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arxiv: 2606.29569 · v1 · pith:7T4BMWBQnew · submitted 2026-06-28 · 🌌 astro-ph.EP · astro-ph.IM

The impact of interpolation in high-resolution spectroscopy -- The overlooked role of interpolation in radial velocity extraction

A. M. Silva , D. Doshi , K. Al Moulla , E. A. S. Cristo , \'E. Artigau , P. T. P. Viana , N. C. Santos , J. H. C. Martins
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C. M. J. Marques S. G. Sousa C. San Nicolas Martinez T. L. Campante A. Cabral S. Cristiani
This is my paper

Pith reviewed 2026-06-30 01:55 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.IM
keywords radial velocitystellar spectroscopyinterpolationtemplate matchingsystematic errorsESPRESSOhigh-resolution spectra
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The pith

The choice of interpolation algorithm when constructing stellar templates and extracting radial velocities can introduce systematic biases of up to 25 m/s.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests how spectral interpolation affects radial velocity time series produced by template-based methods. It creates synthetic spectra from sums of Gaussian profiles matched to an observed star and runs them through the s-BART pipeline while swapping interpolation routines. The same swap is then applied to real ESPRESSO spectra of four stars observed either in a single night or across multiple nights. In both synthetic and real data the extracted RVs differ systematically according to the interpolation choice, with the size of the difference depending on signal-to-noise ratio and the range of barycentric Earth radial velocity covered by the observations.

Core claim

Synthetic datasets reveal systematic biases with the largest peak-to-peak amplitudes reaching ∼20 m/s in low SNR cases, decreasing as SNR rises and still present at the mm/s level in noise-free spectra. High-cadence real observations with small BERV variation show peak-to-peak residuals as large as ∼25 m/s in the lower-SNR case and ∼1 m/s in the higher-SNR case. Observations spread over a larger BERV window limit the scatter from this signal to an upper bound of 20 cm/s.

What carries the argument

The interpolation algorithm used inside the s-BART pipeline both when building the stellar template and when performing the subsequent radial-velocity extraction step.

If this is right

  • Low-SNR, high-cadence observations with limited BERV range are most susceptible to interpolation-induced RV offsets of tens of m/s.
  • The bias shrinks below 1 m/s once SNR is high and is bounded by 20 cm/s once observations span a wide BERV window.
  • Even perfectly noise-free spectra still carry a residual interpolation bias at the mm/s level.
  • Template-based RV pipelines must therefore treat the interpolation routine as a controllable source of systematic error.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Surveys that combine data from different instruments or pipelines may need to reprocess all spectra with a single interpolation choice to avoid artificial offsets.
  • Small-planet searches that rely on sub-m/s stability over many nights could be limited by this effect unless observations are deliberately scheduled across a wide BERV range.
  • Future higher-precision instruments may need to propagate interpolation uncertainty into the final RV covariance matrix rather than treating it as negligible.

Load-bearing premise

Differences seen when swapping interpolation algorithms are produced by interpolation itself rather than by interactions with other fixed steps in the pipeline or by the Gaussian approximation used to generate the synthetic spectra.

What would settle it

Re-extracting RVs from the identical set of spectra after deliberately varying one other pipeline step while keeping interpolation fixed would show whether the bias amplitude remains unchanged.

Figures

Figures reproduced from arXiv: 2606.29569 by A. Cabral, A. M. Silva, C. M. J. Marques, C. San Nicolas Martinez, D. Doshi, \'E. Artigau, E. A. S. Cristo, J. H. C. Martins, K. Al Moulla, N. C. Santos, P. T. P. Viana, S. Cristiani, S. G. Sousa, T. L. Campante.

