An Updated \synthpop Model for Microlensing Simulations I: Model Description, Evaluation, and Microlensing Event Rates Near the Galactic Center

This paper presents and evaluates an updated \synthpop Galactic model tuned for the Nancy Grace Roman Space Telescope's Galactic Bulge Time Domain Survey, demonstrating good agreement with observational data across most of the bulge while identifying specific inconsistencies near the Galactic plane that require further investigation.

The Gist

The Galactic "Weather Forecast" for the Nancy Grace Roman Telescope

Imagine you are about to launch a massive, high-tech camera into space to take a time-lapse video of a very crowded, dusty city square. Your goal is to spot tiny, invisible ghosts (free-floating planets) drifting through the crowd. To do this successfully, you need a perfect map of the city: you need to know exactly how many people are there, how fast they are walking, and where the thick fog (dust) is hiding.

This paper is essentially the blueprint and quality check for a new, super-accurate map of our Milky Way galaxy, specifically designed for the upcoming Nancy Grace Roman Space Telescope.

Here is the breakdown of what the authors did, using some everyday analogies:

1. The Problem: The Old Maps Were a Bit "Blurry"

For years, astronomers have used old "city maps" (Galactic models) to predict what the Roman telescope would see. Think of these old maps like a 1980s tourist brochure. They were okay for general directions, but if you tried to use them to navigate a busy, modern subway station (the center of our galaxy), they failed.

• They underestimated how many stars were there.
• They got the "traffic flow" (how stars move) wrong.
• They didn't account for the "fog" (dust) correctly, which makes it hard to see stars in the optical (visible light) range.

Because of these errors, predictions about how many planets the telescope would find were likely off.

2. The Solution: Building a "Digital Twin" (SP-H25)

The authors built a new, updated model called SP-H25 inside a flexible software framework called SynthPop.

• The Analogy: Instead of using a static paper map, they built a dynamic, 3D digital twin of the galaxy's center.
• How they did it: They didn't just guess. They took the best parts of previous maps (like the "Besançon model") and mixed them with fresh data from recent surveys (like OGLE and Gaia).
• The Ingredients: They carefully calculated:
  • Density: How many "people" (stars) are in the crowd.
  • Kinematics: How fast and in what direction the "people" are walking.
  • Extinction: How thick the "fog" is in different parts of the city.
  • The "Nuclear Stellar Disk": They added a specific layer for the very center of the galaxy, which previous maps often ignored.

3. The Stress Test: Does the Map Match Reality?

Before trusting this new map for the Roman telescope, the authors ran it against real-world data. They treated the model like a flight simulator and compared its predictions to actual observations.

• The Good News: In most of the "Galactic Bulge" (the crowded city center), the new map is spot on. It predicts the number of stars and their colors almost perfectly. It's a huge improvement over the old brochures.
• The Bad News (The "Foggy" Zone): When they looked at the very, very center of the galaxy (within 0.5 degrees of the galactic plane), the map started to get a little wobbly.
  • Analogy: It's like the map works great for the suburbs and the main downtown, but right in the middle of the busiest intersection, it starts to overestimate how many cars are there.
  • Why? The dust (fog) is so thick and patchy in the center that even the best 3D maps struggle to see through it. The model sometimes thinks there are more stars than there actually are, or it gets the "traffic flow" (star movement) slightly wrong because the dust is confusing the sensors.

4. The "Microlensing" Connection: Finding the Invisible

The main job of the Roman telescope is gravitational microlensing.

• The Analogy: Imagine a massive truck (a star or black hole) driving past a streetlamp (a distant star). The truck's gravity acts like a lens, bending the light and making the streetlamp briefly glow brighter. If a tiny, invisible drone (a free-floating planet) is riding on the truck, it creates a tiny blip in that brightness.
• The Goal: The authors used their new map to predict how often these "glows" will happen.
• The Result: For the optical (visible light) surveys, the model predicts more events than we currently see in the data (about 20-50% more). This suggests the old models were underestimating the chaos, but the new model might be slightly overestimating it, or perhaps the real data is missing some faint events.
• The Infrared Twist: When they looked at infrared data (seeing through the fog), the results were mixed. The model seemed to predict fewer events than the raw data suggested, but because the infrared data wasn't fully "cleaned" of errors, it's hard to say for sure yet.

