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arxiv: 2605.22615 · v1 · pith:LNR6RTC5new · submitted 2026-05-21 · 🌌 astro-ph.SR

Decoding the Radial Velocity Signatures of Solar Faculae with 3D MHD Simulations

Florian Kr\"oll , Sowmya Krishnamurthy , Alexander Shapiro , Andrew Collier Cameron , Veronika Witzke , Sami Khan Solanki , Ignasi Ribas , Sergiy Shelyag
show 3 more authors
Greg Kopp Nina Elisabeth N\`emec Sophie Stucki
This is my paper

Pith reviewed 2026-05-22 03:28 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar faculaeradial velocityMHD simulationsconvective blueshiftcenter-to-limb variationstellar activitySun-like starsphotospheric flows
0
0 comments X

The pith

Solar faculae produce a redshift near disk center but switch to blueshift beyond 60 degrees from center.

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

The paper models the radial velocity signal from a transiting facular patch on the Sun using 3D radiative MHD simulations. It shows that magnetic fields suppress the convective blueshift and create a redshift when the facula is near disk center. At larger heliocentric angles the effect reverses to a blueshift because magnetic fields alter horizontal flows and how those flows are seen from Earth. The reversal produces a complex RV curve during transit with a phase lag between the signal peak and the facula's central meridian crossing. The strength of the effect also changes with the chosen spectral line, unlike the wavelength-independent signal from a planet.

Core claim

Faculae inhibit convective blueshift near disk centre and produce a relative redshift, but at heliocentric angles greater than about 60° the same magnetic fields affect horizontal flows and their visibility to produce a relative blueshift instead. Combined with solar rotation, this centre-to-limb dependence yields a complex RV profile during facular transit and a phase lag between the RV maximum and central meridian crossing. The facular signal varies strongly with spectral line, in contrast to stellar reflex motion.

What carries the argument

Center-to-limb variation of facular radial velocity extracted from MURaM 3D MHD photospheric simulations and MPS-ATLAS spectral synthesis for a transiting facular patch.

If this is right

  • The facular RV maximum occurs after the feature crosses the central meridian because the blueshift contribution grows toward the limb.
  • The amplitude and detailed shape of the facular RV signal change markedly with the spectral line used for the measurement.
  • Stellar activity corrections for Sun-like stars must incorporate this position-dependent facular contribution to avoid systematic errors in radial velocity time series.

Where Pith is reading between the lines

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

  • The phase lag between RV peak and central meridian crossing could help distinguish facular signals from planetary orbits in long-term monitoring data.
  • Multi-line observations might reduce the impact of facular noise on precision radial velocity measurements of Sun-like stars.
  • The same simulation approach could be used to predict radial velocity contributions from other magnetic structures such as network or plage.

Load-bearing premise

The chosen facular patch and MURaM simulation parameters capture the real center-to-limb radial velocity behavior of solar faculae without major numerical artifacts.

What would settle it

Measure the radial velocity time series of the Sun while a tracked facular region crosses from center to limb and test whether the signal reverses to blueshift beyond 60 degrees with a phase lag matching the simulated transit profile.

Figures

Figures reproduced from arXiv: 2605.22615 by Alexander Shapiro, Andrew Collier Cameron, Florian Kr\"oll, Greg Kopp, Ignasi Ribas, Nina Elisabeth N\`emec, Sami Khan Solanki, Sergiy Shelyag, Sophie Stucki, Sowmya Krishnamurthy, Veronika Witzke.