Figure 1
Figure 1. Figure 1: Flux effect of interpolating a Gaussian line (first row) on the blue (left column) and red (right column) wavelengths of ESPRESSO. The rows after the first one present the residuals between the interpolated gaussian line and the expected one, in parts per million (ppm). pixels – leads to higher residuals, as a consequence of the inter￾polation relying more on our underlying assumptions regarding line shape… view at source ↗
Figure 2
Figure 2. Figure 2: Top: Asymmetry of the ARES-fitted spectral lines as esti￾mated by integrating the interpolation artifacts when the BERV coverage is enough to fully probe one pixel. Bottom: Median percentage decrease of line depth, computed over the interpo￾lation artifacts when the BERV coverage is enough to fully probe one pixel; The lines, spread over ESPRESSO’s wave￾length range, are color-coded by the amount of pixels… view at source ↗
Figure 3
Figure 3. Figure 3: RV curve of the same gaussian profile placed on di [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Impact of adding Poisson noise to the RV curve of the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: RV signal from two simulated datasets consisting of a [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: RV residuals between the s-BART RVs obtained with a cubic-spline interpolation (default) and other interpolation al￾gorithms. The analysis is done for two stars, Proxima Centauri (left column) and HD39091 (right column). We present RV time￾series when using the full spectrum (top row), and only the red and blue detectors (second and third row, respectively). In each panel we present the median RV uncertain… view at source ↗
Figure 6
Figure 6. Figure 6: Residuals between s-BART RVs with a cubic spline interpolation (the default one) and s-BART RVs when using different interpolations. The top row presents the comparison for the low-SNR HD40307 start, whilst the bottom one presents the data of ϵ Indi. This analysis was carried out using only the blue (left column) and red (middle column) detectors, as well as using the full spectra (right column). 7. Conclu… view at source ↗
read the original abstract

We explore the impact of spectral interpolation in radial velocity (RV) time-series extracted through template-based methods. We build synthetic datasets with Gaussian profiles to evaluate flux residuals and line asymmetry that are a result from changing the sampling location of the lines. We generate synthetic spectra as a sum of Gaussian functions whose parameters were determined through an observed spectrum. The s-BART pipeline was applied to them, allowing to evaluate any biases in RV extraction introduced by its internal assumptions in line shape. Lastly, we apply the s-BART pipeline to ESPRESSO observations of four stars: two that use high-cadence observations over a single night, and two that have observations spread over multiple nights. When extracting RVs from stellar spectra, we change the interpolation algorithm, used in the process of constructing the stellar template and, afterwards, during RV extraction, comparing them with RVs extracted with a widely-used cubic-spline interpolation. We find that synthetic datasets reveal systematic biases with the largest peak-to-peak amplitudes reaching $\sim$ 20 m/s in low SNR cases, with the amplitude decreasing as the SNR of the spectra increases. In the extreme case of noise-free data, we still recover a systematic bias, albeit at the mm/s level, significantly smaller than the RV precision of state-of-the-art instruments. With real observations we find that those from high-cadence observations with small BERV variation are impacted by the choice of the interpolation algorithm. This impact is smaller in higher-SNR cases, where the peak-to-peak amplitude reaches $\sim$ 1 m/s. In the comparatively lower-SNR case we find peak-to-peak residuals as large as $\sim$ 25 m/s . In cases where the observations are spread over a larger BERV window, we find an upper limit of 20 cm/s of RV scatter for this systematic signal.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that the choice of interpolation algorithm (compared to cubic spline) during stellar template construction and subsequent RV extraction in the s-BART pipeline introduces systematic biases in radial velocity time series. Synthetic spectra generated as sums of Gaussian profiles show peak-to-peak RV bias amplitudes up to ~20 m/s at low SNR (decreasing with higher SNR, down to mm/s in noise-free cases). Real ESPRESSO observations of four stars reveal similar effects, with peak-to-peak residuals up to ~25 m/s in high-cadence low-SNR cases with small BERV variation, ~1 m/s in higher-SNR high-cadence cases, and an upper limit of 20 cm/s when observations span a larger BERV window.

