5.2 Active regions and sunspots

5.2.1 Ordered flows near complexes of magnetic activity

Here we consider flows near regions of enhanced magnetic activity. We do not discuss local flows associated with sunspots, but larger-scale flows around complexes of magnetic activity. Using local helioseismology, synoptic maps of local horizontal flows can be constructed by averaging the data in time in a frame of reference that co-rotates with the Sun. Weak $50 m s- 1$ surface flows that converge toward active regions were detected by Gizon et al. (2001 ) with time-distance helioseismology (Figure 39 ). These flows, which exist as far as $30o$ from the centers of active regions, are also seen in ring diagram analyses with a coarser resolution (Haber et al., 2001 ). We note that Hindman et al. (2004 ) have shown that the two methods give remarkably similar results near the surface. Recently, both time-distance (Zhao and Kosovichev, 2004 ) and ring-diagram (Haber et al., 2004 ) analyses have provided depth inversions of horizontal flows down to about $15 Mm$ . Depths inversions indicate that, below $10 Mm$ , horizontal flows often diverge from active-region centers with velocities on the order of $-1 50 m s$ . Figure 40 shows the flows measured by Haber et al. (2004 ) around a particular active region. Although vertical flows have not been directly measured yet, motions appear to be organized in the form of a toroidal cell with a surface inflow and a deeper outflow. The picture is not so simple on time scales that are shorter than a week since flows do evolve from day to day.

Figure 39:

Map of near-surface horizontal flows obtained for Carrington rotation 1949 using f-mode time-distance helioseismology. A smooth rotation profile has been subtracted. The dark shades are shorter travel time anomalies that correspond to regions of enhanced magnetic activity. Local flows converge toward complexes of activity with an amplitude of $50 m s- 1$ . Notice also the poleward meridional flow. From Gizon et al. (2001 ).

The observed flows around active regions could be caused by the magnetic field. Indeed, the model of Spruit (2003 ) mentioned earlier predicts a surface inflow toward regions of enhanced magnetic field. An alternative explanation by Yoshimura (1971 ) suggests that the longitudinal ordering of solar magnetic fields could be due to the existence of large convective patterns that favor the formation of active regions at particular sites on the solar surface. We note that far away from active regions, complex flows like meanders, jets, and vortices are seen in the synoptic maps (Figure 39

); Toomre (2002 ) suggested that they may be related to the largest scales of deep convection.

Figure 40:

Left column: OLA inversion of horizontal flows around active region NOAA 9433 on 23 April 2001 obtained using ring-diagram analysis. The depths shown are $7 Mm$ (upper panel) and $14 Mm$ (lower panel). The green and red shades are for the two polarities of the magnetic field. The horizontal and vertical axes give the longitude and the latitude in heliospheric degrees. Right panel: Horizontal flows around NOAA 9433 as a function of depth and latitude, averaged over the longitude range $o o (142.5 ,157.5 )$ and the time period 23-27 April 2001. The transition between inflow and outflow occurs near $10 Mm$ depth. From Haber et al. (2004 ).

5.2.2 Effect on longitudinal averages of large-scale flows

An important question is to know whether the local flows that surround active regions contribute significantly to the solar-cycle variations of the longitudinal averages of rotation and meridional circulation in the upper layers of the convection zone (as discussed in Section5.1.1 and Section5.1.2). In other words, are the time-varying components of rotation and meridional circulation global phenomena or are they modulated in longitude by the presence of active regions?

In order to help answer this question, we consider synoptic maps of surface flows obtained in 1999 for Carrington rotations 1948 and 1949. By excluding the local areas of magnetic activity from the computation of the longitudional averages of rotation and meridional circulation, we obtain “quiet-sun” estimates that can be compared to the flows averaged over all longitudes (see Gizon, 2003 , for details). From Figure 41 it is obvious that the torsional oscillation (rotational shear at active latitudes) is present in between active longitudes. Thus the time-varying zonal flows appear to be mostly independent of longitude as they slowly drift in latitude through the solar cycle. Yet, active regions do rotate a little faster than their surroundings, thus affecting the mean rotation rate at active latitudes (see, e.g., Zhao et al., 2004 ). The influence of local active-region flows on longitudinal averages of north-south flows is more serious. Indeed, the $50 m s-1$ organized flows that surround active regions introduce a kink at active latitudes in the average meridional circulation profile, on the order of $-1 ±5 m s$ . Thus the solar-cycle variations of the meridional circulation (Section 5.1.2) would appear to be caused by active regions: convergence toward active latitudes near the surface and, presumably, divergence below $10 Mm$ .

