Investigating the differential limb coupling effect for diffraction-limited spectrographs with PARVI

Technical Summary: Investigating Differential Limb Coupling with PARVI

Problem Statement
The field of Extreme-Precision Radial Velocity (EPRV) aims to detect Earth-mass planets by measuring stellar Doppler shifts at the <10 cm/s level. A promising new architecture for EPRV spectrographs involves using diffraction-limited instruments fed by single-mode fibers (SMF) and adaptive optics (AO). However, this architecture introduces a specific systematic error known as Differential Limb Coupling (DLC). Because target stars are partially resolved at the diffraction limit, imperfect centering of the stellar point spread function (PSF) on the input fiber causes unequal coupling of the red- and blue-shifted limbs of the stellar disk. This asymmetry distorts spectral line profiles, inducing spurious radial velocity (RV) shifts. Simulations suggest that for future instruments like HISPEC on Keck II, a pointing error of merely 1 mas could produce RV errors of 1–2 m/s, potentially overwhelming the instrumental error budget and masking planetary signals. While DLC is theoretically understood, its on-sky impact has not been directly measured with high-precision spectrographs, and mitigation strategies remain unverified.

Methodology
To directly measure DLC-induced RV shifts and develop mitigation strategies, the authors designed and executed an observing campaign using PARVI (PAlomar Radial Velocity Instrument), a diffraction-limited spectrograph operating at the Palomar 200-inch Hale Telescope (5.1 m).

• Experimental Design: The team utilized PARVI's tip-tilt stages to deliberately offset target stars from the center of the input fiber. Based on the scaling relation $\Delta RV \propto \alpha_{offset} D_{tel}^2 \alpha_* v \sin i$, they selected targets with large angular diameters ($\alpha_*$) and high rotational velocities ($v \sin i$), specifically nearby K/M giants and A/F rapid rotators (e.g., Altair, $\mu$ Gem).
• Observing Strategy: Observations involved scanning stars in an "X" pattern centered on the fiber, with steps of 18 mas (0.5 pixels on the guide camera). Two perpendicular scans were performed to account for unknown stellar spin axis orientations. Multiple exposures were taken at each position to boost signal-to-noise (S/N) and assess scatter.
• Instrumentation: PARVI covers the NIR J and H bands (1150–1770 nm) with $R \sim 60,000$. The team used fiber optic attenuators to manage flux from bright targets and employed simultaneous etalon calibration to track instrumental drifts.
• Data Analysis: The team characterized the tip-tilt guide camera's plate scale and pointing accuracy. For RV extraction, they initially employed a template-matching algorithm (SERVAL) adapted for PARVI, stacking spectra to create a master template and calculating relative RVs for each exposure.

Key Results

• Instrument Characterization: The study successfully derived a plate scale of 37 mas/pixel for the PARVI guide camera. However, analysis of the tip-tilt stages revealed that while the general "X" scan pattern was achieved, the actual pointing accuracy deviated from commanded positions by up to 20 mas, and the stages exhibited a systematic bias in the y-direction. Additionally, PSF jitter was measured at 5–10 mas, which may reduce the observable $\Delta RV$ compared to static simulations.
• RV Extraction Challenges: The template-matching RVs exhibited a consistent, unexplained linear slope of hundreds of m/s over the course of single nights. This trend correlated strongly with the Barycentric Earth Radial Velocity (BERV) but not with airmass, suggesting the slope is an algorithmic artifact rather than instrumental drift. The authors attribute this to residual observer-frame contamination (e.g., microtellurics or detector pattern noise) present in the master template, a phenomenon previously noted in ESPRESSO and HARPS data when limited epochs are used for template construction.
• DLC Detection: After fitting out the intra-night RV slopes, the data showed increased RV scatter for off-center positions compared to on-center positions for several targets. However, the authors note that this increased scatter is frequently associated with increased RV error bars due to lower S/N for off-center RVs. Consequently, they refrain from drawing definitive conclusions regarding the direct RV impact of DLC at this stage, though the results show hints of the effect.

Significance and Future Work
This paper represents a significant step in directly measuring DLC-induced RV shifts using a precision RV spectrograph, building upon earlier tentative attempts by Ref. 25. While the experiment successfully characterized the PARVI instrument's pointing performance and identified significant algorithmic challenges in RV extraction, the results are currently modest. The authors conclude that the observed RV scatter provides "hints" of DLC but is not yet sufficient to fully quantify the effect or validate mitigation strategies.

Future work will focus on:

1. Investigating the algorithmic RV slope by modifying SERVAL parameters and comparing results with the classic Cross-Correlation Function (CCF) method, which appears immune to this specific trend.
2. Incorporating pointing jitter into DLC simulations to derive more realistic expectations for $\Delta RV$.
3. Using these findings to develop and validate on-sky mitigation strategies for upcoming instruments like HISPEC, ultimately aiming to ensure the feasibility of diffraction-limited spectrographs for EPRV science.