Significance. If the central attribution holds, the result is significant because it quantifies a previously overlooked systematic that can produce RV scatter at levels comparable to or exceeding typical exoplanet signals, directly relevant to cm/s-precision goals with instruments like ESPRESSO. The combination of controlled synthetic tests (with explicit numerical bias amplitudes) and application to real high-cadence observations provides concrete, falsifiable effect sizes that pipeline developers can use. The analysis relies on direct empirical comparisons rather than circular parameter fitting.

major comments (1)
  1. [synthetic data generation and pipeline application] Synthetic data generation and pipeline application sections: The RV differences are obtained by holding all other s-BART steps fixed while swapping only the interpolator, but the manuscript does not include control experiments in which normalization, line selection, or the Gaussian line-shape model are varied independently. Without these, it remains possible that the reported peak-to-peak amplitudes (~20 m/s in synthetics, ~25 m/s in real data) arise partly from interactions between the interpolator and unvaried pipeline modules rather than from interpolation alone; this attribution is load-bearing for the headline claim.
minor comments (2)
  1. The specific interpolation algorithms tested (beyond the reference cubic spline) are not named or described in sufficient detail for readers to reproduce the exact comparison.
  2. [real observations] The real-observation section would benefit from an explicit table listing the four stars, their approximate SNR, BERV ranges, and number of spectra to make the case distinctions immediately clear.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on attribution. We address it point-by-point below.

read point-by-point responses

  1. Referee: Synthetic data generation and pipeline application sections: The RV differences are obtained by holding all other s-BART steps fixed while swapping only the interpolator, but the manuscript does not include control experiments in which normalization, line selection, or the Gaussian line-shape model are varied independently. Without these, it remains possible that the reported peak-to-peak amplitudes (~20 m/s in synthetics, ~25 m/s in real data) arise partly from interactions between the interpolator and unvaried pipeline modules rather than from interpolation alone; this attribution is load-bearing for the headline claim.

    Authors: We thank the referee for highlighting this point on experimental design. Our approach deliberately fixes all other s-BART modules (normalization, line selection, and the Gaussian line-shape model) while varying only the interpolator; this isolates the contribution of the interpolation step within the pipeline as actually used. In the synthetic case the input spectra are generated exactly as sums of Gaussians, matching the pipeline's internal model, so any RV difference recovered after swapping the interpolator is produced by that change. The same amplitude range appears when the identical pipeline (with its fixed modules) is applied to real ESPRESSO spectra, indicating that the observed bias is the practical effect of the interpolator choice rather than an artifact of untested interactions. We do not claim the bias would be identical under every conceivable pipeline variant; we claim it appears when the interpolator is changed inside this standard template-based workflow. To strengthen clarity we will add a short paragraph in the methods section explaining the controlled-experiment rationale and the limits of attribution. This constitutes a partial revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical comparisons are self-contained

full rationale

The paper conducts direct experiments by generating synthetic spectra as sums of Gaussians, applying the s-BART pipeline while varying only the interpolation algorithm (vs. cubic spline), and measuring resulting RV differences on both synthetics and real ESPRESSO data. No load-bearing step reduces by the paper's own equations or self-citation to its inputs; the central results are measured peak-to-peak RV amplitudes from controlled swaps. No self-definitional relations, fitted inputs renamed as predictions, or uniqueness theorems appear. This is the standard case of an empirical study whose claims rest on observable differences rather than internal re-derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that summed Gaussian profiles capture the relevant line-shape behavior for interpolation testing and that the s-BART pipeline isolates interpolation effects when only that component is changed.

free parameters (1)
  • Gaussian profile parameters
    Parameters fitted to an observed spectrum to generate the synthetic datasets used for bias testing.
axioms (1)
  • domain assumption Summed Gaussian functions sufficiently reproduce the flux residuals and line asymmetry induced by changing the sampling location of spectral lines.
    Invoked when constructing synthetic spectra to evaluate interpolation effects.

pith-pipeline@v0.9.1-grok · 5954 in / 1376 out tokens · 56202 ms · 2026-06-30T01:55:32.994383+00:00 · methodology

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