Prospector SED Fitting Code

• Prospector SED Fitting Code is a high-dimensional, Bayesian inference framework that models galaxies’ spectral energy distributions using nonparametric, physically motivated star formation histories.
• It accurately infers key galaxy properties such as stellar mass and star formation rates by integrating multi-band photometry with FSPS and CLOUDY emission models.
• Dynamic nested sampling and rigorous parameterization improve consistency between SFR and stellar mass estimates, resolving discrepancies seen in traditional SED fitting methods.

The Prospector SED Fitting Code is a high-dimensional, Bayesian inference framework specifically designed for extracting physical properties of galaxies by modeling their spectral energy distributions (SEDs) across broad photometric bands. Originating from the need to marginalize over the complexity inherent in galaxy observations—spanning stellar mass, star formation history (SFH), metallicity, dust attenuation, AGN emission, and nebular processes—Prospector implements non-parametric, physically-motivated models to forward-model the observed data. The Prospector-α model, a core implementation, serves as a benchmark in producing internally consistent stellar mass and star formation rate (SFR) estimates that are robust with respect to dynamical mass constraints and global galaxy evolution metrics.

1. High-Dimensional Physical Model and Parameterization

Prospector-α operates with a 14-parameter model, synthetizing galaxy photometry by leveraging the Flexible Stellar Population Synthesis (FSPS) code with MIST isochrones. Its non-parametric SFH divides the galaxy's age into seven bins, with two bins fixed for very recent star formation activity (0–30 Myr and 30–100 Myr), and remaining bins distributed logarithmically over cosmic time. The model includes:

• SFH “continuity prior”: Regularizes SFR variation across adjacent bins, suppressing artificial bursts and improving physical realism.
• Variable stellar metallicity: Prior informed by a modified mass–metallicity relation (clipped normal distribution).
• Two-component dust attenuation model: Includes diffuse ISM dust and extra birth-cloud attenuation; attenuation curves parameterized flexibly (with possible power-law modifications and empirical relation constraints).
• Nebular emission: Computed via pre-tabulated CLOUDY models, allowing line and continuum emission modeling self-consistent with ionizing photon output.
• Dust emission and AGN torus emission: Energy balance constraints using fixed IR SED shapes; AGN templates included to model mid/far-IR excess.

Six SFR-ratio parameters enable relative weighting of SFRs in adjacent SFH time bins. Total stellar mass, as log(M/Mₒ), is used as a key variable, typically ranging over [7, 12.5].

2. Forward Modeling and Bayesian Inference Workflow

Prospector's inference engine utilizes dynamic nested sampling (dynesty), efficiently traversing the high-dimensional space imposed by the model. The workflow:

• Model SED generation: For each parameter set, Prospector computes the spectrum via FSPS, convolves it with filter transmission curves, and produces synthetic photometry.
• Likelihood evaluation: Model fluxes are compared to observed galaxy photometry (e.g., from 3D-HST survey catalogs) to compute the likelihood.
• Posterior sampling: The nested sampler produces marginalized posterior distributions for all free parameters, quantifying covariances and degeneracies.

A representative SFR conversion formula for traditional analyses is: $$\mathrm{SFR}\; [M_\odot\;\mathrm{yr}^{-1}] = 1.09 \times 10^{-10} (L_\mathrm{IR} + 2.2\, L_\mathrm{UV})$$ Prospector instead models SFR self-consistently across all age bins, capturing both recent and "old star" contributions to dust heating and IR emission.

3. Impact on Inferred Physical Properties

Stellar Masses

Prospector-α systematically infers stellar masses $\sim$0.1–0.3 dex larger than previous SED codes (e.g., FAST). This is attributed to older mass-weighted stellar ages recovered by the flexible, non-parametric SFH: older ages yield higher M/L ratios, increasing the mass required for a given luminosity.

Star Formation Rates (SFRs)

Instantaneous SFRs inferred by Prospector-α are $\sim$0.1–1+ dex lower, especially at low sSFR. This arises from the explicit modeling of dust heating by post-starburst ($t > 100$ Myr) populations. The fractional contribution of old stars to total IR+UV emission is empirically characterized by: $$y = 0.5\,\tanh( a\,\log(\mathrm{sSFR}) + b\,z + c) + 1$$ where $y$ is the old-star fraction; constants $a, b, c$ are determined from fits (typical values: $a=-0.8$, $b=0.09$, $c=-8.4$). Low sSFR galaxies show the strongest old-star contamination, causing traditional UV+IR SFR estimators to overestimate SFR.

