, we compare the radial oxygen gradients that we determined in this paper for old and young progenitor PNe with Gibson et al. (2013)'s models. We plot the radial oxygen gradient slopes, Δlog(O/H)/ΔR_G, versus redshift z from Gibson et al. (2013)'s models as black lines in the figure (dashed lines are models with enhanced feedback). Models by Mollá (2014) would be very similar to those by Gibson et al. (2013) without enhanced feedback. Other simulations have confirmed the effect of feedback as the driving force of turbulence in the disk at high redshifts; see, in particular, Ma et al. (2017), who found a very shallow gradient.

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In the figure, we also plot several Galactic and extragalactic data sets, not necessarily homogeneous, for discussion purposes rather than direct comparison with the models. For redshifted galaxies, we plot the slopes of radial oxygen gradients (or a range thereof) inferred from H ii regions versus z. In these cases, gradients are calculated from abundances of oxygen in H ii regions obtained through strong line analysis, not from direct abundances.

For local galaxies, ordinates (gradient slopes) are determined from direct abundances, while abscissae are calculated from the age of the probe used in the gradient determination. Gradients from H ii regions in local galaxies have z = 0, and those from PNe are plotted at a z representing the age of formation of the PN progenitors. For PNe in the present study, we have assumed that OPPNe probe stars older than t_⋆ > 7.5 Gyr and YPPNe probe stars younger than t_⋆ < 1 Gyr. Redshifts are derived from population ages (lookback times) from a simple cosmological model, where Ω_matter = 0.3, Ω_λ = 0.7, h = 0.7. We plot the gradient slopes that we have found for these two populations, marking both of these points with open circles in Figure 7. The arrows indicate that these are, respectively, a lower and upper limit to the population age for OPPNe and YPPNe.

The vertical lines at z ∼ 3.3 and 1.2 mark, respectively, the range of radial oxygen gradients of the galaxy samples analyzed by Cresci et al. (2010) and Sánchez et al. (2014). The crosses and triangle are from the analysis of lensed galaxies and thus probably not homogeneous with our data sets, due to the difficulty of reconstructing the actual galactic gradient. The filled circles are direct abundances of PNe and H ii regions in M33 and M81.

We find a qualitative agreement between the data and models, especially in the enhanced feedback group, which at this point seems to give a good indication about which models may better represent the majority of stellar populations in star-forming galaxies.

Although in Figure 7, the circle at t_⋆ = 7.5 (corresponding to log(1+z) ∼ 0.35) represents OPPNe with progenitors predominantly in the thick disk, it certainly cannot represent only the thick disk and must be contaminated by a younger population. The fact that OPPNe at R_G > 14 kpc have a mean oxygen abundance lower than those at R < 10 kpc (hence producing a gradient) probably means that they belong to an outer disk, which is thought to be a different population than the "chemically defined" thick disk, which is essentially limited to R_G < 10 kpc (Cheng et al. 2012). In this case, restricting the measured gradient to R_G < 10 kpc, where the thick disk is more dominant, makes more sense, and we can consider the gradient to be essentially flat (see Section 6.2). A flat metallicity gradient is a natural outcome of simulations with feedback, which induce sufficient turbulence to mix metals on large scales in less than a Galactic time. Hence, in Gibson et al. (2013), the MaGICC simulations (strong feedback) have a gradient limited to about −0.02 dex kpc⁻¹ at the epoch of thick disk formation (redshift ∼2). Similarly, in Ma et al. (2017), the disk between 1 and 2 kpc from the Galactic plane has a gradient that varies from −0.01 to +0.01 dex kpc⁻¹, passing by no gradient at $| z|$ = 1.5 kpc. It is interesting to note how this points to the same picture advocated in Haywood et al. (2013, 2015) and M. Haywood et al. (2018, in preparation), where we argued that the chemical evolution of the thick disk must have been very homogeneous and incompatible with the standard assumed inside-out evolution. The inside-out formation scenario means that star formation operates at a faster rate toward the inner disk, inducing radial gradients and dispersion in metallicity and α-abundances at a given age (e.g., Minchev et al. 2014; Kubryk et al. 2015) that are not observed (Haywood et al. 2015, submitted).