arXiv subjects

T. Roudier

Publications and source records attributed to T. Roudier.

At least 19 recordsLinked to original sources

arXiv2026

Application of the coherent structure tracking to solar Doppler maps to determine horizontal velocity fields at the Sun's surface

Coherent Structure Tracking (CST) is a technique for determining the solar surface horizontal flows at high spatial and temporal resolution by tracking the proper motion of granules. CST has been traditionally applied to solar intensity images in the continuum, which clearly depict the granular patterns. However, solar granulation is also visible in the Dopplergrams. We aim to show that CST can be applied to solar Dopplergrams to derive the solar surface horizontal velocity fields with the same level of confidence as those determined by CST on intensity images. For this purpose, we apply the CST to continuum intensity images and Dopplergrams obtained from SDO/HMI and also from a numerical simulation of granulation. We then compare the resulting solar surface horizontal velocity fields and their derivatives for different time windows. Pearson's linear global correlation coefficient (GCC) between the horizontal velocity fields determined from CST on Doppler and on intensity images of a relatively less active Sun is about 73% for a 30 min time average, while the corresponding local correlation coefficient (LCC) near the disk center is about 80%. For the divergence of the horizontal velocity field, we obtain a GCC of 72% and a near disk center LCC of 84%. The curl of the horizontal velocity field being more noisy exhibits somewhat reduced GCC and LCC. These coefficients increase with increasing time window. A similar trend is exhibited by Spearman's and Kendall's rank-order correlation coefficients, although they are somewhat smaller in value. The different correlation coefficients slightly decrease for magnetically more active Sun with sunspots or emerging pores in a plage region. A high correlation is obtained between the horizontal flows derived by applying CST to intensity and vertical velocity maps from a numerical simulation.

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arXiv2024

Automated detection of exploding granules with SDO/HMI data

Exploding granules on the solar surface play a major role in the dynamics of the outer part of the convection zone, especially in the diffusion of the magnetic field. We aim to develop an automated procedure able to investigate the location and evolution of exploding granules over the solar surface and to get rid of visual detection. We used sequences of observations of intensity and Doppler velocity, as well as magnetograms, provided by the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory. The automated detection of the exploding granules was performed by applying criteria on either three or two parameters: the granule area, the amplitude of the velocity field divergence, and, at the disc centre, the radial Doppler velocity. Our analyses show that granule area and divergence amplitudes are sufficient to detect the largest exploding granules; thus, we can automatically detect them, not only at the disc centre, but across the whole solar surface. Using a 24-hour-long observation sequence, we have demonstrated the important contribution of the most dynamic exploding granules in the diffusion of the magnetic field in the quiet Sun. Indeed, we have shown that the most intense exploding granules are sufficient to build a large part of the photospheric network. We have also applied our procedure on Hinode observations to locate the exploding granules relative to trees of fragmenting granules (TFGs). We conclude that, during a first phase of about 300 minutes after the birth of a TFG, exploding granules are preferentially located on its edge. Finally, we also show that the distribution of exploding granules is homogeneous (at the level of our measurement errors) over the solar surface without a significant dependency on latitude.

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arXiv2024

Observational characterisation of large-scale transport and horizontal turbulent diffusivity in the quiet Sun