Figure 41:

Left column: Longitudinal averages of surface horizontal flows obtained with f-mode time-distance helioseismology (Carrington rotations 1948 and 1949 in 1999). The vertical lines show the mean latitude of activity. The solid curves show zonal flows and meridional circulation averaged over all longitudes and both hemispheres. The zonal flows are obtained after subtraction of a smooth three-term fit to the rotation profile. The dashed curves are averages that exclude local areas in and around active regions (all points within $5o$ of strongly magnetized regions). Right panel: Sketch of surface flows around active regions: (a) $± 10 m s-1$ zonal shear flow, (b) $50 m s- 1$ inflow, (c) active region super-rotation, and (m) $- 1 20 m s$ background meridional circulation. From Gizon (2003 ).

5.2.3 Sunspot flows

Here we consider flows in the immediate vicinity of sunspots, which should not be confused with the flows discussed in the previous two sections. Duvall Jr et al. (1996 ) used the technique of time-distance helioseismology to measure the travel time difference between incoming and outgoing p-mode wavepackets around sunspots. They suggested that the observations are consistent with the existence of a downflow below sunspots with a velocity of about $-1 2 km s$ . It was estimated that the downflow persists down to a depth of $2 Mm$ below the surface. Kosovichev (1996 ) performed a 3D inversion of travel time measurements. The inversion results are consistent with $1 km s-1$ downflows that can reach depths of about $25 Mm$ .

Lindsey et al. (1996 ) employed “knife-edge” diagnostics to estimate horizontal flows around sunspots. In knife-edge diagnostics the Fourier transform of the data is multiplied by some filter $F (k,w)$ , and then transformed back to the space-time domain. The square of the absolute value of the signal is then averaged over time. The filter is constructed to let through the part of the signal that has been Doppler shifted by a flow in a particular direction. An estimate of the $x$ component, for example, of the flow is then formed by subtracting the local amplitudes that correspond to waves that have been Doppler shifted in the $+^x$ and $- ^x$ directions. Using this technique, Lindsey et al. (1996 ) were able to detect a horizontal outflow from the center of sunspots at depths of about $15 Mm$ . The amplitude of this flow reaches a maximum of about $180 m s-1$ at a distance of $40 Mm$ from the center of a sunspot.

The Hankel analysis also has the capability of detecting flows below sunspots by interpreting the phase shifts between inward and outward traveling acoustic waves. Braun et al. (1996 ) applied this technique to south pole data from 1988 and 1991, and reported phase shifts that are consistent with the Doppler effect of a radial outflow from sunspots. The mean horizontal outflow appears to increase with depth and reaches $-1 200 m s$ at a depth of $20 Mm$ . A more detailed analysis by Sun et al. (1997 ) using TON data demonstrates that there is a positive frequency shift between outgoing and ingoing waves which corresponds to a $40 -80 m s-1$ radial outflow from sunspots. These results exhibit properties similar to those reported by Lindsey et al. (1996 ).

In order to gain some confidence about flow measurements in sunspots, it is useful to infer surface flows with local helioseismology and check for consistency with direct Doppler measurements. Gizon et al. (2000 ) used f-mode time-distance helioseismology to study flows very close to the surface ( $1 Mm$ deep). Wave-based sensitivity kernels for horizontal flows were used in an iterative deconvolution of the travel times. Figure 42 shows a map of the horizontal flows near the surface for a sunspot observed on 1998 December 6 (the spatial resolution is about $3 Mm$ ). A horizontal outflow around sunspots is observed with an amplitude of about $500 m s-1$ , which extends to roughly twice the penumbral radius. A high correlation was found between the mean Dopplergram and the projection of the inferred horizontal flows onto the line of sight, confirming the validity of the time-distance inversion. This outflow, often called the moat flow, was seen earlier using surface Dopplergrams (Sheeley, 1972 ) and magnetic tracers (see, e.g., Brickhouse and Labonte, 1988 ). The moat flow is believed to be driven by a pressure gradient caused by the blockage of heat by sunspots (see, e.g., Nye et al., 1988 ).

