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arxiv: 2605.04587 · v2 · submitted 2026-05-06 · 🌌 astro-ph.EP · astro-ph.IM· astro-ph.SR

Recognition: unknown

Mitigating stellar radial velocity jitter using orthogonal activity indices and a time-aware neural network

Jordi Blanco-Pozo , Manuel Perger , Guillem Anglada-Escud\'e , Ignasi Ribas , David Baroch , Marina Lafarga , Juan Carlos Morales , \`Oscar Porqueras-Le\'on
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Sophie Stucki David Vallmanya Poch
Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:49 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.IMastro-ph.SR
keywords radial velocitystellar activityexoplanetsneural networkscross-correlation functionspectroscopy
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The pith

A time-aware neural network trained on simulated line distortions reduces stellar activity jitter in radial velocity data to 52.5 percent and 62.4 percent of the original levels.

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

The paper develops a way to disentangle stellar activity from planetary signals in radial velocity measurements by decomposing the cross-correlation function into orthogonal components that isolate pure line shifts from shape distortions. A convolutional attention network called CANSTAR is trained on time series of these distortion coefficients generated by a stellar simulator to capture how activity features evolve. When the trained network is applied to real observations of the active stars epsilon Eridani and TZ Arietis, it removes most of the activity-induced scatter and produces tighter constraints on the orbit of TZ Arietis b than Gaussian process regression achieves. The work shows that networks incorporating temporal context can handle complex activity patterns more effectively than current standard methods.

Core claim

The central claim is that a time-aware convolutional attention network trained exclusively on synthetic orthogonal coefficients of line-shape distortions can learn the temporal evolution of stellar activity and subtract its contribution from observed radial velocities, lowering the RMS to 52.5 percent of the uncorrected value for epsilon Eridani and 62.4 percent for TZ Arietis while yielding more precise orbital parameters for TZ Arietis b than Gaussian process regression.

What carries the argument

The CANSTAR time-aware convolutional attention network, which ingests orthogonal coefficients obtained from Gram-Schmidt decomposition of the cross-correlation function and models their temporal evolution to predict activity-induced radial velocity contributions.

If this is right

  • The correction enables detection of smaller planets by lowering the effective noise floor in radial velocity time series.
  • Neural networks that incorporate temporal context outperform Gaussian process regression for stars with complex activity patterns.
  • Future refinements to the simulator could close the remaining gap between synthetic training data and real observations.

Where Pith is reading between the lines

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

  • The orthogonal decomposition technique could be combined with other activity proxies to further isolate planetary signals.
  • If the simulation-to-reality transfer improves, the same training strategy might apply to data from additional spectrographs or stars.
  • The temporal modeling approach might extend to other time-series problems where instrumental or intrinsic variations must be separated from target signals.

Load-bearing premise

The synthetic line-shape distortion coefficients from the stellar simulator must accurately capture the real temporal evolution of stellar activity features so the network generalizes to telescope observations without large mismatch.

What would settle it

If the network-corrected radial velocities for the test stars still exhibit strong correlations with activity indicators or produce no improvement in the precision of the planet's orbital parameters relative to Gaussian process regression, the mitigation claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.04587 by David Baroch, David Vallmanya Poch, Guillem Anglada-Escud\'e, Ignasi Ribas, Jordi Blanco-Pozo, Juan Carlos Morales, Manuel Perger, Marina Lafarga, \`Oscar Porqueras-Le\'on, Sophie Stucki.

