arXiv subjects

L. Gizon

Publications and source records attributed to L. Gizon.

At least 37 records · Page 2Linked to original sources

arXiv2023

Wavefront error of PHI/HRT on Solar Orbiter at various heliocentric distances

We use wavefront sensing to characterise the image quality of the the High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (SO/PHI) data products during the second remote sensing window of the Solar Orbiter (SO) nominal mission phase. Our ultimate aims are to reconstruct the HRT data by deconvolving with the HRT point spread function (PSF) and to correct for the effects of optical aberrations on the data. We use a pair of focused--defocused images to compute the wavefront error and derive the PSF of HRT by means of a phase diversity (PD) analysis. The wavefront error of HRT depends on the orbital distance of SO to the Sun. At distances $>0.5$\,au, the wavefront error is small, and stems dominantly from the inherent optical properties of HRT. At distances $<0.5$\,au, the thermo-optical effect of the Heat Rejection Entrance Window (HREW) becomes noticeable. We develop an interpolation scheme for the wavefront error that depends on the thermal variation of the HREW with the distance of SO to the Sun. We also introduce a new level of image reconstruction, termed `aberration correction', which is designed to reduce the noise caused by image deconvolution while removing the aberrations caused by the HREW. The computed PSF via phase diversity significantly reduces the degradation caused by the HREW in the near-perihelion HRT data. In addition, the aberration correction increases the noise by a factor of only $1.45$ compared to the factor of $3$ increase that results from the usual PD reconstructions.

astro-ph.SR↗

arXiv2023

Direct assessment of SDO/HMI helioseismology of active regions on the Sun's far side using SO/PHI magnetograms

Earth-side observations of solar p modes can be used to image and monitor magnetic activity on the Sun's far side. Here we use magnetograms of the far side obtained by the Polarimetric and Helioseismic Imager (PHI) onboard Solar Orbiter (SO) to directly assess -- for the first time -- the validity of far-side helioseismic holography. We wish to co-locate the positions of active regions in helioseismic images and magnetograms, and to calibrate the helioseismic measurements in terms of magnetic field strength. We identify three magnetograms on 18 November 2020, 3 October 2021, and 3 February 2022 displaying a total of six active regions on the far side. The first two dates are from SO's cruise phase, the third from the beginning of the nominal operation phase. We compute contemporaneous seismic phase maps for these three dates using helioseismic holography applied to time series of Dopplergrams from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO). Among the six active regions seen in SO/PHI magnetograms, five active regions are identified on the seismic maps at almost the same positions as on the magnetograms. One region is too weak to be detected above the seismic noise. To calibrate the seismic maps, we fit a linear relationship between the seismic phase shifts and the unsigned line-of-sight magnetic field averaged over the active region areas extracted from the SO/PHI magnetograms. SO/PHI provides the strongest evidence so far that helioseismic imaging provides reliable information about active regions on the far side, including their positions, areas, and mean unsigned magnetic field.

astro-ph.SR↗

arXiv2023

Spectropolarimetric investigation of magnetohydrodynamic wave modes in the photosphere: First results from PHI on board Solar Orbiter

In November 2021, Solar Orbiter started its nominal mission phase. The remote-sensing instruments on board the spacecraft acquired scientific data during three observing windows surrounding the perihelion of the first orbit of this phase. The aim of the analysis is the detection of magnetohydrodynamic (MHD) wave modes in an active region by exploiting the capabilities of spectropolarimetric measurements. The High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (SO/PHI) on board the Solar Orbiter acquired a high-cadence data set of an active region. This is studied in the paper. B-$ω$ and phase-difference analyses are applied on line-of-sight velocity and circular polarization maps and other averaged quantities. We find that several MHD modes at different frequencies are excited in all analysed structures. The leading sunspot shows a linear dependence of the phase lag on the angle between the magnetic field and the line of sight of the observer in its penumbra. The magnetic pore exhibits global resonances at several frequencies, which are also excited by different wave modes. The SO/PHI measurements clearly confirm the presence of magnetic and velocity oscillations that are compatible with one or more MHD wave modes in pores and a sunspot. Improvements in modelling are still necessary to interpret the relation between the fluctuations of different diagnostics.

