PandExo: Exoplanet Noise Simulator

• PandExo is an open-source Python package that provides rapid, self-consistent noise estimates for time-series exoplanet spectroscopy using JWST and HST data.
• It automates synthetic observation construction by integrating the STScI Pandeia ETC, ensuring precise noise propagation and instrument-specific configuration.
• PandExo is vital for planning and retrieval workflows, enabling flexible, API-driven simulations for optimizing exoplanet atmospheric characterization.

Pandexo is an open-source Python package and web interface providing the exoplanet community with rapid, self-consistent, and instrument-specific estimates of time-series spectroscopic noise for the James Webb Space Telescope (JWST) and the Hubble Space Telescope (HST). Designed to be both flexible in its application and rigorously benchmarked against independent simulators and actual HST data, PandExo enables planning, optimization, and retrieval-readiness for transmission, emission, and eclipse spectroscopy of exoplanet atmospheres. By incorporating the Space Telescope Science Institute's Pandeia exposure time calculator (ETC) for JWST and HST, PandExo delivers detailed synthetic observations with per-channel uncertainties, seamlessly integrating upstream improvements in instrument characterization, background models, and detector properties (Batalha et al., 2017).

1. Architecture and Scope

PandExo wraps the STScI Pandeia ETC back end, automating the construction of synthetic time-series observations for all JWST and HST time-resolved spectroscopic modes. It handles user-supplied stellar spectral energy distributions (commonly from the PHOENIX grid), planet models (transmission or emission spectra), and scheduling parameters (e.g., transit duration $T_{14}$, number of events, in- versus out-of-transit time fractions).

At its core, PandExo automates:

• Readout configuration and optimal group/integration settings to maximize duty cycle while avoiding detector saturation.
• Calculation of in- and out-of-transit spectra using the underlying Pandeia formalism, including full propagation of photon noise, read noise, background, and optional systematic noise floors.
• Output of wavelength-resolved spectra and uncertainties suitable for proposal planning, instrument configuration, and forward-modeling or retrieval pipelines.

Through its online interface and Python package, PandExo is accessible for batch runs, API-driven parameter searches, and interactive design of observing campaigns (Batalha et al., 2017).

2. Supported Observing Modes and Key Parameters

PandExo supports all major spectroscopic modes for time-series exoplanet studies with JWST (NIRISS SOSS, NIRSpec Prism and gratings, NIRCam grism, MIRI LRS) and HST/WFC3 spatial-scanning spectroscopy (Batalha et al., 2017, Stevenson et al., 2019). Key instrumental parameters—wavelength coverage, resolving power, per-frame read noise—are inherited directly from Pandeia’s instrument database, ensuring accurate throughput, PSF, and detector characteristic modeling. For example:

Instrument/Mode	$\lambda$ ($\mu$m)	$R$	Read Noise (e$^-$/frame)
JWST NIRISS SOSS	0.6–2.8	700	11.55
JWST NIRSpec G395H	2.9–5.0	2700	16.8
JWST MIRI LRS	5–14	100	32.6
HST WFC3 G141	1.12–1.65	130	20.0

Instrument-specific settings such as subarrays, readout modes, integration times, and noise floors are customizable by the user and automatically checked for saturation, duty cycle, and anticipated systematics (Batalha et al., 2017).

3. Mathematical Formalism and Noise Propagation

The foundation of PandExo's noise calculations is the Pandeia engine’s full treatment of noise for nondestructive readouts in IR detectors, including the LMF ("Last-Minus-First") and MULTIACCUM approaches. In the default general use, the LMF scheme dominates, incorporating:

• Photon (shot) noise and background (zodiacal, telescope thermal) noise, calculated for each extraction pixel and channel.
• Read noise, propagated for all relevant pixels and integrations.
• Dark current, using detector-specific rates.

The total propagated variance in each wavelength channel ($\lambda$) is:

$$\sigma_{\mathrm{tot}}^2 = \sigma_{\mathrm{shot}}^2 + \sigma_{\mathrm{bkg}}^2 + \sigma_{\mathrm{read}}^2$$

where individual terms follow the scaling described in the provided equations (Batalha et al., 2017). A user-imposed systematic "noise floor" $\sigma_{f,\lambda}$ is enforced, such that if the propagated error $\sigma_{\mathrm{prop},\lambda}$ falls below $\sigma_{f,\lambda}$, the latter is reported. For all HST/WFC3 support, empirically determined multipliers are applied (1.07$\times$ photon noise for G141) based on long-term monitoring (Stevenson et al., 2019). Systematic sources such as slitless contamination, position drift, and in-flight stellar/instrument time-correlated behavior are flagged for user attention, but not explicitly modeled (Batalha et al., 2017, Stevenson et al., 2019).