Figure 1
Figure 1. Figure 1: Time-averaged CCFs (templates) of ϵ Eri (red) and TZ Ari (blue) with the corresponding Gaussian model fit for ϵ Eri (orange) and the two-component Gaussian model fit for TZ Ari (cyan). 410 420 RV (m/s) 100 20 10 5 Period (d) 0.0 0.2 0.4 Power 41.0 41.1 41.2 CON (%) 0.00 0.25 0.50 Power 6440 6460 6480 FWHM (m/s) 0.00 0.25 0.50 Power 8775 8800 8825 8850 t (BJD-2450000) 30 40 BIS (m/s) 0.0 0.1 0.2 freq (d 1 )… view at source ↗
Figure 2
Figure 2. Figure 2: Time series (left) and GLS periodograms (right) of the RV view at source ↗
Figure 5
Figure 5. Figure 5: Explained variance ratio (solid) and cumulative vari view at source ↗
Figure 6
Figure 6. Figure 6: Cross-correlation function decomposition of view at source ↗
Figure 7
Figure 7. Figure 7: Same as Fig view at source ↗
Figure 8
Figure 8. Figure 8: Schematic representation of CANSTAR (bottom), a convolutional attention network de￾signed to predict the stellar activity contribu￾tion to line shifts, κ(t), from the time series of distortion coefficients, gi(t). The input coeffi￾cients are treated as independent channels and processed through a series of one-dimensional convolutional layers that extract local tem￾poral features. The convolutional outputs… view at source ↗
Figure 9
Figure 9. Figure 9: Residual relative error of ϵ Eri (top) and TZ Ari (bottom) StarSim data after correction with CANSTAR (solid line with cir￾cle marker) and an FCN (dashed line with square marker) for the noiseless case (blue) and for the case with noise equivalent to the observations (green). bach et al. (2022) but restricting their multi-instrument dataset to CARMENES only (Appendix G). We compare in view at source ↗
Figure 10
Figure 10. Figure 10: Top: Radial velocity time series (left) and GLS periodogram (right) of the HARPS view at source ↗
Figure 11
Figure 11. Figure 11: Detection limits in the ϵ Eri residuals after applying CANSTAR’s correction, shown as a function of the difference between injected and retrieved frequencies (left) and semi-amplitudes (right) for the different injected frequencies and semi-amplitudes sinusoidal signals. might necessitate three or more Gaussians. A robust and auto￾mated approach to determine the optimal number of Gaussians for the mother … view at source ↗
Figure 12
Figure 12. Figure 12: Histograms showing the posterior distribution of the shared parameters between the view at source ↗
Figure 13
Figure 13. Figure 13: Radial velocity time series and GLS periodograms for TZ Ari showing view at source ↗
Figure 14
Figure 14. Figure 14: Residual time series (left) and GLS periodogram (right) after subtracting the GP view at source ↗
Figure 15
Figure 15. Figure 15: Top: Radial velocity time series (left) and GLS periodogram (right) of the HARPS view at source ↗
read the original abstract

Despite recent advances in the precision of high-resolution spectrographs, the detection of Earth-like exoplanets is still limited by the effects of stellar activity, which introduce radial velocity variations at the metre-per-second level or larger. We present a framework to disentangle stellar effects from planetary signals by exploiting high-order distortions of the cross-correlation function (CCF; a measure of the average spectral line profile), thus moving beyond the commonly applied Gaussian fit approximation. We decomposed the CCF using a Gram-Schmidt orthogonal basis function, enabling the separation of pure line shifts from line-shape distortions. To model activity-induced contributions to the radial velocities, we have developed a time-aware convolutional attention network dubbed CANSTAR. This network was trained on synthetic line-shape distortion coefficients produced with the realistic stellar simulator StarSim to learn the temporal evolution of stellar activity features. We validated our framework using HARPS and CARMENES observations of two active stars, ${\epsilon}$ Eridani and TZ Arietis. The network effectively mitigates stellar activity, reducing the radial velocity RMS to 52.5 % and 62.4 % of the uncorrected variability, respectively. This correction enables a more precise determination of the orbital parameters of TZ Arietis b compared to a Gaussian process regression. Our results demonstrate that neural networks that incorporate the temporal context can outperform state-of-the-art methods in complex activity regimes. Future improvements on StarSim that will allow us to train CANSTAR on 3D magnetohydrodynamic spectra and more complex instrumental modelling are expected to bridge the performance gap between synthetic and real data, offering a robust pathway towards detecting Earth-mass planets around Sun-like stars.

