Rotational Light-Curve Recovery & Predictions of the LSST Yield of Hildas

TL;DR

The study addresses how LSST Rubin Observatory data will reveal and characterize Hilda asteroids in Jupiter's $3:2$ resonance. It constructs a synthetic Hilda population with orbital, size, color, and collisional-family structure, and runs end-to-end Sorcha simulations to forecast detections and rotation-state recovery using a multiband Lomb–Scargle approach. The results show LSST could discover ~33,400 Hildas (about five times the current count) and recover periods for ~46.5% of a LCDB-based sample, with recovery strongly influenced by light-curve amplitude and cadence-related effects. This work provides a framework for interpreting future LSST rotation data and highlights biases and model limitations that guide debiasing and population-inference efforts for the outer Solar System.

Abstract

The Hilda population occupies the stable 3:2 mean-motion resonance of Jupiter and provides a window into Solar System evolution, including collisional processes. The NSF-DOE Vera C. Rubin Observatory will conduct the ten-year Legacy Survey of Space and Time (LSST). We present a simulation of Rubin's discovery of Hildas with the Sorcha (Merritt et al. 2025; Holman et al. 2025) survey simulator and the recovery of their light curves. We constructed a synthetic Hilda population model which includes distributions of orbital properties, sizes, collisional families and colors. We included two color classes corresponding to the Jupiter Trojan populations (Wong & Brown 2017). We applied three distinct populations of sinusoidal light-curves to this same orbit-size-color model: (1) a Gaussian kernel density estimate (KDE) fit to rotational periods and amplitudes from the Lightcurve Database (LCDB; Warner et al. 2009) (2) a super-fast rotator (SFR) population (0-3 hours) and (3) a super-slow rotator (SSR) population (100-1400 hours). Over the ten-year simulated survey, we predict LSST will discover ~33,400 Hildas, a fivefold increase over the known population. Using a multiband Lomb-Scargle Periodogram via Astropy (Price-Whelan et al. 2022) we confidently recover ~46.5% of Hildas in our LCDB-based population, higher than typical in observational searches. This suggests our light-curve population model may differ from the intrinsic population. We find strong biases in light-curve amplitude, with recovery efficiency dropping sharply below 0.1 magnitudes, while biases from rotational period are comparatively weak aside from cadence-related features such as LSST's ~36 minute revisit cadence. ...

Figures (7)

• Figure 1: Comparison of the known Hilda population from the Minor Planet Center (left) and our synthetic Hilda population (right) in semi-major axis ($a$) and absolute magnitude ($H$). The vertical line at $a = 3.971$ AU marks the location of the 3:2 mean-motion resonance with Jupiter, which defines the Hilda population. Our input sample reproduces the observed distribution in both $a$ and $H$, while extending to fainter magnitudes beyond the MPC limit.
• Figure 2: Distribution of our 485,807 simulated Hildas projected onto 2D planes of their proper orbital parameters. (i) (a, e) top left; (ii) (a, $\sin (i)$) bottom left; and (iii) (e, $\sin (i)$) bottom right. Each dark point represents an object from our simulated Hilda population. Approximate locations of the two largest collisional families associated with (153) Hilda (blue marker) and (1911) Schubart (red marker) are indicated for reference daviddavid.
• Figure 3: Comparison of simulated and observed Hilda light-curve distributions. This shows a 2D histogram of rotational period versus light-curve amplitude for the combined simulated population, created by sampling periods and amplitudes from the KDE associated with each object's collisional family. White points indicate Hildas from the LCDB catalog. Our KDE-based sample is consistent with the rotational properties of observed Hildas.
• Figure 4: Comparison of absolute magnitude ($H$) distributions for the known, input and discovered Hilda populations. The orange histogram shows the currently-known Hildas from the MPC. The blue distribution represents the Hildas discovered in our simulated survey with the gray being the full input population. The synthetic discoveries extend $\sim$1.5–2 magnitudes fainter than the known population, demonstrating LSST’s ability to probe substantially deeper and expand the observed Hilda population beyond current detection limits.
• Figure 5: Distributions of the reduced inverse power metric $R$ (Equation \ref{['reduced_inv_pow']}) for the SFR, LCDB and SSR simulated light–curve populations, separated into the correctly and incorrectly recovered rotational periods. The vertical dashed line shows the confidence threshold $R = 0.01017$, defined as the value below which at least 99% of SFR periods are accurately recovered (including half/double-period harmonics). Correct fits (blue) concentrate strongly at low $R$, while incorrect fits (red) populate a broader tail toward larger $R$, demonstrating that smaller $R$ values correspond with more reliable period recoveries.