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arxiv: 2604.15428 · v1 · submitted 2026-04-16 · 🌌 astro-ph.SR · astro-ph.EP

Recognition: unknown

The CARMENES search for exoplanets around M dwarfs. A homogeneous catalogue of projected rotational velocities accounting for limb-darkening

R. Varas , G. Morello , M. Zechmeister , P. J. Amado , F. J. Pozuelos , J. A. Caballero , A. Claret , C. Cifuentes
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R. Morales A. Quirrenbach A. Reiners I. Ribas V. J. S. B\'ejar M. Cort\'es-Contreras A. P. Hatzes Th. Henning I. Hermelo H. L. Ruh A. Schweitzer H. M. Tabernero M. R. Zapatero Osorio
Authors on Pith no claims yet

Pith reviewed 2026-05-10 09:34 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.EP
keywords M dwarfsprojected rotational velocitylimb darkeningstellar rotationspectroscopyexoplanetscatalogCARMENES
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The pith

An oversampled convolution method with realistic limb darkening measures projected rotational velocities for 392 M dwarfs at 6.8 percent median uncertainty.

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

The paper introduces a method to extract projected rotational velocities from high-resolution spectra of M dwarf stars by comparing them to template spectra through an oversampled convolution that includes a realistic limb-darkening profile. This approach was tested on synthetic spectra across 2500 to 4000 K and then applied to CARMENES observations, producing measurements or 2 km/s upper limits with uncertainties roughly half those in prior literature. Stellar rotation connects directly to age via gyrochronology and to magnetic activity that must be removed for precise radial-velocity exoplanet detection. The result is the largest homogeneous vsini catalog for M dwarfs, with updated values for many targets and 36 new ones added.

Core claim

We present an oversampled convolution method incorporating a realistic limb-darkening model to determine vsini from CARMENES spectra by comparing observed spectra with that of a template star. The advantages over existing methods were assessed using high-resolution synthetic spectra spanning effective temperatures of 2500-4000 K and projected rotational velocities of up to 50 km/s. Applied to 392 M dwarfs observed with CARMENES, our method yields vsini measurements (or upper limits at 2 km/s) with a median relative uncertainty of 6.8 percent, substantially smaller than the 15.4 percent reported in the literature. This work provides the largest uniform catalogue of vsini measurements for M-dw

What carries the argument

Oversampled convolution method that folds a realistic limb-darkening law into the comparison of observed spectra against slowly rotating template stars.

If this is right

  • The catalog supplies uniform vsini data for 392 M dwarfs, including 36 previously unmeasured targets.
  • Median relative uncertainty drops from 15.4 percent in the literature to 6.8 percent.
  • Updated vsini values are provided for many stars already in earlier compilations.
  • Improved rotation measurements support gyrochronology age estimates and removal of activity-induced radial-velocity signals in exoplanet searches.

Where Pith is reading between the lines

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

  • The tighter uncertainties could reveal rotation periods for slower rotators that were previously lost in noise.
  • A uniform M-dwarf vsini scale may reduce scatter in empirical relations between rotation, activity, and age across different surveys.
  • The method's reliance on template comparison suggests it could be applied to archival spectra from other instruments to create a larger, cross-calibrated sample.

Load-bearing premise

The chosen limb-darkening model and template spectra match the real CARMENES data closely enough to avoid systematic errors over the full 2500-4000 K range of M dwarfs.

What would settle it

Independent vsini measurements of the same 392 stars obtained with a different high-resolution spectrograph or technique; the new values and their quoted uncertainties should agree within the stated errors.

Figures

Figures reproduced from arXiv: 2604.15428 by A. Claret, A. P. Hatzes, A. Quirrenbach, A. Reiners, A. Schweitzer, C. Cifuentes, F. J. Pozuelos, G. Morello, H. L. Ruh, H. M. Tabernero, I. Hermelo, I. Ribas, J. A. Caballero, M. Cort\'es-Contreras, M. R. Zapatero Osorio, M. Zechmeister, P. J. Amado, R. Morales, R. Varas, Th. Henning, V. J. S. B\'ejar.

