PNe in Cosmological Simulations (PICS)

• PICS is a modeling framework that predicts planetary nebula populations in hydrodynamical cosmological simulations using realistic stellar ages, metallicities, and kinematics.
• It maps stellar particle properties through lifetime functions, IFMRs, and post-AGB tracks to generate synthetic PN brightness and replicate the observed PNLF bright-end cutoff.
• The framework incorporates circumnebular extinction and dynamical tracing, enhancing extragalactic distance measurements and galaxy formation studies.

PICS, abbreviated from PNe In Cosmological Simulations, is a modeling framework for predicting planetary nebula (PN) populations directly within hydrodynamical cosmological simulations, thereby linking PN formation to realistic stellar populations with simulation-derived star formation histories, ages, metallicities, spatial distributions, and kinematics (Valenzuela et al., 2024). Its central scientific target is the planetary nebula luminosity function (PNLF), especially the long-standing problem of the apparently universal bright-end cutoff in $\mathrm{[O\,III]}\,\lambda 5007$, which had previously been modeled mainly with artificial stellar populations and often fixed metallicity assumptions (Valenzuela et al., 2024). Within this framework, PN populations occur naturally in galaxies with diverse evolutionary pathways, and the resulting models are used both to interpret extragalactic distance measurements and to connect PN observables to galaxy formation and stellar population physics (Valenzuela et al., 29 Jan 2025).

1. Definition, scope, and nomenclature

PICS was introduced to move PN population synthesis from idealized stellar populations to the self-consistent stellar content of cosmological simulations and observations (Valenzuela et al., 29 Jan 2025). In this usage, each stellar particle is treated as a single stellar population (SSP), and PN properties are derived from the particle’s age, mass, metallicity, and initial mass function, then placed back into the galaxy with inherited positional and kinematic information (Valenzuela et al., 2024). This makes PICS simultaneously a population-synthesis framework and a bridge between post-AGB stellar evolution, nebular emission, and galaxy assembly histories.

The framework is explicitly motivated by two deficiencies in earlier PNLF models: the limited realism of artificially constructed or fixed-metallicity parent populations, and the lack of a solid theoretical explanation for the bright-end universality of the PNLF across galaxy types (Valenzuela et al., 29 Jan 2025). PICS is therefore designed to be modular, allowing substitution and testing of different lifetime prescriptions, initial-to-final mass relations (IFMRs), post-AGB tracks, nebular models, and extinction treatments (Valenzuela et al., 29 Jan 2025).

The acronym is potentially ambiguous. An unrelated astrophysical pipeline, also called PICS, denotes the Pipeline for Images of Cosmological Strong lensing, which simulates strong gravitational lensing in galaxy clusters rather than planetary nebulae (Li et al., 2015). In PN studies, however, PICS refers specifically to PNe In Cosmological Simulations (Valenzuela et al., 2024).

2. Modeling architecture and population-synthesis workflow

The core PICS workflow is a staged mapping from an SSP to a synthetic PN population. The sequence is stated as

$$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$

This chain converts a parent stellar population into PN brightnesses and, by aggregation over stellar particles, into a galaxy-wide PNLF (Valenzuela et al., 2024).

For each stellar particle, PICS uses age, total mass, metallicity, and IMF as the SSP input. The stellar lifetime function maps the age of the population to the masses of stars reaching the post-AGB phase; the IFMR then determines the central-star mass from the initial mass and metallicity; post-AGB tracks provide the luminosity and effective temperature evolution of the central star; and the nebular model converts these stellar properties into observable $\mathrm{[O\,III]}\,\lambda 5007$ emission (Valenzuela et al., 2024). In the fiducial implementations described in the project papers, the framework adopts metallicity-sensitive lifetimes, IFMRs, and post-AGB tracks from Miller Bertolami (2016), and an empirical PN emission model from Valenzuela et al. (2019) that includes both optically thick and optically thin nebulae (Valenzuela et al., 2024).