The Sun is a magnetic star, and the only spatio-temporally resolved astrophysical system displaying turbulent MHD thermal convection. This makes it a privileged object of study to understand fluid turbulence in extreme regimes and its interactions with magnetic fields. Global analyses of high-resolution solar observations provided by the NASA Solar Dynamics Observatory can shed light on the physical processes underlying large-scale emergent phenomena such as the solar dynamo cycle. Combining a Coherent Structure Tracking reconstruction of photospheric flows, based on photometric data, and a statistical analysis of virtual passive tracers trajectories advected by these flows, we characterise one of the most important such processes, turbulent diffusion, over an unprecedentedly long monitoring period of 6 consecutive days of a significant fraction of the solar disc. We first confirm, and provide a new global view of the emergence of a remarkable dynamical pattern of Lagrangian Coherent Structures tiling the entire surface. These structures act as transport barriers on the time and spatial scale of supergranulation and, by transiently accumulating particles and magnetic fields, regulate large-scale turbulent surface diffusion. We then further statistically characterise the turbulent transport regime using two different methods, and obtain an effective horizontal turbulent diffusivity $D=2-3\times10^8~\mathrm{m}^2~\mathrm{s}^{-1}$ on the longest timescales probed. This estimate is consistent with the transport coefficients required in large-scale mean-field solar dynamo models, and is in broad agreement with the results of global simulations. Our analysis may also have implications for understanding the connections between solar-surface, coronal and solar-wind dynamics, and provides valuable lessons to characterise turbulent transport in other, unresolved turbulent astrophysical systems.

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arXiv2023

Texture of average solar photospheric flows and the donut-like pattern

Detailed knowledge of surface dynamics is one of the key points in understanding magnetic solar activity. The motions of the solar surface, to which we have direct access via the observations, tell us about the interaction between the emerging magnetic field and the turbulent fields. The flows computed with the coherent structure tracking (CST) technique on the whole surface of the Sun allow for the texture of the velocity modulus to be analyzed and for one to locate the largest horizontal flows and determine their organization. The velocity modulus maps show structures more or less circular and closedwhich are visible at all latitudes; here they are referred to as donuts. They reflect the most active convective cells associated with supergranulation. These annular flows are not necessarily joined as would seem to indicate the divergence maps. The donuts have identical properties (amplitude, shape, inclination, etc.) regardless of their position on the Sun. The kinematic simulation of the donuts' outflow applied to passive scalar (corks) indicates the preponderant action of the selected donuts which are, from our analysis, one of the major actors for the magnetic field diffusion on the quiet Sun. The absence of donuts in the magnetized areas (plages) indicates the action of the magnetic field on the strongest supergranular flows and thus modifies the diffusion of the magnetic field in that location. The detection of the donuts is a way to locate in the quiet Sun the vortex and the link with the jet, blinkers, coronal bright points (campfires), or other physical structures. Likewise, the study of the influence of donuts on the evolution of active events, such as the destruction of sunspots, filament eruptions, and their influences on upper layers via spicules and jets, could be done more efficiently via the detection of that structures.

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arXiv2021

Changes in granulation scales over the solar cycle seen with SDO/HMI and Hinode/SOT

The Sun is the only star where the superficial turbulent convection can be observed at very high spatial resolution. The Solar Dynamics Observatory (SDO) has continuously observed the full Sun from space with multi-wavelength filters since July 2010. In particular, the Helioseismic and Magnetic Imager (HMI) instrument takes high-cadence frames (45 seconds) of continuum intensity in which solar granulation is visible. We aimed to follow the evolution of the solar granules over an activity cycle and look for changes in their spatial properties. We investigated the density of granules and their mean area derived directly from the segmentation of deconvolved images from SDO/HMI. To perform the segmentation, we define granules as convex elements of images. We measured an approximately 2% variation in the density and the mean area of granules over the cycle, the density of granules being greater at solar maximum with a smaller granule mean area. The maximum density appears to be delayed by about one year compared to classical activity indicators, such as the sunspot number. We complemented this study with high-spatial-resolution observations obtained with Hinode/SOTBFI (Solar Optical Telescope Broadband Filter Imager), which are consistent with our results. The observed variations in solar granulation at the disc centre reveal a direct insight into the change in the physical properties that occur in the upper convective zone during a solar cycle. These variations can be due to interactions between convection and magnetic fields, either at the global scale or, locally, at the granulation scale.