5. Why This Matters for the Future

The Nancy Grace Roman telescope is launching in 2026. It will spend years staring at the center of our galaxy, looking for planets that don't orbit any star.

• The Takeaway: This new SP-H25 model is the best tool we have right now to tell the telescope operators exactly where to look and how many planets they might find.
• The Caveat: While the map is excellent for the "Lower Bulge" (the slightly less crowded parts of the center), the very heart of the galaxy (the Galactic Center field) is still a bit of a mystery. The authors admit they need to refine the "fog" calculations and the "traffic flow" in that specific zone.

In short: The authors have built a much better GPS for the center of our galaxy. It's not perfect yet—it still gets a little lost in the thickest fog—but it's a massive leap forward. It will help the Roman telescope avoid getting lost in the data and ensure we find the most interesting "invisible ghosts" (planets) hiding in the Milky Way's core.

Technical Summary

Here is a detailed technical summary of the paper "An Updated SynthPop Model for Microlensing Simulations I: Model Description, Evaluation, and Microlensing Event Rates Near the Galactic Center."

1. Problem Statement

The Nancy Grace Roman Space Telescope's upcoming Galactic Bulge Time Domain Survey (GBTDS) aims to characterize cold and free-floating exoplanets via gravitational microlensing. However, the optimization and interpretation of these surveys rely heavily on accurate Galactic models to predict stellar densities, kinematics, and event rates.

• Limitations of Existing Models: Previous models, particularly the widely used Besançon model (versions 1106 and 1307), have been shown to under-predict microlensing event rates by factors of 2–3 compared to observational data from surveys like OGLE and MOA.
• Specific Challenges: Existing models struggle to accurately replicate the stellar content of the inner Galactic bulge, the Nuclear Stellar Disk (NSD), and the complex extinction patterns near the Galactic plane ($|b| \lesssim 0.5^\circ$). These inaccuracies hinder the precise prediction of survey yields and the interpretation of exoplanet demographics.

2. Methodology

The authors present SP-H25, an updated Galactic population synthesis model implemented within the SynthPop framework (version v1.1.1). This model is specifically tuned for the Roman GBTDS.

Model Construction (SP-H25)

The model synthesizes components from various existing models and observational datasets:

• Stellar Densities & Kinematics:
  • Bulge: Adopts the triaxial bar/bulge density model from Cao et al. (2013) (E3 model, Bessel function) and kinematics from Koshimoto et al. (2021) (solid-body rotation + streaming motion).
  • Disk: Uses a 7-component thin disk and 1 thick disk model based on Besançon and Koshimoto et al. (2021), incorporating Gaia DR2-motivated kinematics (skewed azimuthal velocity distributions).
  • Nuclear Stellar Disk (NSD): Includes a self-consistent dynamical model (Sormani et al. 2022) for the inner $\sim 1^\circ$ of the Galactic plane, a component often missing in previous microlensing simulations.
  • Halo: Uses standard Besançon spheroid density and kinematics.
• Stellar Properties & Evolution:
  • Uses MIST (MESA Isochrones and Stellar Tracks) isochrones (v1.2) for stellar evolution and photometry.
  • Assigns Initial Mass Functions (IMF) based on Kroupa (2001).
  • Handles stellar remnants (White Dwarfs, Neutron Stars, Black Holes) using Initial-Final Mass Relations (IFMR) from Kalirai et al. (2008) and PopSyCLE/Sukhbold et al., treating them as lenses only.
• Extinction:
  • Utilizes a 2D extinction map from Surot et al. (2020) as the baseline at the Galactic center distance (8.15 kpc).
  • Scales extinction in 3D using a double-exponential dust disk scheme (similar to Galaxia) to handle foreground and background dust.
  • Adopts a custom extinction law with $R_V = 2.5$ for the bulge direction.