The principal observable is the absolute $\lambda 5007$ magnitude,

$M(5007) = -2.5 \log I(5007) - 13.74,$

where $I(5007)$ is the intensity at 10 pc distance (Valenzuela et al., 29 Jan 2025). The PNLF is then constructed as the distribution

$\frac{dN}{dM(5007)},$

with $N$ the number of PNe (Valenzuela et al., 2024).

A compact summary of the main components is as follows.

Component	Source or prescription	Role
SSP input	Age, mass, metallicity, IMF	Parent population
Lifetime function	Miller Bertolami (2016) fits/interpolation	Time to PN phase
IFMR	Miller Bertolami (2016) and alternatives	Central-star mass
Post-AGB tracks	Miller Bertolami (2016)	$L$ and $T_\mathrm{eff}$ evolution
PN model	Valenzuela et al. (2019)	$$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$0 output
Extinction treatment	Later project extensions	Emergent flux modification

Because PNe are assigned to stellar particles, they inherit the stellar particle’s location and velocity, so the synthetic populations are not only photometric but also spatially and kinematically embedded in the host galaxy (Valenzuela et al., 2024).

3. Metallicity, helium abundance, and the theoretical origin of the bright end

The central physical result of PICS is that realistic stellar populations, especially their metallicity distributions and metallicity-dependent lifetimes, are required to reproduce the bright end of the PNLF across galaxy types (Valenzuela et al., 2024). The framework finds that the bright-end cutoff is reproduced only when the dependence of stellar lifetimes on metallicity is included; in old, metal-rich systems, neglecting metallicity yields too few high-mass central stars and hence too few very bright PNe (Valenzuela et al., 2024). The stated theoretical implication is that the universality of the PNLF bright end is not fundamental, but depends on whether the relevant stellar physics is modeled within each galaxy’s true evolutionary context (Valenzuela et al., 2024).

The project’s first installment generalizes this result by isolating the roles of metallicity, helium abundance, and the IFMR (Valenzuela et al., 29 Jan 2025). Metallicity affects the time to reach the PN phase, the mapping from initial to final mass, and the post-AGB luminosity and temperature evolution. A key outcome is that old metal-rich populations can harbor much brighter PNe than old metal-poor ones, and that the observed bright end can be reached even for stellar populations of 10 Gyr at high metallicity (Valenzuela et al., 29 Jan 2025). This directly addresses the tension between the old stellar populations of massive early-type galaxies and their apparently invariant $$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$1 values.

Helium abundance enters at high metallicity. PICS explores a linear increase of $$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$2 with $$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$3 and a “cutoff He” case in which helium saturates above solar metallicity. The study identifies helium abundance as a vital ingredient at high metallicities and examines how helium saturation changes lifetime behavior and thus the availability of bright PN progenitors (Valenzuela et al., 29 Jan 2025). This suggests that the bright end cannot be understood from metallicity alone when the stellar population reaches super-solar regimes.

The IFMR is likewise a controlling parameter. The project finds that the PNLFs of old stellar populations are sensitive to the IFMR, allowing for the production of bright PNe, and that the bright end for old populations is especially sensitive to the low-initial-mass portion of the relation (Valenzuela et al., 29 Jan 2025). In practical terms, small shifts in the IFMR can materially change whether a nominally old population still produces central stars massive enough to populate $$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$4.

4. Comparison with observations in the Milky Way and early-type galaxies

PICS was directly compared with the local Milky Way PNLF by simulating a region of a Milky Way-like disk galaxy and contrasting it with the empirical PNLF for PNe within 2 kpc of the Sun, described as statistically complete down to six orders of magnitude below the bright end (Valenzuela et al., 2024). The modeled PNLF closely matches the observed shape, including normalization over six magnitudes, with only minor differences of approximately $$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$5 dex at the dim end and slight discrepancies at the bright end that are attributed to expected galaxy-to-galaxy variation and observational uncertainties such as circumstellar dust not modeled in the Milky Way data comparison (Valenzuela et al., 2024). This establishes that the same framework can reproduce both the bright-end behavior and the overall PN population in a realistic galactic environment.