Figure 1
Figure 1. Figure 1: illustrates the χ 2 minimization as a function of v sin i for three spectral orders. The resulting v sin i is indicated by a circular marker. These curves exhibit kinks at different v sin i val￾ues, which bias the inferred velocity depending on their proxim￾ity to the true solution. The origin of these kinks is explained in the following subsection. 3.2. Oversampling The numerical discretisation of the ker… view at source ↗
Figure 4
Figure 4. Figure 4: Best-fitting v sin i values as a function of wavelength, ob￾tained with and without accounting for limb-darkening during the convolution. Horizontal solid lines indicate the median val￾ues, and the shaded regions represent the standard deviations. The dashed line marks the target value v sin i = 8 km s−1 , for spectra with Teff = 3000 K. The normalised kernel for a linear limb-darkening law in Equation B.9… view at source ↗
Figure 3
Figure 3. Figure 3: Best-fitting v sin i values as a function of wavelength for different oversampling factors, obtained without account￾ing for limb-darkening in the convolution process. Horizontal lines correspond to the median values. The spectra correspond to Teff = 3000 K and a target value of v sin i = 8 km s−1 . 600 650 700 750 800 850 900 Wavelength [nm] 7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 v sin i [ k m s 1 ] No limb-… view at source ↗
Figure 5
Figure 5. Figure 5: Normalized difference between input and fitted v sin i as a function of input v sin i and spectra’s Teff, for oversampled con￾volution (top panel) and numerical integration (bottom panel). 3.4. Numerical integration Carvalho & Johns-Krull (2023) developed a method to broaden spectra due to projected rotation, incorporating linear limb￾darkening via direct numerical integration. We find that this ap￾proach … view at source ↗
Figure 6
Figure 6. Figure 6: v sin i values obtained in this work using the oversam￾pled convolution method compared with literature measure￾ments. Newly determined v sin i values not previously available are shown in the shaded area at v sin i (literature) = 100 km s−1 . The solid line indicates the 1:1 relation, while the dashed lines correspond to a 10 % deviation. Grey dashed lines and the shaded area mark the 2 km s−1 limit of CA… view at source ↗
Figure 8
Figure 8. Figure 8: Histogram of the normalized difference between the v sin i value (> 2 km s−1 ) computed with oversampled convolu￾tion and the literature, excluding the outliers. The median is marked with a horizontal solid line. 10 100 vsini OC [kms 1 ] 10 100 v sin i NI [ k m s 1 ] 0 0.05 0.1 0.15 Normalized residual 0 20 40 60 Count Median = 0.0001 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Top panel: comparison between v sin i computed with numerical integration (NI) and oversampled convolution (OC). Dashed lines represent the 2 km s−1 limit, and diagonal lines mark the 1:1 relation ± 10 %. Bottom panel: histogram of the normalized residuals respect to the 1:1 relation for v sin i > 2 km s−1 . Median value represented by a vertical line. about 1–2 % were found for slow and intermediate rotat… view at source ↗
read the original abstract

Stellar rotation is closely linked to both age and magnetic activity. Through gyrochronology, it provides a means to estimate stellar ages and trace the evolution of planetary systems, and it is also crucial to constrain and correct stellar activity effects for robust exoplanet detection and characterisation. CARMENES is a dual-channel, high-resolution (R > 80000) spectrograph that has been highly successful in detecting exoplanets around M-dwarf stars using the radial-velocity technique, and it also enables precise measurements of the projected rotational velocity (vsini) from spectral line broadening. We present an oversampled convolution method incorporating a realistic limb-darkening model to determine vsini from CARMENES spectra by comparing observed spectra with that of a template star. The advantages over existing methods in the literature have been assessed using high-resolution synthetic spectra spanning effective temperatures of 2500-4000 K and projected rotational velocities of up to 50 km/s. Applied to 392 M dwarfs observed with CARMENES, our method yields vsini measurements (or upper limits at 2 km/s) with a median relative uncertainty of 6.8%, substantially smaller than the 15.4% reported in the literature. This work provides the largest uniform catalogue of vsini measurements for M dwarfs, including significantly updated values for several targets, along with 36 new targets.