Evaluation Strategy

The model was validated against multiple observational datasets:

1. Luminosity Functions & CMDs: Compared against Hubble WFC3 Treasury Program, OGLE-IV, VVV (VISTA Variables in the Via Lactea), and GNS (Galactic Nucleus Survey) data.
2. Kinematics: Validated against proper motions from WFC3, Gaia DR3, and radial velocities from the BRAVA survey.
3. Microlensing Rates: Calculated optical depth ($\tau$), event rates per star ($\Gamma_*$), event rates per area ($\Gamma_\Omega$), and timescales ($t_E$) via Monte Carlo integration of lens-source pairs. These were compared against OGLE-IV, UKIRT, and VVV survey results.

3. Key Results

Stellar Counts and Photometry

• General Agreement: SP-H25 shows good agreement with observed star counts and Color-Magnitude Diagrams (CMDs) in the main Galactic bulge fields (e.g., Stanek Window, Baade's Window). Predicted star counts are generally within 20% of observed values.
• Discrepancies at Low Latitudes: Significant deviations occur at $|b| \lesssim 0.5^\circ$.
  • The model overpredicts star counts by $\sim 50\%$ in the Nuclear Stellar Disk (GNS fields) and near the Arches/Quintuplet clusters.
  • Red Clump Smearing: The model produces a "smeared" Red Clump in CMDs, likely due to overly broad metallicity distributions, unphysical line-of-sight extinction scaling, or inaccuracies in the bar angle.
• Extinction Issues: The 2D extinction map scaled by an exponential disk fails to capture complex 3D dust structures in the inner few kiloparsecs, leading to kinematic biases in simulated proper motions for nearby disk stars.

Kinematics

• Bulge Stars: Proper motion dispersions and mean velocities for bulge stars agree well with WFC3 and Gaia data (within $<2\sigma$).
• Disk Stars: The model underpredicts velocity dispersions for disk stars near the plane. There is a systematic gradient in the difference between simulated and Gaia proper motions ($\mu_l$) at low latitudes, suggesting the extinction model biases the sample of simulated stars.

Microlensing Event Rates

• Optical Surveys (OGLE-IV): SP-H25 overpredicts optical microlensing rates:
  • Event rate per unit area: $\sim 1.5\times$ observed.
  • Event rate per source star: $\sim 1.2\times$ observed.
  • Optical depth: $\sim 1.1\times$ observed.
  • Average timescale: Underpredicted by $\sim 0.9\times$ (likely due to the lack of stellar multiplicity in the current model version).
• Infrared Surveys (UKIRT/VVV): Results are inconclusive due to a lack of detection efficiency corrections in the observational data. However, raw comparisons suggest the model might underpredict IR event rates in the inner few degrees, contradicting the optical overprediction trend.

4. Key Contributions

1. SP-H25 Model: A new, flexible Galactic model implementation within SynthPop that integrates the NSD component and updated kinematic/density prescriptions from Koshimoto et al. (2021) and Sormani et al. (2022).
2. Comprehensive Validation: The first rigorous evaluation of a SynthPop-based model against a wide range of optical/IR photometry, proper motions, and microlensing rates specifically for the Roman survey footprint.
3. Identification of Systematic Errors: Pinpointed specific failure modes, particularly the overprediction of star counts in the NSD and the limitations of current 3D extinction scaling near the Galactic plane.
4. Framework for Future Work: Established a baseline for "Paper II," which will apply this model to simulate the Roman GBTDS yield.

5. Significance and Future Outlook

• Roman Survey Optimization: While SP-H25 provides a significant improvement over previous models for the contiguous lower bulge fields, its performance near the Galactic Center ($|b| < 0.5^\circ$) remains uncertain. This suggests that predictions for the Roman Galactic Center field require caution and further refinement.
• Model Refinement Needs: The authors highlight that the current overprediction of optical rates and underprediction of IR rates (potentially) indicates that factors like stellar multiplicity (currently excluded in SynthPop v1.1.1) and 3D dust mapping are critical.
• Path Forward: The paper sets the stage for SynthPop v2, which will incorporate stellar multiplicity and improved dust maps (hybrid 3D/2D). Future data from Roman and Gaia DR4 will be essential to re-optimize the NSD and NSC components, ultimately resolving the remaining inconsistencies in the central few degrees of the Galaxy.

In summary, SP-H25 represents a major step forward in Galactic modeling for microlensing, offering a robust tool for the Roman mission while clearly delineating the specific areas (inner plane, NSD, extinction) that require further theoretical and observational investigation.