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

3 major / 2 minor

Summary. The paper introduces a framework that decomposes cross-correlation functions (CCFs) via Gram-Schmidt orthogonalization to isolate line-shape distortions from pure shifts, then employs a convolutional attention network (CANSTAR) trained exclusively on synthetic activity-induced distortions generated by StarSim to predict and subtract activity contributions to radial velocities. Applied to HARPS and CARMENES observations of ε Eridani and TZ Arietis, the method is reported to reduce RV RMS to 52.5% and 62.4% of the raw values, respectively, and to yield tighter orbital constraints on TZ Arietis b than a Gaussian-process regression baseline.

Significance. If the synthetic-to-real generalization holds, the approach would represent a meaningful advance for mitigating stellar jitter in precision RV exoplanet searches, particularly in regimes with complex spot/plage evolution where temporal context matters. Strengths include the explicit separation of shift and shape components via an orthogonal basis and the direct comparison against a state-of-the-art GP method on real data; the controlled training on StarSim also offers a reproducible pathway for future 3D-MHD extensions.

major comments (3)
  1. [Abstract / Results] Abstract and Results: the headline RMS reductions (52.5 % and 62.4 %) and the claim of improved orbital-parameter precision for TZ Arietis b are presented without reported statistical significance tests, bootstrap or cross-validation uncertainties, or propagation of network-prediction errors into the final RV time series. These omissions leave the quantitative superiority over GP regression only partially supported.
  2. [Methods / Validation] Methods and Validation: training occurs solely on StarSim-generated coefficient trajectories while evaluation uses independent real HARPS/CARMENES CCFs, yet no quantitative domain-shift diagnostics (e.g., MMD, PCA overlap, or correlation-time statistics between synthetic and observed coefficient distributions) or ablation injecting realistic instrumental noise are provided. Because the central claim rests on successful transfer of the learned activity mapping, this gap is load-bearing.
  3. [Results (TZ Arietis b analysis)] Orbital-fit comparison: the statement that CANSTAR enables “more precise determination” of TZ Arietis b parameters lacks the specific fitted values, uncertainties, model-comparison metrics (BIC, residual RMS, or posterior widths), or details on how the activity-corrected RVs were incorporated into the Keplerian model relative to the GP case.
minor comments (2)
  1. [Introduction] The acronym CANSTAR is introduced only in the abstract; its expansion and architectural details should be restated at first use in the main text for clarity.
  2. [Methods] Notation for the Gram-Schmidt coefficients and the precise definition of the time-aware attention mechanism would benefit from an explicit equation or diagram early in the Methods section.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments have helped us identify areas where the manuscript can be strengthened with additional statistical analysis, validation metrics, and reporting details. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and Results: the headline RMS reductions (52.5 % and 62.4 %) and the claim of improved orbital-parameter precision for TZ Arietis b are presented without reported statistical significance tests, bootstrap or cross-validation uncertainties, or propagation of network-prediction errors into the final RV time series. These omissions leave the quantitative superiority over GP regression only partially supported.

    Authors: We agree that the presentation of the RMS reductions and orbital-parameter improvements would be strengthened by explicit statistical support. In the revised manuscript we have added bootstrap resampling (1000 iterations) to derive uncertainties on the reported RMS reduction factors for both stars. We also include k-fold cross-validation results on the real HARPS and CARMENES datasets to demonstrate the stability of the CANSTAR versus GP performance difference. Network-prediction uncertainties are now propagated via Monte Carlo sampling of the CANSTAR ensemble outputs, and the resulting error bars are incorporated into the final RV time series used for all subsequent analyses. revision: yes

  2. Referee: [Methods / Validation] Methods and Validation: training occurs solely on StarSim-generated coefficient trajectories while evaluation uses independent real HARPS/CARMENES CCFs, yet no quantitative domain-shift diagnostics (e.g., MMD, PCA overlap, or correlation-time statistics between synthetic and observed coefficient distributions) or ablation injecting realistic instrumental noise are provided. Because the central claim rests on successful transfer of the learned activity mapping, this gap is load-bearing.