Figure 1
Figure 1. Figure 1: Comparison of the quiet Sun (QS; solid) and faculae (dashed) intensity spectra for the representative Fe I λ4390 line (Table A1 in Appendix A). Panel (a): spectra at four disk positions going from disk centre (µ = 1) towards the limb (µ = 0.1). The solid and dashed vertical lines denote the position of the line centre of gravity (COG) for QS and faculae profiles, respectively. Panels (b)–(e): line profiles… view at source ↗
Figure 2
Figure 2. Figure 2: A snapshot from our equatorial facular transit setup. It shows a projected solar disk with a circular patch of faculae (having a radius of 15◦ , represented in yellow shades) located at −35◦ longitude. The colour scales indicate µ values. notation ‘∆RV’ for differences between two model scenarios (e.g. rotating minus non-rotating). Positive RV values correspond to redshifts (receding motions), whereas nega… view at source ↗
Figure 3
Figure 3. Figure 3: Disk-integrated RV signals induced by a transiting facular patch, as seen in five representative Fe I and Fe II spectral lines (see Tables A1 and A2 for line parameters). The RV signals from the ‘rotating case’ are plotted as a function of the longitude of the centre of the facular patch. The longitude range extends to ±105◦ (i.e., ±(90◦ + 15◦ )) so the 15◦ -radius circular patch is initially just beyond t… view at source ↗
Figure 4
Figure 4. Figure 4: Decomposition of the facular transit RV profile for the Fe I λ4390 line. Panel (a): RV profile in the ‘rotating case’ (green, marker: diamonds) is compared to the profile in the ‘non-rotating case’ (red, marker: circles). The green curve is the same as the black solid line in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic illustration of how faculae and solar rotation modify a spectral line profile (line changes are exaggerated for clarity). Panels (a)–(d) show line profiles in the absence of solar rotation, while panels (e)–(h) include rotation. From top to bottom, the rows correspond to: QS only, a facular patch at disk centre, a facular patch on the approaching hemisphere, and a facular patch on the receding he… view at source ↗
Figure 6
Figure 6. Figure 6: RV signal induced by facular suppression of CB as a function of µ for the Fe I λ4390 line. RV due to LOS Doppler shifts arising only from vertical velocities (magenta), only from horizontal velocities (orange), and both vertical and horizontal convective velocities (red). All RVs are computed from raw µ-dependent facular spectra, using the corresponding QS spectrum as the reference. experiment returns subs… view at source ↗
Figure 7
Figure 7. Figure 7: Cartoon illustrating how surface corrugation affects the flux-weighted RV as a function of µ in quiet Sun and faculae. Panels (a) and (b) show the QS case at disk centre (µ = 1) and for an inclined view (µ = 0.5), respectively. Panels (c) and (d) show the corresponding facular cases with strong magnetic concentrations in intergranular lanes (grey field lines) and a Wilson depression. Granules are shaded or… view at source ↗
Figure 8
Figure 8. Figure 8: Facular transit RV profiles for 60 perfectly isolated (blend-free) Fe I (red shades) and Fe II (blue shades) lines. Panel (a): rotating case, panel (b): non-rotating case, and panel (c): difference between the rotating and non-rotating cases, highlighting the line-dependent rotation–faculae coupling (so that it is not a pure ‘rotation-only’ signal; see Section 3.2). The RV profiles are colour coded accordi… view at source ↗
read the original abstract

We model the solar radial velocity (RV) signal induced by faculae, the dominant contributor to RV variability in Sun-like stars. We use a representative case of a facular patch transiting the visible solar disk as the Sun rotates to disentangle various physical effects contributing to the RV signal. Our approach is based on 3D radiative magnetohydrodynamic (MHD) simulations of the solar photosphere and upper convection zone with the MURaM code and spectral synthesis with the MPS-ATLAS code. We show that the faculae-induced RV strongly depends on the facular position on the solar disk. Near disk centre, facular magnetic fields inhibit the convective blueshift and thus produce a relative redshift of the solar spectrum. Surprisingly, when located closer to the limb, namely at heliocentric angles greater than about $60^\circ$, faculae produce a relative blueshift. This transition from redshift to blueshift is caused by the effect of magnetic fields on horizontal flows, which dominate the signal near the limb, and on the visibility of these flows. In combination with solar rotation, this centre-to-limb dependence of the facular effect leads to a complex RV profile during the facular transit and, in particular, to a phase lag between the maximum of the RV signal and the facular crossing of the central meridian. We further show that, in contrast to stellar reflex motion, the facular signal strongly depends on the spectral line in which it is measured.

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 models the radial velocity (RV) signal induced by a transiting solar facular patch using 3D radiative MHD simulations with the MURaM code and spectral synthesis with MPS-ATLAS. It claims that faculae produce a relative redshift near disk center by inhibiting convective blueshift, but a relative blueshift at heliocentric angles greater than about 60° due to the influence of magnetic fields on horizontal flows and their visibility; this center-to-limb dependence, combined with solar rotation, produces a complex RV profile during transit with a phase lag between RV maximum and central-meridian crossing, and the signal is strongly line-dependent unlike stellar reflex motion.

Significance. If the center-to-limb sign reversal and resulting phase lag hold, the work supplies a physically grounded, forward-model explanation for the dominant stellar-activity contribution to RV variability in Sun-like stars. This is directly relevant to exoplanet detection and could guide more accurate activity mitigation strategies. The use of self-consistent 3D MHD plus spectral synthesis on a representative facular configuration is a clear methodological strength.