4. Self-Consistency and Scientific Implications

Prospector-α's fits produce internally consistent galaxy evolution metrics:

• Older and more quiescent Universe: Both star-forming and quiescent galaxies have older stellar ages; observed SFRDs are lower and mass growth higher, reconciling prior discrepancies in the cosmic SFH.
• Resolution of SFRD–stellar mass growth tension: Summed SFR and derivative-based (from mass growth) SFRD estimates converge—disagreement of $\sim$0.3 dex found in earlier literature is reduced to $\lesssim$0.1 dex.
• Enhanced agreement with independent metrics: Inferred stellar masses align with dynamical mass constraints, and SFHs better predict observed evolution of the stellar mass function.
• Improved physical realism: Mass-weighted and light-weighted ages, and reconstructed SFHs, model galaxy evolution over longer, smoother periods compared to exponentially declining or parametrized burst models typical in legacy codes.

Traditional codes, using simplified assumptions, return younger ages, lower masses, and higher SFRs, underscoring the impact of SFH, dust, and metallicity flexibility on inferences.

5. Degeneracy Breaking and the Role of Ancillary Data

Despite the dimensionality and physically-motivated priors in Prospector-α, degeneracies remain among key parameters, especially stellar age, dust attenuation, and metallicity. The framework is primed for improved constraints via:

• Spectroscopic measurements: Absorption indices (Hδ, Fe) and emission-line EWs (e.g., Brγ) provide direct constraints on age and metallicity, decoupling dust effects present in broad-band SEDs.
• Mid/Far-IR photometry: Data from Herschel/ALMA constrains IR SED shape, isolating dust heating contributions from old and young populations.
• Spatially-resolved data: IFU observations elucidate star-dust geometry, offering direct assessment of spatial variations in dust and SFH, improving SFR and mass determinations.
• Redshift precision: Spectroscopic (or grism) redshifts minimize parameter uncertainties propagated from redshift errors.

These data types, when incorporated into priors or as additional parameters, enhance posterior constraints and facilitate more accurate recovery of physical parameters, as evidenced by covariance analyses between Prospector-α posteriors and observables.

6. Comparative Features, Limitations, and Future Directions

Prospector-α is differentiated from contemporaries by:

• Non-parametric SFH modeling: Increased flexibility, regularized with continuity priors, allows more realistic age and SFR histories.
• Self-consistent nebular and dust emission modeling: Emission lines and continuum modeled via CLOUDY grids; dust energy balance enforced with IR templates.
• Integrated AGN component: AGN torus emission modeled and marginalized over, enabling robust host galaxy parameter inference in AGN hosts.
• Posterior predictive checks and evidence evaluation: Dynamic nested sampling supports robust uncertainty quantification and goodness-of-fit assessments.

Remaining limitations include:

• Degeneracies between age, dust, and metallicity that cannot be fully resolved by broad-band photometry alone.
• Model complexity: Computational demand is nontrivial, requiring efficient sampling (dynesty) and careful prior selection.
• Parameterization of IR SED and abundance patterns: Current models employ fixed templates; future iterations may require the introduction of new free parameters (e.g., for α-element enhancements or IR SED shape).

Prospector-α is structured to accommodate new data modalities and evolving astrophysical priors, with a modular Bayesian design supporting expansion.

7. Summary Table: Core Prospector-α Model Ingredients

Ingredient	Description	Implementation
SFH	Nonparametric (7 time bins; continuity prior)	SFR ratios between adjacent bins
Metallicity	Variable; prior from mass–metallicity relation	Clipped normal distribution
Dust Attenuation	Two-component (birth cloud, diffuse); flexible curve	Power-law modification; energy balance
Nebular Emission	Self-consistent line & continuum (CLOUDY grid)	Pre-tabulated grids
Dust Emission	Energy balance; fixed IR SED template	IR reradiation model
AGN Torus Emission	Optional; marginalized in fit	Torus emission templates

Prospector-α's methodology represents a significant advancement in SED-based galaxy property inference, achieving higher physical fidelity in mass and SFR estimates and demonstrating improved consistency with independent constraints and cosmic evolution benchmarks relative to previous approaches (Leja et al., 2018).