Observations of umbral dots and their physical models

S1-1 Publ. Astron. Soc. Japan (2014) 66 (SP1), S1 (1–8) doi: 10.1093/pasj/psu102 Advance Access Publication Date: 2014 November 27 Observations of umbral dots and their physical models Hiroko WATANABE Unit of Synergetic Studies for Space, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, Kyoto 606-8502, Japan E-mail: Received 2014 January 25; Accepted 2014 February 21 Abstract The Hinode satellite opens a new era in sunspot research, because of its high spatial resolution and temporal stability. Fine-scale structures in sunspots, called umbral dots (UDs), have become one of the hottest topics in terms of close observations of magnetoconvection. In this paper, a brief review of the observed properties of UDs is given based on recent literature. UDs born in the periphery of the umbra exhibit inward migration, and their speeds are positively correlated with the magnetic field inclination. Longer-lasting UDs tend to be larger and brighter, while the lifetimes of UDs show no relation to their background magnetic field strength. UDs tend to disappear, or stop their proper motion by colliding with a locally strong field region. The spatial distribution of UDs is not uniform over an umbra, but is rather located at the boundaries of cellular patterns. From our two-dimensional correlation analysis, we measured the characteristic width of the cell boundaries (≈ 0. 5) and the size of the cells (≈ 6 ). We then performed a simplified analysis to obtain statistics of how the UD distribution is random or clustered using Hinode blue continuum images. We have found a hint that the UDs become less dense and more clustered for later-phase sunspots. These results may be related to the evolutional change of the subsurface structure of a sunspot. Based on these observational results, we discuss their physical models by means of numerical simulations of magnetoconvection. Key words: convection — Sun: magnetic fields — Sun: photosphere — sunspots 1 Introduction Observations and analyses of sunspots have been performed ever since the age of Galileo. Although we have an accumulation of more than 400 years of observational data, sunspots remain one of the biggest unsolved problems in solar physics. We have still not reached any consensus about the subsurface structure of a sunspot, e.g., whether the magnetic field is clustering or monolithic (Gokhale & Zwaan 1972; Parker 1979; Solanki 2003), how their strong magnetic fields are born, and what determines their lifetime (Cheung et al. 2010; Rempel 2011). Understanding sunspots is highly important for astrophysics, because violent solar activities in the strong magnetic field of a sunspot are driven by a common mechanism with many cosmic eruptive events (accretion jets, stellar flares, auroras, . . . ). We have found a new path for solving these problems in the research of fine-scale bright points, called umbral dots (UDs, figure 1; reviews are found in Borrero & Ichimoto 2011). UDs are transient brightenings observed in sunspot  C The Author 2014. Published by Oxford University Press on behalf of the Astronomical Society of Japan. All rights reserved. For Permissions, please email: S1-2 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. SP1 based on the analysis and discussion, we conclude how UD analysis can be one of the most important topics in solar physics in section 4. 2 Review of recent analyses Fig. 1. Blue continuum image of NOAA 10944 observed by the Hinode SOT on 2007 March 2. The FOV is about 17 × 17 . The arrows indicate two prominent UDs in the umbra. umbrae and pores, with typical scales of 300 km diameter and a 10 min lifetime (Sobotka et al. 1997a, 1997b; Kitai et al. 2007; Riethmüller et al. 2008; Louis et al. 2012). The magnetic properties around UDs have been studied by many authors (Riethmüller et al. 2008; Sobotka & Jurčák 2009; Watanabe et al. 2012), who have reached a consensus that UDs exhibit a local reduction of the field strength at a deep layer. Upflow inside UDs and confined down-flowing regions outside of them have been observed in recent highresolution observations (Ortiz et al. 2010; Watanabe et al. 2012; Riethmüller et al. 2013). A UD is considered to be a natural consequence of the interaction between the convection and the magnetic field based on the monolithic sunspot model (Schüssler & Vögler 2006; Bharti et al. 2010). One of the most sophisticated computer simulations of magnetoconvection, performed by Rempel (2012), succeeded in reproducing the overall structure of a sunspot. The convective motions inside the umbra push out the boundary of the magnetic field lines inside the convective cell, creating a region of strongly reduced field strength, and forming a cusp or canopy field configuration. Since UDs are strongly linked with the subsurface through an interaction with the deep convective layer, they have the potential to provide information about the unreachable subsurface structure and its dynamics. This paper is organized as follows. A review of recent observational analyses, and our new analysis on UD distribution, are given in section 2. In section 3, we discuss how these observational results are consistently interpreted by means of numerical studies of magnetoconvection. Finally, The observation of fine-scale structure, like UDs, needs high spatial resolution. The Hinode Solar Optical Telescope (SOT) has a main mirror of 50 cm aperture, and achieves a diffraction limit of 0. 2–0. 3 always because of its seeing-free environment (Tsuneta et al. 2008; Suematsu et al. 2008). This temporal stability is a great advantage for reliable analysis on the structure’s temporal evolution. On the other hand, the Swedish Solar Telescope (SST: Scharmer et al. 2003) has an effective aperture of 1 m, twice as large as that of Hinode. Further, they possess a spectropolarimetric imaging system, called CRISP, which enables scanning sequences of magnetic sensitive lines rapidly only in few-minute intervals. The analyses given below utilize the optimum observations for their individual purposes. 2.1 Inward migration UDs show an apparent motion of so-called inward migration toward the center of the umbra. Important questions that we have to answer are why the UDs always migrate inwards to the umbra center, and why they are better seen in the umbral periphery. Watanabe, Kitai, and Ichimoto (2009) analyzed the apparent motion speed of more than 2000 UDs, and compared them to their background umbral field inclination. The field inclination is vertical at the center of the umbra, and becomes more inclined at the periphery. A positive correlation between the field inclination and speed of UDs was found (figure 2). A least-squares linear fit for Fig. 2. Scatter plots of field inclination versus the apparent motion speed of 2268 UD samples. The average bins of 3◦ are shown with square symbols, and vertical solid lines denote the standard error deviation errors (...truncated)