    Authors: The referee correctly highlights the importance of quantifying the synthetic-to-real domain shift. We have added two quantitative diagnostics to the Methods section: (i) Maximum Mean Discrepancy (MMD) computed on the Gram-Schmidt coefficient distributions, and (ii) overlap statistics from a joint PCA of synthetic and observed coefficients, including correlation-time comparisons. In addition, we performed an ablation experiment in which realistic HARPS/CARMENES instrumental noise (derived from the actual error bars) was injected into the StarSim training trajectories before retraining CANSTAR; the resulting performance degradation is now reported. These additions directly address the transferability concern. revision: yes

  3. Referee: [Results (TZ Arietis b analysis)] Orbital-fit comparison: the statement that CANSTAR enables “more precise determination” of TZ Arietis b parameters lacks the specific fitted values, uncertainties, model-comparison metrics (BIC, residual RMS, or posterior widths), or details on how the activity-corrected RVs were incorporated into the Keplerian model relative to the GP case.

    Authors: We accept that the orbital analysis requires more explicit documentation. The revised manuscript now contains a dedicated table listing the best-fit Keplerian parameters (period, K, eccentricity, argument of periastron, and time of periastron) together with 1σ uncertainties for three cases: raw RVs, GP-corrected RVs, and CANSTAR-corrected RVs. We report BIC, post-fit residual RMS, and the 68 % credible-interval widths of the MCMC posteriors for each case. The text now clarifies that the CANSTAR-corrected RV time series (with propagated uncertainties) were supplied to the identical Keplerian fitting pipeline (same priors, same MCMC settings, same jitter term treatment) used for the GP comparison, ensuring a controlled head-to-head evaluation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; training on independent synthetics and external validation on real observations

full rationale

The paper trains the CANSTAR network exclusively on synthetic line-shape distortion coefficients generated by the StarSim simulator to learn temporal activity evolution from Gram-Schmidt orthogonal CCF components. All reported performance metrics, including RMS reductions to 52.5% and 62.4% of uncorrected variability plus improved orbital parameters for TZ Arietis b versus GP regression, are evaluated on separate real HARPS and CARMENES observations of ε Eridani and TZ Arietis. No derivation step, equation, or claim reduces these results to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations; the central claims remain externally benchmarked against independent real data rather than internally forced by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The framework rests on assumptions about signal separability and synthetic data fidelity rather than new physical axioms; the neural network introduces fitted parameters but no new physical entities.

free parameters (2)
  • CANSTAR network weights and hyperparameters
    Fitted during training on synthetic StarSim data to capture temporal activity evolution.
  • Order and choice of Gram-Schmidt basis functions
    Selected to decompose CCF into shift and distortion components.
axioms (2)
  • domain assumption Stellar activity induces radial velocity variations primarily through separable line-shape distortions in the CCF.
    Invoked to justify orthogonal decomposition separating planetary Doppler shifts from activity.
  • domain assumption StarSim synthetic spectra faithfully reproduce the statistical and temporal properties of real stellar activity.
    Required for the trained network to generalize to observed data from epsilon Eridani and TZ Arietis.
invented entities (1)
  • CANSTAR network no independent evidence
    purpose: Time-aware model to predict activity-induced RV contributions from orthogonal distortion coefficients.
    Newly introduced architecture for this specific application.

pith-pipeline@v0.9.0 · 5656 in / 1628 out tokens · 112635 ms · 2026-05-08T16:49:30.884253+00:00 · methodology

discussion (0)

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