A&A 611, A92 (2018) https://doi.org/10.1051/0004-6361/201732014 Astronomy & © ESO 2018 Astrophysics Large-scale photospheric motions determined from granule tracking and helioseismology from SDO/HMI data Th. Roudier1, M. Švanda2,3, J. Ballot1, J. M. Malherbe4, and M. Rieutord1 1 Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS, UPS, CNES, 14 avenue Edouard Belin, 31400 Toulouse, France e-mail: [email protected] 2 Astronomical Institute (v. v. i.), Czech Academy of Sciences, Fricovaˇ 298, 25165 Ondrejov,ˇ Czech Republic 3 Charles University, Astronomical Institute, Faculty of Mathematics and Physics, V Holešovickáchˇ 2, 18000 Prague 8, Czech Republic 4 LESIA, Observatoire de Paris, Section de Meudon, 92195 Meudon, France Received 28 September 2017 / Accepted 5 December 2017 ABSTRACT Context. Large-scale flows in the Sun play an important role in the dynamo process linked to the solar cycle. The important large-scale flows are the differential rotation and the meridional circulation with an amplitude of km s−1 and few m s−1, respectively. These flows also have a cycle-related components, namely the torsional oscillations. Aims. Our attempt is to determine large-scale plasma flows on the solar surface by deriving horizontal flow velocities using the techniques of solar granule tracking, dopplergrams, and time–distance helioseismology. Methods. Coherent structure tracking (CST) and time-distance helioseismology were used to investigate the solar differential rotation and meridional circulation at the solar surface on a 30-day HMI/SDO sequence. The influence of a large sunspot on these large-scale flows with a specific 7-day HMI/SDO sequence has been also studied. Results. The large-scale flows measured by the CST on the solar surface and the same flow determined from the same data with the helioseismology in the first 1 Mm below the surface are in good agreement in amplitude and direction. The torsional waves are also located at the same latitudes with amplitude of the same order. We are able to measure the meridional circulation correctly using the CST method with only 3 days of data and after averaging between ±15◦ in longitude. Conclusions. We conclude that the combination of CST and Doppler velocities allows us to detect properly the differential solar rotation and also smaller amplitude flows such as the meridional circulation and torsional waves. The results of our methods are in good agreement with helioseismic measurements. Key words. Sun: atmosphere – Sun: granulation – Sun: helioseismology – Sun: rotation 1. Introduction concentrated magnetic field, which serves as a proxy, is anchored in the underlying solar plasma; both the magnetic field and the Large-scale motions in the solar convection zone are important solar plasma interact strongly in the convective zone, where the elements to understand the evolution of solar magnetism. Vari- plasma β parameter, which is the ratio of the plasma pressure ous methods (Paternò 2010), based on helioseismology (Gizon to the magnetic pressure (β = 2µP=B2), is large. In this way, the & Rempel 2008; Komm et al. 2014; Zhao et al. 2014), Doppler study of the movements of proxies is delicate (Sudar et al. 2017) velocities measurements (Duvall 1979; Hathaway 1987), solar because observational biases can lead to contradictory results, magnetic tracers (e.g. sunspots, sunspot groups, faculae, bright such as in the measurement of the meridional circulation, the points; see Hathaway & Upton 2014) or surface feature (e.g. amplitude of which is only about 10 m s−1. Helioseismology cur- supergranule) tracking (Švanda et al. 2008; Hathaway 2012; rently provides the best measurement inside the Sun up to near Löptien et al. 2017) are used to infer the large-scale solar the surface of the plasma flows [from 30 to 1 Mm] (Howe 2009; flows. Advantages and disadvantages of various techniques are Zhao 2016). discussed and summarized by Hathaway & Upton(2014). One of the attempts to determine plasma motions on the sur- In particular, magnetic features do not behave as ideal trac- face of the full-disc Sun was made by Švanda et al.(2008) and ers because of their interactions with the surrounding plasma in a recent work by Löptien et al.