4. Integration With Forward Modeling and Retrieval Workflows

PandExo is widely utilized as an output node in forward-modeling and atmospheric retrieval pipelines. Arbitrary transmission or emission spectra from external radiative transfer codes (e.g., ATMO (Goyal et al., 2017), petitRADTRANS (Arenales-Lope et al., 12 Nov 2024), Pyrat Bay (Blumenthal et al., 2017), 3D GCM models (Lines et al., 2018)) are ingested as planet/star flux ratio or eclipse depth spectral files. PandExo then simulates the corresponding noisy, instrument-specific observations, including realistic per-bin uncertainties and noise correlations.

For retrieval studies, PandExo-simulated error bars are coupled directly into Bayesian frameworks (e.g., MULTINEST) to derive robust detection thresholds on atmospheric constituents, such as polycyclic aromatic hydrocarbons (PAHs), or to quantify the detectability of equilibrium versus non-equilibrium chemistry (Arenales-Lope et al., 12 Nov 2024, Blumenthal et al., 2017).

Grid-based atmospheric spectrum libraries (e.g., ATMO, 460,000 synthetic spectra) are designed with PandExo compatibility in file formats and wavelength bins, facilitating efficient parameter-space exploration and interpolation in JWST proposal planning (Goyal et al., 2017).

5. Empirical Validation and Best Practices

PandExo’s predictions for JWST noise are benchmarked against each instrument team's independent sensitivity calculators using the same formalism, consistently showing agreement within 10% across supported modes (Batalha et al., 2017). For HST/WFC3, PandExo reproduces published emission spectrum noise to better than 10%, validated against actual campaign performance and the WFC3 spatial scan monitor (>8 years). Key best practice guidelines include:

• For HST/WFC3, the scan rate–fluence relation incorporates both J-band magnitude and $J-H$ color, with an empirical calibration derived from 8 years of spatial-scan data for optimal precision and scan/schedule planning (Stevenson et al., 2019).
• Use instrument-appropriate noise floors (e.g., 20 ppm for NIRISS, 30 ppm for NIRCam, 50 ppm for MIRI) to account for yet-unknown systematics in JWST time-series data (Batalha et al., 2017).
• Always ensure modeled spectra are appropriately matched in resolution to that of the planned instrument mode; PandExo automatically rebins as necessary (Goyal et al., 2017).
• Incorporate drift and guide star advisories, especially for HST WFC3 spatial scans, to avoid “marginal” or “failed” visits (Stevenson et al., 2019).

6. Applications and Scientific Impact

PandExo is integral to feasibility and optimization studies for JWST and HST spectroscopic surveys. Examples include:

• Predicting the detectability thresholds of specific atmospheric tracers (e.g., THz–PAH absorption, silicate clouds, CO/CO$_2$ disequilibrium signatures) as a function of planetary temperature, metallicity, and C/O ratio, directly based on simulated PandExo noise (Arenales-Lope et al., 12 Nov 2024, Lines et al., 2018, Blumenthal et al., 2017).
• Enabling direct comparison of forward models with sensitivity-limited datasets, informing target selection, binning strategies, and instrument configuration.
• Providing standardized, reproducible predictions to guide the design of large survey programs and support competitive JWST and HST proposal submissions.

In cloud studies, for example, PandExo simulations show that JWST/MIRI-LRS, at a 50 ppm noise floor, can robustly distinguish grey cloud opacity from mineralogical silicate features at >5$\sigma$ confidence in a single transit (Lines et al., 2018). For atmospheric constituents such as PAHs, PandExo noise levels at ~30–50 ppm in JWST/NIRSpec PRISM single-transit observations set quantitative detection limits—10$^{-7}$ for C$_{54}$H$_{18}$ in optimal $T$, [Fe/H], and C/O cases (Arenales-Lope et al., 12 Nov 2024).

7. Limitations and Ongoing Development

PandExo does not model time-correlated stellar or instrumental systematics beyond published empirical floors, nor does it simulate slitless contamination, intra-pixel sensitivity variations, or detailed 3D limb inhomogeneities in planetary atmospheres (Batalha et al., 2017, Goyal et al., 2017). Users must be attentive to the potential for unmodeled systematics, especially for high-precision, multi-visit programs. For atmospheric spectrum synthesis, all assumptions on cloud/haze microphysics, radiative transfer, and chemistry remain the responsibility of the user or the upstream modeling library (Goyal et al., 2017, Lines et al., 2018).

Development is ongoing to support additional modes (e.g., HST STIS), improved treatment of known systematics as JWST flight data become available, and deeper integration within exoplanet workflow frameworks.

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Pandexo thus constitutes an essential, community-vetted backbone for next-generation exoplanet atmospheric characterization campaigns, ensuring consistency, traceability, and up-to-date realism in simulation-driven proposal and analysis pipelines for JWST and HST (Batalha et al., 2017, Goyal et al., 2017, Blumenthal et al., 2017, Lines et al., 2018, Stevenson et al., 2019, Arenales-Lope et al., 12 Nov 2024).