astro-ph.SR↗

arXiv2023

Interaction of solar inertial modes with turbulent convection. A 2D model for the excitation of linearly stable modes

Inertial modes have been observed on the Sun at low longitudinal wavenumbers. These modes probe the dynamics and structure of the solar convection zone down to the tachocline. While linear analysis allows the complex eigenfrequencies and eigenfunctions of these modes to be computed, it gives no information about their excitation nor about their amplitudes. We tested the hypothesis that solar inertial modes are stochastically excited by the turbulent motions entailed by convection. We have developed a theoretical formalism where the turbulent velocity fluctuations provide the mechanical work necessary to excite the modes. The modes are described by means of a 2D linear wave equation, relevant for the quasi-toroidal modes observed on the Sun, with a source term, under the beta plane approximation. Latitudinal differential rotation is included in the form of a parabolic profile that approximates the solar differential rotation at low and mid latitudes. We obtain synthetic power spectra for the wave's latitudinal velocity, longitudinal velocity, and radial vorticity, with azimuthal orders between 1 and 20. The synthetic power spectra contain the classical equatorial Rossby modes, as well as a rich spectrum of additional modes. The mode amplitudes are found to be of the same order of magnitude as observed on the Sun (~ 1 m/s). There is a qualitative transition between low and high azimuthal orders: the power spectra for m < 5 show modes that are clearly resolved in frequency space, while the power spectra for m > 5 display regions of excess power that consist of many overlapping modes. The general agreement between the predicted and observed inertial mode amplitudes supports the assumption of stochastic excitation by turbulent convection. Our work shows that the power spectra are not easily separable into individual modes, thus complicated the interpretation of the observations.

astro-ph.SR↗

arXiv2023

Magnetic fields inferred by Solar Orbiter: A comparison between SO/PHI-HRT and SDO/HMI

The High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager on board the Solar Orbiter spacecraft (SO/PHI) and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both infer the photospheric magnetic field from polarised light images. SO/PHI is the first magnetograph to move out of the Sun--Earth line and will provide unprecedented access to the Sun's poles. This provides excellent opportunities for new research wherein the magnetic field maps from both instruments are used simultaneously. We aim to compare the magnetic field maps from these two instruments and discuss any possible differences between them. We used data from both instruments obtained during Solar Orbiter's inferior conjunction on 7 March 2022. The HRT data were additionally treated for geometric distortion and degraded to the same resolution as HMI. The HMI data were re-projected to correct for the $3^{\circ}$ separation between the two observatories. SO/PHI-HRT and HMI produce remarkably similar line-of-sight magnetograms, with a slope coefficient of $0.97$, an offset below $1$ G, and a Pearson correlation coefficient of $0.97$. However, SO/PHI-HRT infers weaker line-of-sight fields for the strongest fields. As for the vector magnetic field, SO/PHI-HRT was compared to both the $720$-second and $90$-second HMI vector magnetic field: SO/PHI-HRT has a closer alignment with the $90$-second HMI vector. In the weak signal regime ($< 600$ G), SO/PHI-HRT measures stronger and more horizontal fields than HMI, very likely due to the greater noise in the SO/PHI-HRT data. In the strong field regime ($\gtrsim 600$ G), HRT infers lower field strengths but with similar inclinations (a slope of $0.92$) and azimuths (a slope of $1.02$). The slope values are from the comparison with the HMI $90$-second vector.

astro-ph.SR↗

arXiv2023

The ratio of horizontal to vertical displacement in solar oscillations estimated from combined SO/PHI and SDO/HMI observations

In order to make accurate inferences about the solar interior using helioseismology, it is essential to understand all the relevant physical effects on the observations. One effect to understand is the (complex-valued) ratio of the horizontal to vertical displacement of the p- and f-modes at the height at which they are observed. Unfortunately, it is impossible to measure this ratio directly from a single vantage point, and it has been difficult to disentangle observationally from other effects. In this paper we attempt to measure the ratio directly using 7.5 hours of simultaneous observations from the Polarimetric and Helioseismic Imager on board Solar Orbiter and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. While image geometry problems make it difficult to determine the exact ratio, it appears to agree well with that expected from adiabatic oscillations in a standard solar model. On the other hand it does not agree with a commonly used approximation, indicating that this approximation should not be used in helioseismic analyses. In addition, the ratio appears to be real-valued.