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

2 major / 2 minor

Summary. The manuscript presents an oversampled convolution method incorporating a realistic limb-darkening model to measure projected rotational velocities (vsini) from CARMENES high-resolution spectra of M dwarfs. The technique is validated on synthetic spectra spanning Teff = 2500–4000 K and vsini ≤ 50 km/s, then applied to 392 real targets to produce a homogeneous catalogue yielding vsini values or 2 km/s upper limits with a median relative uncertainty of 6.8% (versus 15.4% in the literature), plus 36 new measurements and updates for several stars.

Significance. If the precision improvement and uniformity hold, the resulting catalogue would be a valuable resource for gyrochronology, stellar activity studies, and correction of activity-induced radial-velocity signals in exoplanet searches around M dwarfs. The large, uniformly processed sample size is a clear asset for the field.

major comments (2)
  1. [Synthetic spectra validation] Synthetic spectra validation (methods/results section): The tests use noise-free synthetic spectra and therefore omit telluric lines, finite SNR variations, instrumental broadening changes, template mismatches, and activity-induced line distortions present in actual CARMENES data. These omissions leave open the possibility that the reported 6.8% median relative uncertainty is optimistic; a direct test re-reducing the same real spectra with a standard (non-limb-darkened) kernel or comparison against independent vsini anchors is needed to substantiate the improvement claim.
  2. [Uncertainty derivation] Uncertainty derivation (methods section): The manuscript provides insufficient detail on how formal uncertainties are obtained from the template comparison, including error propagation, treatment of covariances with the limb-darkening coefficients, and the precise criterion used to set the 2 km/s upper limits. Without this information it is difficult to judge whether the quoted uncertainties are realistic or whether the factor-of-two improvement over literature values is robust.
minor comments (2)
  1. [Abstract] The abstract and text would benefit from an explicit statement of how 'relative uncertainty' is defined (e.g., σ_vsini/vsini) and how the literature comparison sample was selected and homogenized to ensure an apples-to-apples assessment.
  2. [Catalogue presentation] A supplementary table or figure summarizing the vsini distribution, uncertainty histogram, and direct comparison with literature values for overlapping targets would improve clarity and allow readers to assess the updates quantitatively.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and have revised the manuscript to incorporate clarifications and additional analyses where needed.

read point-by-point responses

  1. Referee: Synthetic spectra validation (methods/results section): The tests use noise-free synthetic spectra and therefore omit telluric lines, finite SNR variations, instrumental broadening changes, template mismatches, and activity-induced line distortions present in actual CARMENES data. These omissions leave open the possibility that the reported 6.8% median relative uncertainty is optimistic; a direct test re-reducing the same real spectra with a standard (non-limb-darkened) kernel or comparison against independent vsini anchors is needed to substantiate the improvement claim.

    Authors: We agree that the synthetic validation is idealized and does not capture all real-data complexities. The 6.8% median relative uncertainty is measured from the actual fits to the 392 CARMENES spectra, and the comparison to the literature 15.4% value is performed on overlapping targets. To directly address the concern, the revised manuscript includes a new subsection comparing our limb-darkening-aware results against a standard non-limb-darkened convolution applied to the same real spectra for a representative subset, as well as cross-matches to independent vsini values from the literature for common stars. These additions quantify the improvement under realistic conditions. revision: yes

  2. Referee: Uncertainty derivation (methods section): The manuscript provides insufficient detail on how formal uncertainties are obtained from the template comparison, including error propagation, treatment of covariances with the limb-darkening coefficients, and the precise criterion used to set the 2 km/s upper limits. Without this information it is difficult to judge whether the quoted uncertainties are realistic or whether the factor-of-two improvement over literature values is robust.

    Authors: We acknowledge the manuscript lacked sufficient detail on this point. The revised Methods section now contains an expanded subsection on uncertainty estimation. Formal uncertainties are obtained from the covariance matrix of the least-squares template fit; covariances with limb-darkening coefficients are accounted for by treating the coefficients as fixed (interpolated from Teff) or as nuisance parameters with Gaussian priors; the 2 km/s upper limit is set when the best-fit vsini is consistent with zero at the 1-sigma level or falls below the approximate instrumental resolution limit. A short discussion of error propagation has also been added. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents a new oversampled convolution method with limb-darkening for vsini extraction from CARMENES spectra, validates recovery on independent high-resolution synthetic spectra (Teff 2500-4000 K, vsini up to 50 km/s), and applies the fitted model to 392 real observed spectra to produce a catalogue. Reported uncertainties are formal fit uncertainties on the observed data; the median 6.8% relative uncertainty and comparison to the external literature value of 15.4% do not reduce by construction to any fitted parameter or self-citation chain within the paper. No self-definitional steps, fitted-input predictions, or load-bearing self-citations appear in the derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard stellar spectroscopy assumptions plus a specific implementation choice for convolution and limb darkening; no new entities are postulated.

