The Interpolation Constraint in the RV Analysis of M Dwarfs Using Empirical Templates

Abstract Precise radial velocity (pRV) measurements of M dwarfs in the near-infrared rely on empirical templates due to the lack of accurate stellar spectral models in this regime. Templates are assumed to approximate the true spectrum when constructed from many observations or in the high signal-to-noise limit. We develop a numerical simulation that generates SpectroPolarimètre InfraRouge (SPIRou)-like pRV observations from PHOENIX spectra, constructs empirical templates, and estimates radial velocities (RVs). This simulation solely considers photon noise and evaluates when empirical templates remain reliable for pRV analysis. Our results reveal a previously unrecognized noise source in templates created from stacking registered observations, establishing a noise floor for such template-based pRV measurements. We find that these templates inherently include distortions in stellar line shapes due to imperfect interpolation at the detector’s sampling resolution. The magnitude of this interpolation error depends on sampling resolution and RV content. Consequently, for stars with higher RV content, such as cooler M dwarfs, interpolation noise has a larger relative impact, making their performance comparable to hotter M dwarfs when using detectors with low sampling. For a typical M4V star, SPIRou’s spectral and sampling resolution imposes an RV uncertainty floor of 0.5–0.8 m s −1 , independent of the star’s magnitude or the telescope’s aperture. These findings reveal a limitation of template-based pRV methods, underscoring the need for improved spectral modeling and better-than-Nyquist detector sampling to reach the next level of RV precision.