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arXiv2021

Photospheric downflows observed with SDO/HMI, HINODE, and an MHD simulation

Downflows on the solar surface are suspected to play a major role in the dynamics of the convection zone. We investigate the existence of the long-lasting downflows whose effects influence the interior of the Sun and the outer layers. We study the sets of Dopplergrams and magnetograms observed with SDO and Hinode spacecrafts and a MHD simulation. All of the aligned sequences, which were corrected from the satellite motions and tracked with the differential rotation, were used to detect the long-lasting downflows in the quiet-Sun at the disc centre. To learn about the structure of the flows below the solar surface, the time-distance local helioseismology was used. The inspection of the 3D data cube (x, y, t) of the 24-hour Doppler sequence allowed us to detect 13 persistent downflows. Their lifetimes lie in the range between 3.5 and 20 hours with sizes between 2" and 3" and speeds between -0.25 and -0.72 km/s. These persistent downflows are always filled with the magnetic field with an amplitude of up to 600 G. The helioseismic inversion allows us to describe the persistent downflows and compare them to the other (non-persistent) downflows in the field of view. The persistent downflows seem to penetrate much deeper and, in the case of a well-formed vortex, the vorticity keeps its integrity to the depth of about 5 Mm. In the MHD simulation, only sub-arcsecond downflows are detected with no evidence of a vortex comparable in size to observations at the surface of the Sun. The long temporal sequences from the space-borne allow us to show the existence of long-persistent downflows together with the magnetic field. They penetrate inside the Sun but are also connected with the anchoring of coronal loops in the photosphere, indicating a link between downflows and the coronal activity. A link suggests that EUV cyclones over the quiet Sun could be an effective way to heat the corona.

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arXiv2021

Pollux: A weak dynamo-driven dipolar magnetic field and implications for its probable planet

Context: Pollux is considered as an archetype of a giant star hosting a planet. We then discovered a weak magnetic field at its surface using spectropolarimetry. Aims and Methods: We followed up our investigations on Pollux first using ESPaDOnS at CFHT and then Narval at TBL to obtain Stokes I and Stokes V spectra to study their variations for a duration of 4.25 years, that is, for more than two periods of about 590 d of the RV variations. We used the least-squares deconvolution (LSD) profiles to measure the longitudinal magnetic field and to perform a Zeeman Doppler imaging (ZDI) investigation. Results: The longitudinal magnetic field of Pollux is found to vary with a sinusoidal behavior and a period similar to that of the RV variations. From the ZDI investigation a rotation period of Pollux is determined to be equal to 660+/-15 days and possibly different than the period of variations of the RV. As to the magnetic topology, the poloidal component is dominant and almost purely dipolar with an inclination of 10.5° of the dipole with respect to the rotation axis. The mean strength of the surface magnetic field is 0.44 G. Conclusions: As to the origin of the magnetic field of Pollux, we favor the hypothesis that it is maintained through contemporaneous dynamo action. Pollux appears as the representative of a class of slowly rotating and weakly magnetic G-K red giants. To explain the sinusoidal RV variations of Pollux, two scenarios are proposed. If the RV period is different from the rotation period, the observed periodic RV variations are due to the hosted planet and the contribution of Pollux magnetic activity is not significantly detected. In the peculiar case in which the two periods are equal, we cannot discard the possibility that the activity of Pollux could explain the total RV variations and that the planet hypothesis would appear unnecessary.

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arXiv2020

Evolution of exploding granules from coordinated observations by THEMIS, IRIS, SDO/HMI, and HINODE, and a simulation

Exploding granules constitute the strongest horizontal flows on the quiet Sun and contribute to the structure of the surface horizontal velocity fields which build the large-scale organization of the discrete magnetic field. In this work we explore exploding granule expansion through the observations of the ground-based THEMIS telescope, IRIS, SDO, and the Hinode space-borne instruments, and finally with the magnetohydrodynamics simulation. We evaluate the detection and the expansion of exploding granules at several wavelengths and at various spatial and temporal resolutions. To analyze the different temporal sequences, two methods of image segmentation are applied to select the granules. The first allows us to follow individually the exploding granules observed simultaneously by THEMIS, IRIS, and SDO. The second uses long time independent sequences from THEMIS, IRIS, SDO, Hinode, and a simulation. In the first method (called manual) the segmentation isolates the cell of the granules (bright granules and intergranular parts), while in the second method (called statistical) only the bright part of the granules are isolated. The results obtained with simultaneous or distinct temporal observations using the two methods of segmentation are in good agreement. The granule area evolves linearly with an expansion velocity that decreases with the radius. A rapid decrease in the velocity expansion in the first two minutes is observed. The detection and measurement of the dynamics of the explosive granules can be performed from ground- and space-based instruments. Our work reveals the usefulness of SDO data, with low spatial resolution, to study the dynamics of the exploding granules all over the solar surface