The framework was also tested against early-type galaxies (ETGs) observed with VLT-MUSE, in a study that compared $$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$6 and the luminosity-specific PN number at the top 0.5 mag, $$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$7, to stellar population parameters and to matched Magneticum Pathfinder analogue galaxies processed with PICS (Soemitro et al., 12 Sep 2025). The observed ETGs have average mass-weighted ages and metallicities that are typically old,

$$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$8

and rather metal-rich,

$$\text{SSP Properties} \rightarrow \text{Lifetime Function} \rightarrow \text{IFMR} \rightarrow \text{Post-AGB Track} \rightarrow \text{Nebular Model}.$$9

and within these intervals the study finds $\mathrm{[O\,III]}\,\lambda 5007$0 to be independent of age and metallicity (Soemitro et al., 12 Sep 2025).

The same study reports a positive correlation between $\mathrm{[O\,III]}\,\lambda 5007$1 and the mass fraction of stellar populations with ages of $\mathrm{[O\,III]}\,\lambda 5007$2–$\mathrm{[O\,III]}\,\lambda 5007$3 Gyr, and a negative correlation with the fraction older than $\mathrm{[O\,III]}\,\lambda 5007$4 Gyr (Soemitro et al., 12 Sep 2025). Similar trends are found in the PICS analogue galaxies, and the authors state that the presence of at least $\mathrm{[O\,III]}\,\lambda 5007$5 of stellar mass younger than 10 Gyr is, in principle, sufficient to form the $\mathrm{[O\,III]}\,\lambda 5007$6 PNe in ETGs (Soemitro et al., 12 Sep 2025). They further argue that sufficiently massive PN central stars can be produced without invoking exotic binary evolution channels, using the updated post-AGB models incorporated into PICS (Soemitro et al., 12 Sep 2025). A common misconception in the ETG literature is therefore that bright PNe in old, metal-rich systems necessarily require non-standard progenitors; the PICS-based result is that a small intermediate-age component can be sufficient.

For observational fitting, the ETG study uses the analytic PNLF form

$\mathrm{[O\,III]}\,\lambda 5007$7

and defines

$\mathrm{[O\,III]}\,\lambda 5007$8

(Soemitro et al., 12 Sep 2025). Within the PICS interpretation, $\mathrm{[O\,III]}\,\lambda 5007$9 acts as a stellar population tracer, while $\lambda 5007$0 remains relatively invariant over the old, metal-rich parameter space probed in those data (Soemitro et al., 12 Sep 2025).

5. Circumnebular extinction and the bright-end cutoff

A subsequent extension of the framework addresses circumnebular extinction as a mechanism shaping the observed PNLF bright end (Valenzuela et al., 29 Sep 2025). The theoretical problem is that young stellar populations, which host more massive PN central stars, are expected to produce intrinsically brighter $\lambda 5007$1 emission than is observed, whereas the empirical bright-end cutoff remains near a nearly constant $\lambda 5007$2 (Valenzuela et al., 29 Sep 2025). The proposed solution is self-extinction by dust produced in AGB mass loss, especially for higher-mass central stars, which reduces the emergent $\lambda 5007$3 flux and compresses intrinsic differences toward the observed cutoff (Valenzuela et al., 29 Sep 2025).

In this implementation, PICS adds a circumnebular extinction module to the existing birth distribution, IFMR, post-AGB, and nebular-emission machinery. The treatment starts from empirical fits for $\lambda 5007$4 as a function of final mass, expressed as

$\lambda 5007$5

and then converts $\lambda 5007$6 to $\lambda 5007$7 (Valenzuela et al., 29 Sep 2025). Six extinction recipes were tested, differing in sample choice and fitting method, including Orthogonal Regression, Ordinary Least Squares, and an optimized fit for PNLF flatness (Valenzuela et al., 29 Sep 2025).

