CARMENES–CRIRES+ Injection–Recovery

• The paper introduces a comprehensive injection–recovery framework that injects synthetic spectra into high-resolution data to map detection thresholds over cloud-top pressure and metallicity.
• The methodology employs state-of-the-art atmospheric forward models and rigorous SysRem-based systematics removal to isolate planetary signals in HRS observations.
• Results applied to exoplanets like GJ 436 b demonstrate how varying metallicity and cloud conditions yield robust constraints on atmospheric composition.

CARMENES-CRIRES$^+$ injection–recovery refers to a rigorous framework for quantifying the detection sensitivity of high-resolution spectroscopic (HRS) transmission observations of exoplanet atmospheres, specifically as implemented using the near-infrared CARMENES and CRIRES$^+$ spectrographs. Injection–recovery tests address the problem of non-detections by probing the parameter space of cloud-top pressure and atmospheric metallicity: synthetic model signals are injected into real (or simulated) data and the recovery significance after full end-to-end processing reveals which atmospheric scenarios are robustly excluded by the observations. This approach has become central for constraining the atmospheric physics of warm Neptunes and sub-Neptunes, exemplified by recent studies of GJ 436 b and GJ 3090 b (Grasser et al., 9 Jul 2024, Peláez-Torres et al., 3 Dec 2025, Parker et al., 20 Mar 2025).

1. Injection–Recovery Concept and Motivation

Injection–recovery experiments in the CARMENES-CRIRES$^+$ context are designed to overcome the ambiguity inherent in the absence of detected molecular signals in HRS timeseries data. Because exoplanetary atmospheres may be veiled by high-altitude clouds or be extremely metal-rich (both of which can mute transmission features), determining whether non-detections are due to instrumental sensitivity or astrophysical factors requires a quantitative mapping of detection thresholds across atmospheric parameter space.

This methodology involves generating a physically motivated grid of synthetic spectra—varying heavy-element enrichment ($Z$), cloud-top pressure ($p_c$), temperature, and molecular composition—using atmospheric forward models (e.g., petitRADTRANS, FastChem), convolving to instrumental resolution, injecting these signals into the raw or preprocessed data at the appropriate planetary velocities, and then applying the full reduction and analysis pipeline (including telluric and stellar signal removal, typically via SysRem) before attempting to recover the injected signals using cross-correlation or matched-filter techniques. The fraction of recovered signals at various S/N levels as a function of ($Z$, $p_c$) directly yields statistical detection limits for each molecule (Grasser et al., 9 Jul 2024, Peláez-Torres et al., 3 Dec 2025).

2. Data Processing and Systematics Suppression

A critical step in the injection–recovery process is the removal of telluric and stellar contamination, which otherwise dominate the spectroscopic timeseries. Both CARMENES and CRIRES$^+$ pipelines implement order-by-order normalization and outlier rejection, most stringently by masking strong telluric absorption regions (e.g., flux $<20\%$ for CARMENES, $<15\%$ for CRIRES$^+$).

SysRem, a generalized principal component analysis adapted for weighted data [Tamuz et al. 2005], is employed to isolate and subtract time-correlated systematics. The number of SysRem iterations is calibrated by monitoring the incremental reduction in the standard deviation of the residuals, $$\Delta\sigma^{(i)}=\big(\sigma^{(i-1)} - \sigma^{(i)}\big)/\sigma^{(i-1)}$$, with convergence typically at $\Delta\sigma\lesssim1\%$. This ensures dominant systematics are removed without erasing low-level planetary signals. To guarantee self-consistency, synthetic model signals are injected prior to SysRem so that both real and artificial planetary signals are subjected to identical filtering (Peláez-Torres et al., 3 Dec 2025, Parker et al., 20 Mar 2025).

3. Atmospheric Modeling and Signal Injection

Atmospheric forward modeling employs state-of-the-art radiative transfer codes such as petitRADTRANS or GPU-based custom codes, incorporating solar to super-solar metallicities, chemical equilibrium abundances (computed with pRT’s poor_mans_nonequ_chem or FastChem), and isothermal temperature–pressure profiles justified by the short radiative pathlengths probed at HRS ($P\lesssim1$ mbar). Cloud decks are modeled as gray absorbers at fixed pressures $p_c$, with fully opaque layers for $P<p_c$.

The synthetic transmission spectrum $m(\lambda)$ is Doppler-shifted to each exposure’s planetary radial velocity and convolved to the instrumental profile (e.g., Gaussian with FWHM = $\lambda / R$; $R=100\,000$ for CRIRES$^+$, $R=80\,000$ for CARMENES). For each in-transit frame, the processed stellar spectrum is modified according to

$$S_{\rm inj}(\lambda, t) = S_{\rm obs}(\lambda, t) + \alpha\,M(\lambda, t),$$

where $M$ is the model in units of transit depth and $\alpha$ is a normalization scale factor (usually unity). For small signals, this linear approximation is valid (Grasser et al., 9 Jul 2024, Peláez-Torres et al., 3 Dec 2025, Parker et al., 20 Mar 2025).

4. Cross-Correlation Recovery and Detection Thresholds

Post-SysRem, the spectra are cross-correlated against the grid of templates to search for the planetary trace across a grid of trial velocities ($K_p$, $v_{\rm sys}$). The error-weighted cross-correlation function (CCF) per frame and order is defined as

$$\mathrm{CCF}(v,i) = \sum_{j}\sum_{\lambda} \frac{R_{i,j}(\lambda)\,m_j(\lambda, v)}{\hat{\sigma}_{i,j}^2(\lambda)},$$

with $R_{i,j}$ the SysRem-processed residual, $m_j$ the Doppler-shifted template, and $\hat{\sigma}$ the per-pixel propagated uncertainty (Peláez-Torres et al., 3 Dec 2025).