astro-ph.SR↗

arXiv2023

MPS-ATLAS library of stellar model atmospheres and spectra

Stellar spectra contain a large amount of information about the conditions in stellar atmospheres. However, extracting this information is challenging and demands comprehensive numerical modelling. Here, we present stellar spectra synthesized using the recently developed state-of-the-art MPS-ATLAS code on a fine grid of stellar fundamental parameters. These calculations have been extensively validated against solar and stellar observations and can be used for various astrophysical applications. The spectra are available at the Max Planck Digital Library (MPDL, https://edmond.mpdl.mpg.de/dataset.xhtml?persistentId=doi:10.17617/3.NJ56TR) and have been also incorporated into the ExoTiC-LD python package (https://github.com/Exo-TiC/ExoTiC-LD/) which returns stellar limb darkening coefficients used for the software package Exoplanet Timeseries Characterisation (ExoTic).

astro-ph.SR↗

arXiv2022

KIC 6951642: confirmed Kepler $γ$ Doradus-$δ$ Scuti star with intermediate to fast rotation in a possible single-lined binary system

KIC 6951642 has been reported as a candidate hybrid pulsator of type-$γ$ Doradus-$δ$ Scuti from observations of the first quarters of the Kepler mission. We aim to investigate the pulsating nature of KIC 6951642 and to search for the signature of rotation and/or activity in the light curves. We performed an iterative frequency search of both Fourier spectra, and searched for regular patterns in them. We applied spectrum synthesis to determine the atmospheric stellar parameters. Since KIC 6951642 was reported to belong to a spectroscopic binary system, we fitted the time delays derived from the light curves with the radial velocities obtained from published as well as new spectra in an attempt to improve the quality of the first orbit. Follow-up spectroscopy showed that KIC 6951642 is a fast-rotating F0-type star in a possible single-lined binary with a period of $\sim$4.8 yr. In the low-frequency regime, we identified the frequencies of 0.721 d$^{-1}$ as well as of 0.0087 d$^{-1}$. We attribute the first frequency to stellar rotation and the second one to stellar activity with a cycle. We also detected $g$ modes, with the strongest mode located at 2.238 d$^{-1}$, as well as three asymmetric multiplets (with a mean spacing of 0.675$\pm$0.044 d$^{-1}$). In the high-frequency regime, we detected frequencies of type-$δ$ Scuti, with the strongest mode located at 13.96 d$^{-1}$, as well as seven asymmetric multiplets (with a mean spacing of 0.665$\pm$0.084 d$^{-1}$). We subsequently identified a few more frequencies that appear to be combinations of a $g$ or $p$ mode and one of the higher cited frequencies not due to pulsations. We propose that KIC 6951642 accommodates for a fast-rotating $γ$ Dor-$δ$ Sct hybrid star with various rotationally split multiplets of $g$ and $p$ modes and that it also displays a cycle lasting years of (possible) stellar activity.

astro-ph.SR↗

arXiv2022

The on-ground data reduction and calibration pipeline for SO/PHI-HRT

The ESA/NASA Solar Orbiter space mission has been successfully launched in February 2020. Onboard is the Polarimetric and Helioseismic Imager (SO/PHI), which has two telescopes, a High Resolution Telescope (HRT) and the Full Disc Telescope (FDT). The instrument is designed to infer the photospheric magnetic field and line-of-sight velocity through differential imaging of the polarised light emitted by the Sun. It calculates the full Stokes vector at 6 wavelength positions at the Fe I 617.3 nm absorption line. Due to telemetry constraints, the instrument nominally processes these Stokes profiles onboard, however when telemetry is available, the raw images are downlinked and reduced on ground. Here the architecture of the on-ground pipeline for HRT is presented, which also offers additional corrections not currently available on board the instrument. The pipeline can reduce raw images to the full Stokes vector with a polarimetric sensitivity of $10^{-3}\cdot I_{c}$ or better.