Figure 42:

Horizontal flows around a sunspot on 1998 December 6, obtained with f-mode time-distance helioseismology. Overplotted is the line-of-sight magnetic field (MDI high resolution) truncated at $± 0.5 kG$ . The moat flow beyond the penumbra (red) is clearly visible. Adapted from Gizon et al. (2000

Zhao et al. (2001

) used a damped least-squares inversion (Tikhonov, 1963 ) of travel times to infer mass flows around a sunspot below the solar surface. Figure 43

shows the horizontal and vertical components of the flows at three different depths. Converging and downward directed flows were detected at depths of $0- 3 Mm$ , while outflows extending more than $30 Mm$ from sunspot axis were found below the downward and converging flows. Two vertical cuts through the sunspot, shown in Figure 44

, show strong flows across the sunspot at depths of $9 -12 Mm$ , which may provide some evidence in support of the cluster model, as opposed to the monolithic sunspot model. Zhao and Kosovichev (2003b

) also applied their time-distance inversion technique to determine the subphotospheric dynamics of an unusually fast-rotating sunspot observed in August 2000, which revealed that the vortical flows can be seen beneath the visible surface of this active region. On the basis of the three-dimensional velocity fields obtained from the time-distance helioseismology inversions, Zhao and Kosovichev (2003b

) estimated the subsurface kinetic helicity and concluded that it is comparable to the current helicity estimated from vector magnetograms.

Figure 43:

Flow maps around a sunspot at depths of (a) $0- 3 Mm$ , (b) $6- 9 Mm$ , and (c) $9 -12 Mm$ , infered using p-mode time-distance helioseismology. Arrows show the magnitude and direction of horizontal flows. The color background shows vertical flows (positive values for downward). The contours at the center correspond to the umbral and penumbral boundaries. The longest arrow represents $1 km s- 1$ for (a) and $1.6 km s-1$ for (b) and (c). From Zhao et al. (2001

Figure 44:

Vertical cuts through the sunspot shown in Figure 43

. Upper panel: Cut in the east-west direction. Lower panel: Cut in the north-south direction. The location of the umbra and the penumbra is indicated at the top of each frame. The longest arrow corresponds to a velocity of $1.4 km s-1$ . From Zhao et al. (2001 ).

Braun and Lindsey (2003

) have recently extended their applications of helioseismic holography to include Doppler diagnostics of quiet Sun regions. Phase-correlation holography measures travel time perturbations from the temporal correlations between the egression and ingression. By dividing the pupil into four quadrants is is possible to infer vector flows. Braun and Lindsey (2003

) performed the analysis separately for bands of power around $3$ , $4$ , and $5 mHz$ , and the resulting maps were then averaged together. As shown in Figure 45

, it is easy to identify the moat outflow at a focus depths of $3 Mm$ , as well as supergranules ( $24 hr$ time average).

Figure 45:

Horizontal Doppler diagnostics applied to $24 hr$ data from MDI, which includes sunspot group AR 9363. Left: Observed velocity field, shown as vectors, for a focal depth of $3 Mm$ and superimposed a magnetogram. Middle: Same vector field as shown in the left panel, but superimposed over an image of the horizontal divergence of the velocity. Right: Velocity field and its divergence with the focal plane placed $14 Mm$ below the surface. The companion Movie 46

shows the flow field as a function of focus depth. From Braun and Lindsey (2003

Figure 46:

Companion movie to Figure 45

, showing the flow field as a function of focus depth. From Braun and Lindsey (2003

Almost all local helioseismology results seem to indicate that there exists a radial outflow around sunspots down to at least $10 Mm$ , which relates to the moat flow seen at the surface. An exception is the inflow measured with p-mode time-distance helioseismology at a depth of $0- 3 Mm$ . It is especially puzzling that the f-mode and p-mode results are inconsistent. Regarding vertical flows, it is difficult to understand how both downflows and horizontal outflows can coexist just below the sunspot. We caution that many complications introduced by the magnetic field are simply ignored by all local techniques. For example, the effect of the magnetic field on excitation and damping mechanisms is known to introduce a small travel time difference between incoming and outgoing waves (Woodard, 1997 ; Gizon and Birch, 2002 ).