major comments (2)
  1. [Simulation setup and Results sections] The central claim of a redshift-to-blueshift transition at heliocentric angles ≳60° and the consequent complex RV profile rest on results from a single representative MURaM facular patch. The horizontal-flow suppression and visibility effects that dominate the limb signal are sensitive to magnetic-field strength, geometry, box size, and boundary conditions; without additional runs exploring these parameters, it is unclear whether the reported transition angle and phase lag generalize to actual solar faculae or are specific to the chosen setup.
  2. [Spectral synthesis and line-dependence discussion] The manuscript states that the facular RV signal 'strongly depends on the spectral line' but does not quantify the line-to-line differences or demonstrate that the 60° transition angle itself is robust across lines. If the transition angle shifts with line formation height or depth, the predicted phase lag would change, weakening the claim that the behavior is a general property of faculae.
minor comments (2)
  1. [Abstract and §3] The abstract and main text refer to 'about 60°' without stating the precise angle at which the sign change occurs in the simulations or how it was measured from the extracted RV curves.
  2. [Figures] Figure captions and axis labels should explicitly indicate the heliocentric angles corresponding to each RV time series shown during the transit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential importance of this work for understanding stellar activity signals in radial velocity measurements. We address each major comment below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Simulation setup and Results sections] The central claim of a redshift-to-blueshift transition at heliocentric angles ≳60° and the consequent complex RV profile rest on results from a single representative MURaM facular patch. The horizontal-flow suppression and visibility effects that dominate the limb signal are sensitive to magnetic-field strength, geometry, box size, and boundary conditions; without additional runs exploring these parameters, it is unclear whether the reported transition angle and phase lag generalize to actual solar faculae or are specific to the chosen setup.

    Authors: We acknowledge that the analysis is based on a single representative facular patch. This setup was selected because it reproduces observed facular properties in terms of magnetic field strength and spatial scale, allowing a focused examination of the physical mechanisms. The redshift-to-blueshift transition stems from well-established effects: magnetic inhibition of convection near disk center and the increasing contribution of magnetically modified horizontal flows whose visibility changes with heliocentric angle. To address the concern, we will add a paragraph in the revised manuscript that justifies the chosen parameters by reference to solar observations and prior MURaM studies, explicitly discusses possible sensitivities, and identifies broader parameter exploration as future work. revision: partial

  2. Referee: [Spectral synthesis and line-dependence discussion] The manuscript states that the facular RV signal 'strongly depends on the spectral line' but does not quantify the line-to-line differences or demonstrate that the 60° transition angle itself is robust across lines. If the transition angle shifts with line formation height or depth, the predicted phase lag would change, weakening the claim that the behavior is a general property of faculae.

    Authors: We agree that a quantitative demonstration of line-to-line behavior would strengthen the manuscript. In the revised version we will expand the spectral synthesis discussion to include explicit comparisons of the RV time series for several lines spanning a range of formation heights. These additions will show the amplitude variations and confirm that the center-to-limb transition angle remains near 60° across the lines examined, thereby supporting the generality of the predicted phase lag. We will also explain the origin of the line dependence in terms of the height-dependent velocity and magnetic field structure within the facular atmosphere. revision: yes

Circularity Check

0 steps flagged

No circularity: forward-model outputs from standard MHD and spectral synthesis codes

full rationale

The paper's central results—the center-to-limb RV dependence, redshift-to-blueshift transition near 60°, and resulting phase lag—are obtained by running MURaM 3D radiative MHD simulations of a representative facular patch followed by MPS-ATLAS spectral synthesis. These are direct numerical outputs under stated boundary conditions and magnetic configurations; they do not reduce to any fitted parameter, self-defined quantity, or load-bearing self-citation. The derivation chain consists of standard forward modeling steps whose outputs are independent of the target RV observations they are later compared against.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The modeling rests on the standard equations of radiative magnetohydrodynamics and the assumption that the chosen facular patch is representative; no new free parameters are introduced to fit the RV curves themselves.

axioms (2)
  • domain assumption The MURaM code accurately solves the MHD equations and radiative transfer in the solar photosphere and upper convection zone for the chosen resolution and boundary conditions.
    Invoked implicitly when the authors state that the simulations capture the relevant physical effects.
  • domain assumption The MPS-ATLAS spectral synthesis produces realistic line profiles from the simulated atmospheres.
    Required to translate the 3D temperature and velocity fields into observable radial-velocity shifts.

pith-pipeline@v0.9.0 · 5844 in / 1536 out tokens · 39682 ms · 2026-05-22T03:28:39.752061+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Near disk centre, facular magnetic fields inhibit the convective blueshift and thus produce a relative redshift... at heliocentric angles greater than about 60°, faculae produce a relative blueshift. This transition... is caused by the effect of magnetic fields on horizontal flows

  • IndisputableMonolith/Foundation/ArithmeticFromLogic.lean LogicNat.equivNat unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    the facular-transit RV profile is symmetric about its central meridian crossing. Including rotational Doppler shifts produces an asymmetric RV curve and a phase lag

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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