astro-ph.SR↗

arXiv2022

Faculae cancel out on the surfaces of active Suns

Surfaces of the Sun and other cool stars are filled with magnetic fields, which are either seen as dark compact spots or more diffuse bright structures like faculae. Both hamper detection and characterisation of exoplanets, affecting stellar brightness and spectra, as well as transmission spectra. However, the expected facular and spot signals in stellar data are quite different, for instance they have distinct temporal and spectral profiles. Consequently, corrections of stellar data for magnetic activity can greatly benefit from the insight on whether the stellar signal is dominated by spots or faculae. Here, we utilise a surface flux transport model (SFTM) to show that more effective cancellation of diffuse magnetic flux associated with faculae leads to spot area coverages increasing faster with stellar magnetic activity than that by faculae. Our calculations explain the observed dependence between solar spot and facular area coverages and allow its extension to stars more active than the Sun. This extension enables anticipating the properties of stellar signal and its more reliable mitigation, leading to a more accurate characterisation of exoplanets and their atmospheres.

astro-ph.SR↗

arXiv2022

Impact of spatially correlated fluctuations in sunspots on metrics related to magnetic twist

The twist of the magnetic field above a sunspot is an important quantity in solar physics. For example, magnetic twist plays a role in the initiation of flares and coronal mass ejections (CMEs). Various proxies for the twist above the photosphere have been found using models of uniformly twisted flux tubes, and are routinely computed from single photospheric vector magnetograms. One class of proxies is based on $α_z$, the ratio of the vertical current to the vertical magnetic field. Another class of proxies is based on the so-called twist density, $q$, which depends on the ratio of the azimuthal field to the vertical field. However, the sensitivity of these proxies to temporal fluctuations of the magnetic field has not yet been well characterized. We aim to determine the sensitivity of twist proxies to temporal fluctuations in the magnetic field as estimated from time-series of SDO/HMI vector magnetic field maps. To this end, we introduce a model of a sunspot with a peak vertical field of 2370 Gauss at the photosphere and a uniform twist density $q= -0.024$ Mm$^{-1}$. We add realizations of the temporal fluctuations of the magnetic field that are consistent with SDO/HMI observations, including the spatial correlations. Using a Monte-Carlo approach, we determine the robustness of the different proxies to the temporal fluctuations. The temporal fluctuations of the three components of the magnetic field are correlated for spatial separations up to 1.4 Mm (more than expected from the point spread function alone). The Monte-Carlo approach enables us to demonstrate that several proxies for the twist of the magnetic field are not biased in each of the individual magnetograms. The associated random errors on the proxies have standard deviations in the range between $0.002$ and $0.006$ Mm$^{-1}$, which is smaller by approximately one order of magnitude than the mean value of $q$.

astro-ph.SR↗

arXiv2022

Stellar limb darkening. A new MPS-ATLAS library for Kepler, TESS, CHEOPS, and PLATO passbands

The detection of the first exoplanet paved the way into the era of transit photometry space missions with a revolutionary photometric precision that aim at discovering new exoplanetary systems around different types of stars. With this high precision, it is possible to derive very accurately the radii of exoplanets which is crucial for constraining their type and composition. However, it requires an accurate description of host stars, especially their center-to-limb variation of intensities (so called limb darkening) as it affects the planet-to-star radius ratio determination. We aim at improving the accuracy of limb darkening calculations for stars with a wide range of fundamental parameters. We used the recently developed 1D MPS-ATLAS code to compute model atmosphere structures and to synthesize stellar limb darkening on a very fine grid of stellar parameters. For the computations we utilized the most accurate information on chemical element abundances and mixing length parameters including convective overshoot. The stellar limb darkening was fitted using the two most accurate limb darkening laws: the power-2 and 4-parameters non-linear laws. We present a new extensive library of stellar model atmospheric structures, the synthesized stellar limb darkening curves, and the coefficients of parameterized limb-darkening laws on a very fine grid of stellar parameters in the Kepler, TESS, CHEOPS, and PLATO passbands. The fine grid allows overcoming the sizable errors introduced by the need to interpolate. Our computations of solar limb darkening are in a good agreement with available solar measurements at different view angles and wavelengths. Our computations of stellar limb darkening agree well with available measurements of Kepler stars. A new grid of stellar model structures, limb darkening and their fitted coefficients in different broad filters is provided in CDS.

