PSLS: PLATO Light-Curve Simulator

• PSLS is a modular simulator that synthesizes light-curves by combining stellar oscillations, granulation, and magnetic activity using Fourier space methods.
• It integrates comprehensive instrumental noise modeling, including photon noise, CTI, and pointing jitter, through detailed PIS-driven simulations.
• The simulator supports analytic transit injection for exoplanet detection, enabling yield forecasting and validation against Kepler data.

The PLATO Solar-like Light-curve Simulator (PSLS) is a modular, computationally efficient tool designed to generate simulated light-curves that closely approximate the photometric signals and instrumental systematic effects anticipated for ESA’s PLATO mission. PSLS is specifically engineered to mimic solar-like oscillations, stellar granulation, magnetic activity, and a complete range of instrumental and data reduction effects linked to the PLATO multi-telescope concept, with the additional capability to inject transits from exoplanets. Its outputs facilitate detailed hare-and-hound exercises critical for mission preparation, detection yield estimation, and optimization of light-curve analysis algorithms (Samadi et al., 2019, Heller et al., 2022).

1. Architecture and Processing Flow

PSLS orchestrates the synthesis of light-curves through three principal modules:

1. Astrophysical Signal Generation: Stellar oscillations, granulation, and magnetic activity are modeled primarily in Fourier space. Oscillation modes (resolved/unresolved), granulation (dual Harvey-like components), and a Lorentzian activity profile are summed to form the stellar background.
2. Instrumental/Systematic Error Modeling: Using the PLATO Image Simulator (PIS), pixel-level simulations incorporate photon (shot) noise, CCD readout noise, zodiacal background, smearing, intra-pixel and pixel-response non-uniformity (PRNU/IPRNU), charge transfer inefficiency (CTI), long-term drift, and pointing jitter. Photometric extraction uses optimized binary masks to minimize aggregate noise-to-signal ratio (NSR), with dynamic recomputation when mask performance degrades.
3. Transit Injection and Output: The Mandel & Agol (2002) analytic transit model, utilizing quadratic limb darkening, enables the simulation of exoplanetary transits with user-defined planetary and orbital parameters. Output light-curves can be binned (typical cadence 25 s), optionally averaged over multiple cameras, and exported in ASCII or FITS formats.

The modular nature of PSLS allows numerical efficiency; all stellar and instrumental noise terms are combined in Fourier space, assigned random phases, and then inverse-Fourier transformed to the time domain. Realistic systematics are applied in the time domain via the PIS-generated photometric kernel, followed by optional masking corrections and transit multiplication (Samadi et al., 2019, Heller et al., 2022).

2. Physical and Instrumental Noise Modeling

PSLS provides comprehensive and physically motivated models for noise and systematic error sources:

• Stellar Granulation & Magnetic Activity: Granulation is represented as the sum of two "Harvey" type PSD components, parameterized by amplitudes and characteristic timescales empirically scaled to the simulated target (e.g., Kallinger 2014). Magnetic activity is modeled as a single Lorentzian in the PSD:

$$PSD_{\rm act}(f) = \frac{2\,\sigma_A^2\,\tau_A}{1 + (2\pi\,f\,\tau_A)^2}$$

with $\sigma_A$ (amplitude) and $\tau_A$ (timescale) user-defined.

• Solar-like Oscillation Modes: Mode frequencies, heights, and linewidths are synthesized via established stellar modeling frameworks—ADIPLS for main sequence/subgiants and the Universal Pattern for red giants. Gaussian envelopes, mode visibilities, and rotation splitting are incorporated. Uncertainties from mode lifetimes and convective background are stochastically realized.
• Instrumental Noise: PIS provides a table-driven library of noise budgets. NSR values are tabulated for each magnitude, field location, and instrumental state (beginning-of-life/ end-of-life). Noise sources include photon noise ($\propto F_\star$), readout noise, background contributions, drift, and jitter. CTI is modeled using a multi-species trap formalism calibrated to irradiated CCDs. Photometric masks are dynamically adapted to mitigate NSR increases from drift, saturation, or focus changes (Samadi et al., 2019).
• Systematic Error Correction: Following PSF reconstruction via microscanning (detailed below), a "synthetic" reference light-curve is used to divide the extracted photometry, removing first-order drift and aperture-change induced systematics. Remaining residuals are fit in either the frequency domain (two-component PSD) or the time domain (piecewise-cubic splines per mask epoch):

$$I(\nu) = H_1 \left(\frac{\nu_1}{\nu}\right)^{\alpha_1} + \frac{H_2}{1 + (2\pi\tau_2\nu)^{\alpha_2}}$$

or

$$s(t) = \bar{s} \sum_{i} \Pi((t-t_i)/d_i) [1 + p_{3,i} + p_{2,i}x + p_{1,i}x^2 + p_{0,i}x^3]$$

Parameter libraries for these corrections are indexed by magnitude, field, subpixel offset, and camera epoch (Samadi et al., 2019).

