PLATO Light-Curve Simulator

• Plato Synthesizer is a high-fidelity simulation tool that produces synthetic stellar light curves by combining astrophysical variability such as magnetic activity, granulation, and oscillations with instrumental noise.
• It employs a two-step process using detailed power spectral density modeling in the frequency domain followed by time-domain corrections via polynomial fits to simulate realistic observational data.
• Validated against Kepler data, the simulator enables efficient Monte Carlo studies and performance verification for optimizing scientific objectives of the European Space Agency's PLATO mission.

The PLATO Solar-like Light-curve Simulator (PSLS) is a high-fidelity simulation tool designed to generate synthetic stellar light curves that realistically represent both astrophysical variability and the expected instrumental effects of the European Space Agency's PLATO mission. PSLS is essential for preparing science objectives and optimizing data analysis strategies, as it enables massive generation of representative light curves for use in performance verification exercises such as hare-and-hound studies. The simulator models the comprehensive impact of astrophysical signals (magnetic activity, granulation, and oscillations) alongside instrumental noise and systematic errors, derived from in-depth pixel-level simulations and parametric descriptions of the PLATO instrument and its multi-telescope concept (Samadi et al., 2019).

1. Stellar Variability and Power Spectral Modeling

PSLS models the total expected power spectral density (PSD) of a PLATO target as a sum of three uncorrelated components:

$$\overline{\mathcal P}(\nu) = {\cal A}(\nu) + G(\nu) + O(\nu)$$

• Magnetic Activity (${\cal A}(\nu)$): Modeled as a single Lorentzian (Harvey profile),

$${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$

where $\sigma_{A}$ is the RMS amplitude and $\tau_{A}$ is the activity timescale.

• Granulation Background ($G(\nu)$): Represented as a sum of two super-Lorentzians,

$$G(\nu) = \sum_{i=1}^{2}\frac{h_i}{1 + (2\pi\,\tau_i\,\nu)^{4}}$$

with $h_i$ as component heights and $\tau_i$ as time scales determined from scaling relations.

• Solar-like Oscillations ($O(\nu)$): A sum of resolved Lorentzian profiles for each mode,

${\cal A}(\nu)$0

For resolved modes,

${\cal A}(\nu)$1

For unresolved modes (if ${\cal A}(\nu)$2),

${\cal A}(\nu)$3

Mode frequencies ${\cal A}(\nu)$4, widths ${\cal A}(\nu)$5, and heights ${\cal A}(\nu)$6 are set via detailed scaling relations and, for evolved stars, the Universal Pattern.

A realization is generated in the frequency domain as: ${\cal A}(\nu)$7 where ${\cal A}(\nu)$8. Inverse Fourier transformation yields a time-series light curve, with a phase factor to model group shifts between camera sets.

2. Instrumental Noise and Systematic Error Handling

2.1 Random Noise

White-noise in the light curve can be specified either by:

• User-provided noise-to-signal ratio (NSR) in ppm hr${\cal A}(\nu)$9,
• Interpolation from a precomputed table as a function of PLATO magnitude $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$0.

The resulting RMS in the time domain: $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$1 where $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$2 is the cadence (25 s).

2.2 Systematic Errors

Systematic trends are represented via a parametric model based on pixel-level simulations (PLATO Image Simulator, PIS). In the Fourier domain, residual systematics are modeled as: $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$3 with parameters dependent on stellar magnitude, PSF position, sub-pixel phase, and CCD state.

In the time domain, systematics for each 3-month mask segment are described by a piecewise cubic polynomial: $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$4 where $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$5 selects the segment, $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$6 and $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$7 are mask start and duration, and $${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$8 are polynomial coefficients. For multi-camera synthesis, systematics are independently sampled and averaged, reducing uncorrelated errors.