The principal result is differential sensitivity with stellar age. Steeper extinction-mass slopes lead to large changes in the bright-end cutoff for young stellar populations, while older PNe are much less affected because the extinction recipes converge to little or no extinction at long post-AGB ages (Valenzuela et al., 29 Sep 2025). Thus, circumnebular extinction is described as crucial primarily for the youngest PN populations (Valenzuela et al., 29 Sep 2025). At the same time, direct comparison with observed PNe in nearby galaxies shows that the modeled extinctions do not fully reproduce the large observed spread or the highest extinction values, even after adding scatter and applying a global shift of $\lambda 5007$8 to some relations (Valenzuela et al., 29 Sep 2025).

This leaves an unresolved tension. The project states that improvements on both the modeling and observational sides are needed, and lists possible causes including unmodeled PN formation channels, binary evolution, observational bias, or incomplete physics regarding dust formation and ejection (Valenzuela et al., 29 Sep 2025). Relative to the earlier phase of the project, where internal dust extinction had not yet been explicitly incorporated (Valenzuela et al., 29 Jan 2025), the extinction study represents a move from omission of the effect to a parameterized exploration of how strongly it sculpts the PNLF.

6. Dynamical applications, simulation context, and open limitations

Because PICS assigns PNe to star particles with inherited positions and velocities, the framework can be used not only for luminosity functions but also for dynamical studies in low-surface-brightness environments (Valenzuela et al., 15 Apr 2026). In an application to the Magneticum Box4 (uhr) simulation, the method was used to model PNe in a massive elliptical galaxy of stellar mass $\lambda 5007$9 hosting a prominent tidal stream from a progenitor of $M(5007) = -2.5 \log I(5007) - 13.74,$0 (Valenzuela et al., 15 Apr 2026). The study finds that PNe in the brightest 1.5 mag of the luminosity function are sufficient to recover the velocity gradient and dispersion of the massive stream, whereas restricting the tracer set to only the brightest 1.0 mag yields sparse sampling and stronger contamination by halo PNe (Valenzuela et al., 15 Apr 2026). In that context, PNe are presented as an attractive alternative to expensive deep IFU observations for constraining the gravitational potential of galaxy outskirts (Valenzuela et al., 15 Apr 2026).

This dynamical use follows directly from the cosmological embedding of the model. The same properties that make PICS useful for explaining the PNLF bright end—self-consistent star formation histories, chemical enrichment histories, and realistic mixtures of SSPs—also make it suitable for mock tracer catalogues in streams, halos, and other faint structures (Valenzuela et al., 2024). A plausible implication is that PNLF modeling and PN kinematics are no longer separable topics once the tracer population is generated within a resolved cosmological galaxy.

Several limitations remain explicit in the project papers. For very high metallicities, $M(5007) = -2.5 \log I(5007) - 13.74,$1, some stellar models are extrapolated rather than directly simulated (Valenzuela et al., 2024). In the original Milky Way comparison, circumstellar extinction was not yet included and was identified as a source of discrepancy at the dim end (Valenzuela et al., 2024). The simulated galaxies used for local comparisons are similar to, but not exact analogues of, the Milky Way, with differences in bulge and disk populations (Valenzuela et al., 2024). In the dynamical application, stochastic sampling, contamination by halo PNe in projection, and the need to verify assumptions in unusual stellar populations are all noted as practical constraints (Valenzuela et al., 15 Apr 2026).

Taken together, the PICS program establishes a cosmologically grounded PN population-synthesis framework in which the PNLF is interpreted as an emergent consequence of realistic stellar ages, metallicities, helium abundances, IFMR choices, nebular physics, and extinction, rather than as a phenomenon to be reproduced with artificial populations alone (Valenzuela et al., 2024). Its later extensions show that this same framework can be used for distance-scale work, stellar-population inference, and the kinematics of faint galactic substructure (Soemitro et al., 12 Sep 2025).