3. Point Spread Function Reconstruction

Due to the undersampling by PLATO’s $15''$ pixels, sub-pixel point-spread function (PSF) information is critical. PSLS incorporates a microscanning-based algorithm: the line-of-sight is continuously steered on an Archimedean spiral over $\sim1$ pixel (∼430 imagettes in three hours). The high-resolution PSF is reconstructed as a sum over suitable basis functions (e.g., cubic B-splines on a $1/20$ pixel grid):

$f(x,y) = \sum_i a_i \phi_i(x,y)$

Integration over the CCD pixel layout forms a linear inversion problem solved either by multiplicative algebraic reconstruction (MART) with positivity constraints or a regularized least-squares method with a 2D Laplacian penalty on the PSF wings. The latter typically yields superior solutions (Samadi et al., 2019).

4. Transit Injection and Exoplanet Yield Estimation

The PSLS transit module injects analytic Mandel & Agol (2002) transit shapes, parameterized by planetary radius, orbital period, semi-major axis, impact parameter, and quadratic limb darkening. Cadence binning matches PLATO's anticipated 25 s sampling. PSLS supports configuration-driven injection of planet populations for detection yield studies (Heller et al., 2022).

In practice, light-curves generated with PSLS are detrended using the Wōtan software (biweight filter windowing), followed by transit detection via the Transit Least Squares (TLS) algorithm. Detection significance is evaluated using S/N measures and Signal Detection Efficiency (SDE), with adopted thresholds of SDE $\geq$ 9 and S/N $>$ 7 to ensure false positive rates below $10^{-4}$.

Yield predictions for the PLATO P1 sample (∼15,000–20,000 targets) indicate true positive rates (TPR) of $\sim$100% for $R_p\geq1.2\,R_\oplus$ with two observed transits (2 yr, 24 cameras) and for $R_p\geq1.0\,R_\oplus$ with three transits (3 yr, 24 cameras). The expected detection yield for Earth-sized habitable-zone planets falls between 8 and 34, depending on field coverage and mission duration (Heller et al., 2022).

5. Validation and Performance Metrics

PSLS underwent validation against high-quality Kepler data for three typical targets: 16 Cyg B (main sequence), KIC 12508433 (subgiant), and KIC 9882316 (red giant). All principal oscillation/variability features were qualitatively and quantitatively matched to Kepler observations, with:

• Peak-to-peak residuals $<$0.5% RMS for $V \leq 13$
• Power spectral density (PSD) ratios PSLS/Kepler $\sim$1 within $\pm$20% in the oscillation range
• Instrumental systematics found to dominate only at frequencies $\nu \lesssim 20\,\mu$Hz, remaining negligible in the primary oscillation band

Execution efficiency is high: a 2-year light-curve at 25 s cadence for a single camera is generated in $\sim$1 minute on modern hardware, and the code is parallelizable over stars/cameras (Samadi et al., 2019).

6. Configuration and Practical Use

PSLS is configured via YAML files comprising four main blocks: observation (duration, random seed), instrument (sampling, integration time, noise/systematics flags), stellar properties (magnitude, evolutionary state, model type, rotation, inclinations), and signal backgrounds (activity, granulation, transit parameters). Table-driven systematics and camera noise models are referenced automatically, and users may specify the number of simulated cameras (6–24), field placement, and mission epoch.

The codebase is written in Python/Cython, distributed under GNU GPL, and available via http://psls.lesia.obspm.fr with accompanying documentation and analysis tools (Samadi et al., 2019).

7. Applications and Adaptability

PSLS serves as an indispensable tool for PLATO mission planning, enabling end-to-end simulations of light-curve data products for algorithm validation, yield forecasting, and systematic correction assessment (Samadi et al., 2019, Heller et al., 2022). Its modular structure and reliance on external pixel-level simulation/output libraries (PIS, systematics tables) make it adaptable for simulation of other missions, contingent upon provision of analogous instrumental characterization and correction data.

A plausible implication is that comparable simulation architectures could be adopted for future transit or asteroseismic surveys, leveraging instrument-specific modules to generalize the PSLS workflow.