free parameters (1)
  • limb-darkening coefficients
    The realistic limb-darkening model requires coefficients likely taken from stellar atmosphere tables or adjusted for the M-dwarf temperature range.
axioms (1)
  • domain assumption Spectral line broadening is dominated by rotation and can be accurately modeled via convolution with a rotation kernel that includes limb darkening.
    This is the foundational premise of the oversampled convolution method described.

pith-pipeline@v0.9.0 · 5682 in / 1444 out tokens · 84084 ms · 2026-05-10T09:34:19.427663+00:00 · methodology

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Reference graph

Works this paper leans on

6 extracted references

  1. [1]

    R., Jenkins, J

    Barnes, J. R., Jenkins, J. S., Jones, H. R. A., et al. 2014, Monthly Notices of the Royal Astronomical Society, 439, 3094 Baroch, D., Morales, J. C., Ribas, I., et al. 2020, A&A, 641, A69 Bischoff, R., Mugrauer, M., Torres, G., et al. 2020, Astronomische Nachrichten, 341, 908 Bonfils, X., Delfosse, X., Udry, S., et al. 2013, A&A, 549, A109 Browning, M. K....

    2014

  2. [2]

    Most commonly used limb-darkening laws can be written as linear combinations of powers ofµ: I(µ)= X γ cγµγ.(B.5) Replacing the above intensity profile into Equation B.4, the ker- nel becomes: K(x)= X γ cγ Z a −a a2 −y 2 γ 2 dy,a= √ 1−x 2.(B.6) Applying the substitutiony=acost: K(x)= X γ cγaγ+1 Z π 0 (sint )γ+1 dt,a= √ 1−x 2.(B.7) In absence of limb-darken...

    1921

  3. [3]

    C.3: Normalized difference between input and fittedvsini as a function of the inputvsinifor different limb-darkening laws

    Teff = 4000 K Linear Four-coefficient Power-2 Quadratic Fig. C.3: Normalized difference between input and fittedvsini as a function of the inputvsinifor different limb-darkening laws. 10 vsini this work [kms 1] 10vsini literature [kms 1] Passegger et al. (2020) Mas-Buitrago et al. (2024) Fig. E.1: Comparison of ourvsinivalues with the results from Passegg...

    2020

  4. [4]

    E.2: The rms of the residuals between target spectrum and template rotationally broadened using bothvsinifrom this work and Mas-Buitrago et al

    Fig. E.2: The rms of the residuals between target spectrum and template rotationally broadened using bothvsinifrom this work and Mas-Buitrago et al. (2024). ically larger, particularly for slow rotators. Forvsiniabove 10 km s−1, the differences decrease. Both studies also report sys- tematically highervsinivalues than those derived by Reiners et al. (2018...

    2024

  5. [5]

    The rms of the residuals is shown in Fig

    rotationally broadened using both sets of vsinivalues. The rms of the residuals is shown in Fig. E.2. In general, ourvsinimeasurements yield smaller rms values, par- ticularly for slow rotators. This indicates that our results re- produce the observed broadening of the spectral lines in the CARMENES VIS spectra more accurately. Appendix F: Spectrum andvsi...

    2009

  6. [6]

    F.1: Top: chunk of the CARMENES-VIS co-added spec- trum of J14155+046 compared to the spectrum of J03133+047, without and with 6.8 km s−1 rotational broadening (Jenkins et al

    568.1 568.3 568.5 568.7 568.9 569.1 Wavelength [nm] 0.25 0.00 0.25 Residuals rms = 0.043 rms = 0.086 Fig. F.1: Top: chunk of the CARMENES-VIS co-added spec- trum of J14155+046 compared to the spectrum of J03133+047, without and with 6.8 km s−1 rotational broadening (Jenkins et al. 2009). Bottom: residuals with respect to J14155+046. Article number, page 12 of 12

    2009