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arXiv2019

Link between trees of fragmenting granules and deep downflows in MHD simulation

Trees of fragmenting granules (TFG) and associated flows are suspected to playa major role in the formation of the network in the quiet Sun. We investigate the counterparts, in terms of dynamics, of surface structures detectable by high resolution observations in deeper layers up to 15 Mm, which are only available from numerical simulations. The first aim is to demonstrate that TFG can be evidenced either from surface intensitites, vertical (Vz), or Doppler (Vdop) velocities. The second is to show that horizontal flows, which are derived from intensities or Vz/Vdop flows, are in good agreement, and that this is the case for observations and numerical simulations. The third objective is to apply this new Vz-based method to a 3D simulation to probe relationships between horizontal surface flows, TFG, and deep vertical motions. The TFG were detected after oscillation filtering of intensities or Vz/Vdop flows, using a segmentation and labelling technique. Surface horizontal flows were derived from local correlation tracking (LCT) and from intensities or Vz/Vdop flows. These methods were applied to Hinode observations, 2D surface results of a first simulation, and 3D Vz data of a second simulation. We find that TFG and horizontal surface flows (provided by the LCT) can be detected either from intensities or Vz/Vdop component, for high resolution observations and numerical simulations. We apply this method to a 3D run providing the Vz component in depth. This reveals a close relationship between surface TFG (5 Mm mesoscale) and vertical downflows 5 Mm below the surface. We suggest that the dynamics of TFG form larger scales (the 15-20 Mm supergranulation) associated with 15 Mm downflowing cells below the surface. The TFG and associated surface flows seem to be essential to understanding the formation and evolution of the network at the meso and supergranular scale.

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arXiv2018

Horizontal photospheric flows trigger a filament eruption

A large filament composed principally of two sections erupted sequentially in the southern hemisphere on January 26 2016. The central, thick part of the northern section was first lifted up and lead to the eruption of the full filament. This event was observed in H-alpha with GONG and CLIMSO, and in ultraviolet (UV) with the AIA/SDO imager. The aim of the paper is to relate the photospheric motions below the filament and its environment to the eruption of the filament. An analysis of the photospheric motions using SDO/HMI continuum images with the coherent structure tracking (CST) algorithm developed to track granules, as well as large-scale photospheric flows, has been performed. The supergranule pattern is clearly visible outside the filament channel but difficult to detect inside because the modulus of the vector velocity is reduced in the filament channel, mainly in the magnetized areas. The horizontal photospheric flows are strong on the west side of the filament channel and oriented towards the filament. The ends of the filament sections are found in areas of concentration of corks. Whirled flows are found locally around the feet. The strong horizontal flows with an opposite direction to the differential rotation create strong shear and convergence along the magnetic polarity inversion line (PIL) in the filament channel. The filament has been destabilized by the converging flows, which initiate an ascent of the middle section of the filament until the filament reaches the critical height of the torus instability inducing, consequently, the eruption. The "n" decay index indicated an altitude of 60 Mm for the critical height. It is conjectured that the convergence along the PIL is due to the large-scale size cells of convection that transport the magnetic field to their borders.