The co-added CCF in the planet rest frame is then analyzed for significance:

$$\mathrm{S/N}(K_p) = \frac{\max_{v_{\rm rest}} \mathrm{CCF}(v_{\rm rest}, K_p)}{ \sigma_{\rm off}(K_p) },$$

with $\sigma_{\rm off}$ taken from the CCF wings ($|v_{\rm rest}|>20$ km/s). Detection criteria are typically $\mathrm{S/N} \geq 5$ for robust recovery, with the same threshold used to delineate the detectability regions in the ($Z$, $p_c$) parameter space (Grasser et al., 9 Jul 2024, Peláez-Torres et al., 3 Dec 2025, Parker et al., 20 Mar 2025).

5. Detection Limits, Bayesian Retrievals, and Atmospheric Constraints

Injection–recovery output is assembled into 2D grids mapping detection significance across metallicity and cloud-top pressure. For example, the joint CARMENES–CRIRES$^+$ analysis for GJ 436 b yields:

• At $Z=1\times$ solar, clouds above $p_c\lesssim10$ mbar are ruled out.
• At $Z=10$–$100\times$, clouds above $p_c\lesssim1$ mbar are excluded.
• Clear atmospheres ($p_c \gtrsim 1$ bar) are only compatible with $Z \gtrsim 600$–$900\times$ solar (Peláez-Torres et al., 3 Dec 2025).

A representative table from (Grasser et al., 9 Jul 2024) is as follows:

Molecule	$Z$ ($\times Z_\odot$)	$P_\mathrm{cloud}$ (mbar)	$S/N_\mathrm{peak}$
H$_2$O	1	100	6.7
H$_2$O	10	10	4.2
H$_2$O	300	1	2.8
CH$_4$	1	100	3.5
CH$_4$	10	10	2.1
CO	50	100	4.0

Bayesian retrievals leveraging these detection maps as likelihood constraints deliver posterior distributions in $(\log Z, \log p_c, \beta)$ parameter space, where $\beta$ incorporates unknown residual noise scaling. For GJ 436 b, the combined posterior peaks at $p_c \lesssim 10^{-3}$ bar for $Z<10^3$ or at $Z \gtrsim 900\times$, with credible intervals $\log_{10}(Z/Z_\odot) = 0.3 \pm 1.3$, $\log_{10}(p_c/\mathrm{bar}) = -5.1 \pm 2.1$ (Peláez-Torres et al., 3 Dec 2025).

6. Comparative Studies, Instrumental Considerations, and Design Implications

Sensitivity limits are shaped by instrumental parameters—resolution, throughput, telluric coverage, and S/N—as well as astrophysical factors such as planetary mass, equilibrium temperature, and host star properties. The CRIRES$^+$ injection–recovery framework, validated on GJ 3090 b (Parker et al., 20 Mar 2025), can be generalized to other HRS instruments (CARMENES, SPIROU, NIRPS). Reduced resolution (e.g., $R\sim80\,000$ for CARMENES) leads to fewer resolved lines and lower per-line S/N, requiring additional transits or band optimization to achieve equivalent constraints.

A summary of comparative design implications follows:

• K-band ($2.3$ μm) lines are stronger and more numerous than H- and Y-bands, but require AO-corrected stability.
• For sub-Neptunes orbiting M-dwarfs, maximizing velocity separation ($|v_\mathrm{bary} - v_\mathrm{sys}|$) reduces stellar residuals.
• Masking telluric–dominated orders and calibrating the number of SysRem iterations based on injected S/N avoids artificial attenuation or amplification of potential signals.
• Accurate planetary ephemerides ($T_0$, $P$, $e$, $\omega_p$) are critical to prevent velocity–phase smearing.

These criteria serve as blueprints for efficient and robust atmospheric searches with both existing and future spectrographs (Grasser et al., 9 Jul 2024, Peláez-Torres et al., 3 Dec 2025, Parker et al., 20 Mar 2025).

7. Future Directions: Next-Generation Sensitivity and ELT Projections

Simulations with instruments such as ELT/ANDES and tools like EXoPLORE (Peláez-Torres et al., 3 Dec 2025) project a major expansion of accessible parameter space. In-silico datasets indicate that single-transit $R=100\,000$ $YJH$-band observations with ELT/ANDES will probe down to $p_c \sim 0.1$ mbar for $Z=10$–$300\times$ solar metallicity—nearly an order of magnitude below current capabilities. This extension will allow the detection of molecular features in atmospheres presently rendered invisible by clouds or extreme metallicity, facilitating discrimination between cloudy and metal-rich scenarios with a single transit at a photon-limited S/N.

A plausible implication is that, for warm sub-Neptunes and Neptunes, persistent non-detections are best interpreted within a rigorously quantified framework that incorporates both high-altitude aerosols and heavy-element enrichment as degenerate but testable explanations. The CARMENES–CRIRES$^+$ injection–recovery methodology thus represents both the current state-of-the-art and the baseline for anticipated advances with next-generation facilities (Peláez-Torres et al., 3 Dec 2025, Grasser et al., 9 Jul 2024, Parker et al., 20 Mar 2025).