3. Pixel-Level Simulation and Photometric Extraction

3.1 PLATO Image Simulator (PIS)

PIS generates 6×6-pixel "imagettes" every 25 s for up to 90 days, encompassing:

• Optical PSF including manufacturing tolerances,
• Photon shot-noise, readout noise,
• Satellite jitter, long-term drift (up to 1.3 px/90 days), smear, digital saturation,
• Pixel-to-pixel response non-uniformity (PRNU), intra-pixel response (IPRNU), dark current, and charge transfer inefficiency (CTI).

Simulation coverage includes nine stellar magnitudes, multiple CCD field positions, intra-pixel phases, and both CCD life states (beginning/end-of-life), totalling 630 scenarios.

3.2 On-board Aperture Mask Selection

A binary mask of up to 36 pixels is chosen for each target to minimize the aggregate NSR:

1. Pixels are ranked by their single-pixel NSR,
2. The cumulative NSR is computed for increasing mask sizes,
3. The mask with minimum NSR is selected.

Single-camera NSR ranges from approximately 10 ppm hr$${\cal A}(\nu) = \frac{2\,\sigma_{A}^2\,\tau_{A}}{1 + (2\pi\,\tau_{A}\,\nu)^2}$$9 at $\sigma_{A}$0 to $\sigma_{A}$1140 ppm hr$\sigma_{A}$2 at $\sigma_{A}$3. Groups of 24 cameras achieve a $\sigma_{A}$4 reduction in NSR.

3.3 PSF Reconstruction via Microscan

Prior to each 90-day observing run, telescopes undergo microscanning in a quasi-spiral pattern ($\sigma_{A}$5430 steps over 3 hours), enabling sub-pixel sampling of the PSF. High-resolution PSF maps on a 20×20 subpixel grid are reconstructed using either:

• Multiplicative Algebraic Reconstruction Technique (MART),
• Regularized least squares with a Laplacian Tikhonov term,

with positivity constraints imposed. Target-specific PSFs are interpolated from these reference grids.

4. Parametric Correction and Light-curve Synthesis

Due to mask drift and updates, synthesized light curves exhibit both instantaneous flux jumps and slow trends. PSLS fits each mask segment in the PIS-derived light curve with piecewise cubic polynomials, recording coefficient sets across the full parameter grid. For each simulation, coefficients are randomly sampled according to stellar magnitude and segment, and the synthesized light curve reflects these polynomial trends. Any optional transit signal (from Mandel & Agol 2002) is multiplicatively combined: $\sigma_{A}$6

5. Software Structure and Computational Performance

PSLS is implemented in Python with NumPy/SciPy and organized into modular stages:

• Configuration parsing,
• Analytical PSD evaluation,
• Random Fourier amplitude realization and inverse FFT,
• Addition of white noise,
• Generation and aggregation of systematic error time series,
• Optional incorporation of transit signals.

Typical usage involves synthesizing complete two-year, 25 s cadence (∼2.5%%%%26${\cal A}(\nu)$627%%%% points), 24-camera light curves in seconds. Large-scale Monte Carlo studies (10$\sigma_{A}$9 realizations) are feasible overnight on a workstation.

6. Empirical Validation and Reproducibility

Benchmarking of PSLS was performed by direct comparison with real Kepler observations for three targets:

• 16 Cyg B (KIC 12069449): Main-sequence; the oscillation envelope, $\tau_{A}$0, $\tau_{A}$1, and granulation slopes match Kepler data above ∼50 μHz after tuning high-frequency white noise.
• KIC 12508433: Subgiant; envelope width, mode separations, and granulation roll-off are replicated.
• KIC 9882316: Red giant; simulated mixed-mode ridges, spacing $\tau_{A}$2, and heights reproduce Kepler PSD features within $\tau_{A}$310–20% in amplitude.

In all cases, PSLS systematics remain below the Kepler background at frequencies $\tau_{A}$410 μHz, and granulation/oscillation envelopes are within the observed RMS scatter. This demonstrates that PSLS reproduces the statistical and asteroseismic properties of real light curves, while embedding the realistic systematic effects anticipated for PLATO (Samadi et al., 2019).