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arXiv2018

Dynamics of Trees of Fragmenting Granules in the Quiet Sun: Hinode/SOT Observations Compared to Numerical Simulation

We compare horizontal velocities, vertical magnetic fields and evolution of trees of fragmenting granules (TFG, also named families of granules) derived in the quiet Sun at disk center from observations at solar minimum and maximum of the Solar Optical Telescope (SOT on board Hinode) and results of a recent 3D numerical simulation of the magneto-convection. We used 24-hour sequences of a 2D field of view (FOV) with high spatial and temporal resolution recorded by the SOT Broad band Filter Imager (BFI) and Narrow band Filter Imager (NFI). TFG were evidenced by segmentation and labeling of continuum intensities. Horizontal velocities were obtained from local correlation tracking (LCT) of proper motions of granules. Stokes V provided a proxy of the qline of sight magnetic field (BLOS). The MHD simulation (performed independently) produced granulation intensities, velocity and magnetic field vectors. We discovered that TFG also form in the simulation and show that it is able to reproduce the main properties of solar TFG: lifetime and size, associated horizontal motions, corks and diffusive index are close to observations. Largest (but not numerous) families are related in both cases to strongest flows and could play a major role in supergranule and magnetic network formation. We found that observations do not reveal any significant variation of TFG between solar minimum and maximum.

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arXiv2017

Supergranulation and multiscale flows in the solar photosphere: Global observations vs. a theory of anisotropic turbulent convection

The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly anisotropic, self-similar, nonlinear, buoyant dynamical regime. While the theory remains speculative at this stage, it lends itself to quantitative comparisons with future high-resolution acoustic tomography of subsurface layers and advanced numerical models. Such a validation exercise may also lead to new insights into the asymptotic dynamical regimes in which other, unresolved turbulent anisotropic astrophysical fluid systems supporting waves or instabilities operate.

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arXiv2014

The Magnetic Fields at the Surface of Active Single G-K Giants

We investigate the magnetic field at the surface of 48 red giants selected as promising for detection of Stokes V Zeeman signatures in their spectral lines. We use the spectropolarimeters Narval and ESPaDOnS to detect circular polarization within the photospheric absorption lines of our targets and use the least-squares deconvolution (LSD) method. We also measure the classical S-index activity indicator, and the stellar radial velocity. To infer the evolutionary status of our giants and to interpret our results, we use state-of-the-art stellar evolutionary models with predictions of convective turnover times. We unambiguously detect magnetic fields via Zeeman signatures in 29 of the 48 red giants in our sample. Zeeman signatures are found in all but one of the 24 red giants exhibiting signs of activity, as well as 6 out of 17 bright giant stars.The majority of the magnetically detected giants are either in the first dredge up phase or at the beginning of core He burning, i.e. phases when the convective turnover time is at a maximum: this corresponds to a 'magnetic strip' for red giants in the Hertzsprung-Russell diagram. A close study of the 16 giants with known rotational periods shows that the measured magnetic field strength is tightly correlated with the rotational properties, namely to the rotational period and to the Rossby number Ro. Our results show that the magnetic fields of these giants are produced by a dynamo. Four stars for which the magnetic field is measured to be outstandingly strong with respect to that expected from the rotational period/magnetic field relation or their evolutionary status are interpreted as being probable descendants of magnetic Ap stars. In addition to the weak-field giant Pollux, 4 bright giants (Aldebaran, Alphard, Arcturus, eta Psc) are detected with magnetic field strength at the sub-gauss level.

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arXiv2014

The Role of Subsurface Flows in Solar Surface Convection: Modeling the Spectrum of Supergranular and Larger Scale Flows

We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolomogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large scale radiative hydrodynamic simulations. We reach two primary conclusions: 1. The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. 2. Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large scale modes in the deep layers are artificially reduced. Since the large scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small scale convective correlations are maintained through the bulk of the solar convection zone.