astro-ph.SR↗

arXiv2022

The magnetic drivers of campfires seen by the Polarimetric and Helioseismic Imager (PHI) on Solar Orbiter

The Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO) spacecraft observed small extreme ultraviolet (EUV) bursts, termed campfires, that have been proposed to be brightenings near the apexes of low-lying loops in the quiet-Sun atmosphere. The underlying magnetic processes driving these campfires are not understood. During the cruise phase of SO and at a distance of 0.523\,AU from the Sun, the Polarimetric and Helioseismic Imager on Solar Orbiter (SO/PHI) observed a quiet-Sun region jointly with SO/EUI, offering the possibility to investigate the surface magnetic field dynamics underlying campfires at a spatial resolution of about 380~km. In 71\% of the 38 isolated events, campfires are confined between bipolar magnetic features, which seem to exhibit signatures of magnetic flux cancellation. The flux cancellation occurs either between the two main footpoints, or between one of the footpoints of the loop housing the campfire and a nearby opposite polarity patch. In one particularly clear-cut case, we detected the emergence of a small-scale magnetic loop in the internetwork followed soon afterwards by a campfire brightening adjacent to the location of the linear polarisation signal in the photosphere, that is to say near where the apex of the emerging loop lays. The rest of the events were observed over small scattered magnetic features, which could not be identified as magnetic footpoints of the campfire hosting loops. The majority of campfires could be driven by magnetic reconnection triggered at the footpoints, similar to the physical processes occurring in the burst-like EUV events discussed in the literature. About a quarter of all analysed campfires, however, are not associated to such magnetic activity in the photosphere, which implies that other heating mechanisms are energising these small-scale EUV brightenings.

astro-ph.SR↗

arXiv2021

The PLATO field selection process I. Identification and content of the long-pointing fields

PLATO (PLAnetary Transits and Oscillations of stars) is an ESA M-class satellite planned for launch by end 2026 and dedicated to the wide-field search of transiting planets around bright and nearby stars, with a strong focus on discovering habitable rocky planets hosted by solar-like stars. The choice of the fields to be pointed at is a crucial task since it has a direct impact on the scientific return of the mission. In this paper we describe and discuss the formal requirements and the key scientific prioritization criteria that have to be taken into account in the Long-duration Observation Phase (LOP) field selection, and apply a quantitative metric to guide us in this complex optimization process. We identify two provisional LOP fields, one for each hemisphere (LOPS1, LOPN1), and discuss their properties and stellar content. While additional fine-tuning shall be applied to LOP selection before the definitive choice (to be made two years before launch), we expect their position will not move by more than a few degrees with respect to what is proposed in this paper.

astro-ph.EP↗

arXiv2021

The all-sky PLATO input catalogue

Context. The ESA PLAnetary Transits and Oscillations of stars (PLATO) mission will search for terrestrial planets in the habitable zone of solar-type stars. Because of telemetry limitations, PLATO targets need to be pre-selected. Aims. In this paper, we present an all sky catalogue that will be fundamental to selecting the best PLATO fields and the most promising target stars, deriving their basic parameters, analysing the instrumental performances, and then planing and optimising follow-up observations. This catalogue also represents a valuable resource for the general definition of stellar samples optimised for the search of transiting planets. Methods. We used Gaia Data Release 2 (DR2) astrometry and photometry and 3D maps of the local interstellar medium to isolate FGK (V$\leq$13) and M (V$\leq$16) dwarfs and subgiant stars. Results. We present the first public release of the all-sky PLATO Input Catalogue (asPIC1.1) containing a total of 2 675 539 stars including 2 378 177 FGK dwarfs and subgiants and 297 362 M dwarfs. The median distance in our sample is 428 pc for FGK stars and 146 pc for M dwarfs, respectively. We derived the reddening of our targets and developed an algorithm to estimate stellar fundamental parameters (Teff, radius, mass) from astrometric and photometric measurements. Conclusions. We show that the overall (internal+external) uncertainties on the stellar parameter determined in the present study are $\sim$230 K (4%) for the effective temperatures, $\sim$0.1 R$_{\odot}$ (9%) for the stellar radii, and $\sim$0.1 M$_{\odot}$ (11%) for the stellar mass. We release a special target list containing all known planet hosts cross-matched with our catalogue.

