Helioseismology of Sunspots: A Case Study of NOAA Region 9787

L. Gizon 0 H. Schunker 0 C.S. Baldner 0 S. Basu 0 A.C. Birch 0 R.S. Bogart 0 D.C. Braun 0 R. Cameron 0 T.L. Duvall Jr. 0 S.M. Hanasoge 0 J. Jackiewicz 0 M. Roth 0 T. Stahn 0 M.J. Thompson 0 S. Zharkov 0 0 T.L. Duvall Jr. Laboratory for Solar Physics, NASA/Goddard Space Flight Center , Greenbelt, MD 20771, USA Various methods of helioseismology are used to study the subsurface properties of the sunspot in NOAA Active Region 9787. This sunspot was chosen because it is axisymmetric, shows little evolution during 20-28 January 2002, and was observed continuously by the MDI/SOHO instrument. AR 9787 is visible on helioseismic maps of the farside of the Sun from 15 January, i.e. days before it crossed the East limb. Oscillations have reduced amplitudes in the sunspot at all frequencies, whereas a region of enhanced acoustic power above 5.5 mHz (above the quiet-Sun acoustic cutoff) is seen outside the sunspot and the plage region. This enhanced acoustic power has been suggested to be caused by the conversion of acoustic waves into magneto-acoustic waves that are refracted back into the interior and re-emerge as acoustic waves in the quiet Sun. Observations show that the sunspot absorbs a significant fraction of the incoming p and f modes around 3 mHz. A numerical simulation of MHD wave propagation through a simple model of AR 9787 confirmed that wave absorption is likely to be due to the partial conversion of incoming waves into magneto-acoustic waves that propagate down the sunspot. - Wave travel times and mode frequencies are affected by the sunspot. In most cases, wave packets that propagate through the sunspot have reduced travel times. At short travel distances, however, the sign of the travel-time shifts appears to depend sensitively on how the data are processed and, in particular, on filtering in frequency-wavenumber space. We carry out two linear inversions for wave speed: one using travel-times and phase-speed filters and the other one using mode frequencies from ring analysis. These two inversions give subsurface wave-speed profiles with opposite signs and different amplitudes. The travel-time measurements also imply different subsurface flow patterns in the surface layer depending on the filtering procedure that is used. Current sensitivity kernels are unable to reconcile these measurements, perhaps because they rely on imperfect models of the power spectrum of solar oscillations. We present a linear inversion for flows of ridge-filtered travel times. This inversion shows a horizontal outflow in the upper 4 Mm that is consistent with the moat flow deduced from the surface motion of moving magnetic features. From this study of AR 9787, we conclude that we are currently unable to provide a unified description of the subsurface structure and dynamics of the sunspot. 1 Introduction One of the main goals of solar physics is to understand the physical processes responsible for solar magnetism and activity. This requires the study of magnetic flux tubes, their transport and dynamics in the convection zone, and their emergence at the solar surface in the form of sunspots and active regions. The overall nature of sunspots is still a matter of debate. Many open questions remain concerning their structure and, above all, their formation and stability. How can regions of such intense magnetic flux come into existence and remain stable over several days, weeks, and sometimes months? Another common question is whether sunspots are monolithic magnetic flux tubes or have a spaghetti-like structure (Parker 1979). Schssler and Rempel (2005) proposed a scenario whereby a sunspot expands rapidly below the surface during the early stages of its formation, leading to a disconnection from its magnetic roots. This disconnection may allow a transition to a spaghetti-like subsurface structure. As to the stability of sunspots, it may be due to the presence of surface and subsurface collar flows (Parker 1979). Other questions concern the energetics of sunspots, the flow of heat through and around sunspots, and the nature of magnetoconvection at kilogauss fields. What is known about sunspots has been summarized by, e.g., Thomas and Weiss (1992) and Solanki (2003). For a description of various magnetostatic sunspot models, we refer the reader to Jahn (1992) and Rempel et al. (2008). In this paper we will discuss the potential of helioseismology to probe the subsurface structure of sunspots, with the hope of answering, one day, some of the questions listed above. Local helioseismology includes several methods of analysis, which have been described in some detail by Gizon and Birch (2005). All these methods rely on continuous time series of Doppler images of the Suns surface. Fourier-Hankel analysis was developed to study the relationship between ingoing and outgoing waves around a sunspot (Braun et al. 1987; Braun 1995). Ring-diagram analysis consists of analysing the frequencies of solar acoustic waves over small patches of the solar surface (Hill 1988; Antia and Basu 2007). Timedistance helioseismology (TD) measures the travel times of wave packets moving through the solar interior (Duvall Jr. et al. 1993). Helioseismic holography (HH) uses the observed wave field at the solar surface to infer the wave field at different depths (Lindsey and Braun 1997). A summary of recent results is provided by Gizon (2006) and Thompson and Zharkov (2008). There have been several studies of sunspots using helioseismology. Braun et al. (1987, 1992a) and Braun (1995) used Fourier-Hankel decomposition to measure wave absorption and scattering phase shifts caused by sunspots. The absorption is believed to be the result of a partial conversion of incoming p modes into slow magnetoacoustic waves (e.g., Spruit and Bogdan 1992; Cally 2000). Observational signatures of the mode conversion process have been discussed, for example, by Schunker and Cally (2006). Agreement between the observations of Braun (1995) and simplified sunspot models were reported by Fan et al. (1995), Cally et al. (2003), and Crouch et al. (2005) using a forward modeling approach. Timedistance helioseismology and helioseismic holography aim at making images of the solar interior from maps of travel times or phase shifts under the traditional assumption that the Sun is weakly inhomogeneous in the horizontal directions. TD and HH have been used to infer wave speed variations and flows in and around sunspots (e.g., Duvall Jr. et al. 1996; Jensen et al. 2001; Braun and Lindsey 2000; Gizon et al. 2000; Kosovichev et al. 2000; Zhao et al. 2001; Couvidat et al. 2006). Ring-diagram analysis has a coarser horizontal resolution and is used to study the subsurface structure of entire active regions (e.g., Basu et al. 2004; Antia and Basu 2007; Bogart et al. 2008). While these methods and their variants appear to be quite robust, it has not been demonstrated that they are consistent. For instance ringdiagram analysis has not been directly compare (...truncated)