(2017) using local correla- (Paternò 2010). The use of proxies may induce measurement tion tracking (LCT; November 1986). These works detect reliable biases. For example, the velocities measured using sunspots or motion of features that are carried by an underlying larger scale faculae as tracers presumably reflect the properties of deeper velocity field. They also show that a detection of torsional layers and therefore do not give access to the actual surface waves and meridional circulation is possible by applying the plasma motions (Javaraiah 2013; Li et al. 2013). It is well LCT method to MDI/SOHO and HMI/SDO Dopplergrams and establish now that rotation deduced from motion of sunspots is continuum intensity data, respectively. Nevertheless, the LCT systematically faster than that deduced from spectroscopic obser- method is subject to limitations when applied to whole Sun data. vations (Hathaway & Upton 2014). This is partly because the This technique is sensitive to the distance to the centre initially Article published by EDP Sciences A92, page 1 of9 A&A 611, A92 (2018) because the properties (e.g. size and contrast) of the granules 2. SDO/HMI observations change because of projection effects; secondly, the so-called shrinking effect due to the apparent asymmetry of granulation 2.1. SDO/HMI observations depends on the viewing angle inclined from the vertical, in com- bination with the expansion of the granules, gives an apparent The Helioseismic and Magnetic Imager (HMI; Scherrer et al. motion towards the disc centre (Löptien et al. 2016). 2012; Schou et al. 2012) on board the Solar Dynamics Obser- Moreover, the LCT is well known for underestimating the vatory (SDO) provides uninterrupted observations of the full amplitude of the velocities by a factor that depends on a partic- disc of the Sun. This provides a unique opportunity to map sur- ular application and may reach up to factor 2 or 3 (Verma et al. face flows on various spatial and temporal scales. We selected 2013). the SDO/HMI continuum intensity data from 16 August to We propose applying the coherent structure tracking (CST; 14 September 2010. This period was chosen due to its low solar Rieutord et al. 2007; Roudier et al. 2012) code to follow the activity and also to get very small variations of the B0 angle. The proper motions of solar granules in full-disc HMI/SDO data. By solar differential rotation and meridional circulation are deter- measuring the flow field on the solar surface over a long time mined from SDO/HMI continuum intensity and Doppler data period we obtain a representative description of solar plasma taken during this 30-day sequence. A second HMI/SDO time evolution. The CST allows us to get flow field from covering the sequence from 12 to 18 April 2016 was used to describe the spatial scales from 2.5 Mm up to nearly 85% of the solar radius. effects of the flows around a large sunspot to the solar rota- This method is complementary to helioseismic methods of flow tion and meridional circulation. Both sequences use the original cadence of 45 s and the original pixel size of 000: 5. The resolution determination, which describes the flows below the solar sur- 00 face. The CST is a granule tracking technique, which allows us to of the HMI instrument is 1: 0. estimate the field direction and amplitude (Rieutord et al. 2007). The LCT and Fourier local correlation tracking (FLCT; Welsch 2.2. Data analysis et al. 2004; Fisher & Welsch 2008) account for both granules and intergranules when cross-correlating continuum images to The flows were measured with two independent methods. estimate the direction and amplitude of the field. The princi- pal difference between the LCT (FLCT) and CST techniques 2.2.1. Granulation tracking by CST is that the LCT (FLCT) evaluates the similarity of image sub- frames at different positions in different times. These subframes The CST used the solar granules as passive scalars to follow solar are required to contain distinct features (granules, supergranule, plasma motions. In order to be suitable for the CST application, etc.), but these features are not uniquely identified. Thus the sub- the data series of the HMI intensitygrams must first be prepared. frame displacement is evaluated based on an overall similarity. All frames of the sequence were aligned such that the centre of The LCT (FLCT) thus provides a smooth differentiable estimate the solar disc lies exactly on the same pixel in CCD coordinates of the velocity field. In CST, the code identifies individual fea- and the radius of the solar disc was exactly the same for all the tures (granules) and tracks these individual features coherently frames. The reference values for the position of the disc centre through out the image sequence. The resulting velocity field is and the radius were obtained from the first image (obtained on 16 thus discontinuous and the differentiable extension is estimated August 2010 at 00:00:45 UT) of the 30-day series. Then we per- based on multi-resolution analysis. formed the granulation tracking using the CST code (Roudier In this paper, we describe a comparison between velocity et al. 2012) to reconstruct the projection of the photospheric fields on the full Sun obtained by various methods (CST, LCT, velocity field (vx; vy) in the plane of the sky (CCD plane) (Rincon FLCT, and time–distance helioseismology). A 30-day sequence et al. 2017). The application of CST to such a series leads to a of quiet Sun spanning from 16 August to 14 September 2010 is sequence of horizontal velocity field maps in the projection to selected.