astro-ph.EP↗

arXiv2021

Modelling continuum intensity perturbations caused by solar acoustic oscillations

Helioseismology is the study of the solar interior using observations of oscillations at the surface. It suffers from systematic errors, such as a center-to-limb error in travel-time measurements. Understanding these errors requires a good understanding of the nontrivial relationship between wave displacement and helioseismic observables. The wave displacement causes perturbations in the atmospheric thermodynamical quantities which perturb the opacity, the optical depth, the source function, and the local ray geometry, thus affecting the emergent intensity. We aim to establish the most complete relationship up to now between the displacement and the intensity perturbation by solving the radiative transfer problem in the atmosphere. We derive an expression for the intensity perturbation caused by acoustic oscillations at any point on the solar disk by applying the first-order perturbation theory. As input, we consider adiabatic modes of oscillation of different degrees. The background and the perturbed intensities are computed considering the main sources of opacity in the continuum. We find that, for all modes, the perturbations to the thermodynamical quantities are not sufficient to model the intensity. In addition, the geometrical effects due to the displacement must be taken into account as they lead to a difference in amplitude and a phase shift between the temperature at the surface and intensity perturbations. The closer to the limb, the larger the differences. This work presents improvements for the computation of the intensity perturbations, in particular for high-degree modes, and explains differences in intensity computations in earlier works. The phase shifts and amplitude differences between the temperature and intensity perturbations increase towards the limb. This should help to interpret some of the systematic center-to-limb effects observed in local helioseismology.

astro-ph.SR↗

arXiv2021

Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling

Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. Rossby waves create small-amplitude, very-low frequency motions (on the order of the rotation rate and lower), which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well. We analyze 4 and 8 years of Helioseismic and Magnetic Imager (HMI) data and consider coupling between different-degree acoustic modes (of separations 1 and 3 in harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes. We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes (where the azimuthal order is same as harmonic degree, s = |t|). Our results are consistent with prior measurements of Rossby modes with azimuthal orders over the range t = 4 to 16 with maximum power occurring at mode t = 8. The amplitudes of these modes vary from 1 to 2 m/s. We place an upper bound of 0.2 m/s on the sectoral t = 2 mode, which we do not detect in our measurements. This effort adds credence to the mode-coupling methodology in helioseismology

astro-ph.SR↗

arXiv2021

Evolution of solar surface inflows around emerging active regions

Solar active regions are associated with Evershed outflows in sunspot penumbrae, moat outflows surrounding sunspots, and extended inflows surrounding active regions. The latter have been identified on established active regions by various methods. The evolution of these inflows and their dependence on active region properties as well as their impact on the global magnetic field are not yet understood. We aim to understand the evolution of the average inflows around emerging active regions and to derive an empirical model for these inflows. We analyze horizontal flows at the surface of the Sun using local correlation tracking of solar granules observed in continuum images of SDO/HMI. We measure average flows of a sample of 182 isolated active regions up to seven days before and after their emergence onto the solar surface with a cadence of 12 hours. We investigate the average inflow properties with respect to active region characteristics of total flux and latitude. We fit a model to these observed inflows for a quantitative analysis. We find that converging flows of around $20$ to $30$ m/s are first visible one day prior to emergence, in agreement with recent results. These converging flows are present independently of active region properties of latitude or flux. We confirm a recently found prograde flow of about $40$ m/s at the leading polarity during emergence. We find that the time after emergence when the latitudinal inflows increase in amplitude depends on the flux of the active region, ranging from one to four days after emergence and increasing with flux. The largest extent of the inflows is up to about $7 \pm 1^\circ$ away from the center of the active region within the first six days after emergence. The inflow velocities have amplitudes of about $50$ m/s.

astro-ph.SR↗