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arXiv2012

Acoustic Events in the Solar Atmosphere from Hinode/SOT NFI observations

We investigate the properties of acoustic events (AEs), defined as spatially concentrated and short duration energy flux, in the quiet sun using observations of a 2D field of view (FOV) with high spatial and temporal resolution provided by the Solar Optical Telescope (SOT) onboard \textit{Hinode}. Line profiles of Fe \textsc{i} 557.6 nm were recorded by the Narrow band Filter Imager (NFI) on a $82" \times 82"$ FOV during 75 min with a time step of 28.75 s and 0.08$"$ pixel size. Vertical velocities were computed at three atmospheric levels (80, 130 and 180 km) using the bisector technique allowing the determination of energy flux in the range 3-10 mHz using two complementary methods (Hilbert transform and Fourier power spectra). Horizontal velocities were computed using local correlation tracking (LCT) of continuum intensities providing divergences. The net energy flux is upward. In the range 3-10 mHz, a full FOV space and time averaged flux of 2700 W m$^{-2}$ (lower layer 80-130 km) and 2000 W m$^{-2}$ (upper layer 130-180 km) is concentrated in less than 1% of the solar surface in the form of narrow (0.3$"$) AE. Their total duration (including rise and decay) is of the order of $10^{3}$ s. Inside each AE, the mean flux is $1.6 10^{5}$ W m$^{-2}$ (lower layer) and $1.2 10^{5}$ W m$^{-2}$ (upper). Each event carries an average energy (flux integrated over space and time) of $2.5 10^{19}$ J (lower layer) to $1.9 10^{19}$ J (upper). More than $10^{6}$ events could exist permanently on the Sun, with a birth and decay rate of 3500 s$^{-1}$. Most events occur in intergranular lanes, downward velocity regions, and areas of converging motions.

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arXiv2012

MHD simulations of the solar photosphere

We briefly review the observations of the solar photosphere and pinpoint some open questions related to the magnetohydrodynamics of this layer of the Sun. We then discuss the current modelling efforts, addressing among other problems, that of the origin of supergranulation.

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arXiv2012

14 Ceti: A probable Ap-star-descendant entering the Hertzsprung gap

14 Ceti is a subgiant star of F spectral class that displays variations in the S-index of its CaII H & K lines and an X-ray emission that is stronger than the mean observed for its spectral class, which may be due to some magnetic activity. We attempt to Zeeman-detect and study the magnetic field of 14 Ceti and to infer its origin. We used the spectropolarimeter Narval at the Telescope Bernard Lyot, Pic du Midi Observatory, and the least squares deconvolution method to create high signal-to-noise ratio Stokes V profiles. We derived the surface-averaged longitudinal magnetic field Bl. We also measured the S-index, and the radial velocity for each observation. 14 Ceti is Zeeman-detected for the 30 observed dates spanning from August 2007 to January 2012. The average longitudinal magnetic field does not reverse its sign, reaches about -35 G, and shows some month-long-timescale variations in our 2008 and 2011-2012 observations. The S-index follows the same long-term trend as Bl. 14 Ceti is confirmed as a single star without H-K emission cores. The strength of the observed surface magnetic field of 14 Ceti is one order of magnitude greater than the observed one for late F main-sequence stars, and is comparable to the values measured in the active late F pre-main-sequence star HR 1817. On the other hand, taking into account the post-main-sequence evolution of an Ap star, an oblique rotator model can explain the strength of the magnetic field of 14 Ceti. The variations with a timescale of months observed for both the Bl and S-index could be due to the rotation. The most probable scenario to explain our observations appears to be that 14 Ceti is the descendant of a cool Ap star .

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arXiv2011

Magnetic field and convection in the cool supergiant Betelgeuse

We present the outcome of a highly-sensitive search for magnetic fields on the cool supergiant Betelgeuse. A time-series of six circularly-polarized spectra was obtained using the NARVAL spectropolarimeter at Télescope Bernard Lyot (Pic du Midi Observatory), between 2010 March and April. Zeeman signatures were repeatedly detected in cross-correlation profiles, corresponding to a longitudinal component of about 1 G. The time-series unveils a smooth increase of the longitudinal field from 0.5 to 1.5 G, correlated with radial velocity fluctuations. We observe a strong asymmetry of Stokes V signatures, also varying in correlation with the radial velocity. The Stokes V line profiles are red-shifted by about 9 km/s with respect to the Stokes I profiles, suggesting that the observed magnetic elements may be concentrated in the sinking components of the convective flows.

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