5.2.4 Sinks and sources of acoustic waves

The very first success of local helioseismology was the detection of acoustic absorption by sunspots. Braun et al. (1987 ) decomposed the oscillations in the annular region surrounding a sunspot into incoming waves and outgoing waves (Hankel decomposition, Section 4.1) to measure the incoming and outgoing wave power. It was found that sunspots with a typical radius of $20 Mm$ absorb as much as 50% of the incoming acoustic power (Braun et al., 1987 , 1988 ). The absorption coefficient reaches 70% for the giant sunspot group studied by Braun and Duvall (1990 ). Braun et al. (1988 ) found that the absorption coefficient $a$ increases as a function of horizontal wavenumber $k$ . The decrease of $a$ with $m/k$ is consistent with the absorbing region being mostly confined to the sunspot area. Weaker magnetic regions, such as plage, also display a significant level of p-mode absorption. Using $68 hr$ of south pole data, Braun (1995 ) was able to measure the absorption coefficient as a function of degree, azimuthal order, and frequency. It was found that the $m$ dependence is weak for $|m |< 20$ . The $m$ -averaged absorption coefficient is plotted in Figure 47 for two different sunspots as function of frequency and for different harmonic degrees. There is a peak in the absorption around $3 mHz$ .

Figure 47:

Absorption coefficients plotted as a function of frequency. The left panels show results for sunspot NOAA 5254 and the right panels are for sunspot NOAA 5229. The vertical panels represent different bins of harmonic degree. From Braun (1995

Spruit and Bogdan (1992 ) suggested that the partial conversion of the incoming acoustic waves into slow magnetoacoustic waves that propagate downward, channelled by the magnetic field, may explain the observations. Cally and Bogdan (1993 ), Bogdan (1997 ), and Cally et al. (2003

) showed using numerical models that this mechanism is indeed capable of producing strong absorption coefficients, as defined by Braun. The best agreement is obtained when the magnetic field is inclined to the vertical, to simulate a spreading magnetic field with height (Crouch and Cally, 2003 ; Cally et al., 2003

). In these models the maximum absorption is near $o 30$ inclination.

The acoustic absorption by magnetic regions was confirmed by application of acoustic imaging (Chang et al., 1997 ) to data from TON. Acoustic holography, applied to MDI data, is ideal for the detection of sources and sinks of acoustic waves on the Sun. Braun and Fan (1998 ) discovered a region of lower acoustic emission in the $3- 4 mHz$ frequency band which extends far beyond the sunspots (the ’acoustic moat’). Acoustic moats extend beyond magnetic regions into the quiet Sun. In addition, Braun and Lindsey (1999 ) discovered high-frequency emission (’acoustic glories’) surrounding active regions. Figure 48 shows egression power maps of the active region AR 8179 averaged over $24 hr$ , at different focal depths. The acoustic glory is seen in panel (b) as a bright halo of excess $5 mHz$ emission surrounding the entire active region complex. Isolated sunspots usually do not have any acoustic glory. The acoustic glory should not be confused with the ’acoustic halos’ (Doppler acoustic power maps near $6 mHz$ ) that surround all magnetic features (Braun et al., 1992 ). Neither acoustic halos nor acoustic glories are understood phenomena.

We note that acoustic absorption by sunspots may also be studied with local power maps from ring-diagram analysis (e.g., Rajaguru et al., 2001 ; Howe et al., 2004 ), and by comparing cross-correlation amplitudes for incoming and outgoing waves in time-distance helioseismology (Duvall, 2002, private communication).

Figure 48:

Egression power maps of active region complex NOAA 8179 obtained for the $24 yr$ period 1998 March 16. (a) MDI magnetogram. Panels (b), (c), and (d) show $5 mHz$ helioseismic images of the regions with depths at $0$ , $11.2$ and $19.5 Mm$ below the solar surface, respectively. The dark shades correspond to acoustic absorption. The acoustic glory is seen in panel (b) as a bright halo of excess $5 mHz$ emission. The linear gray scale at the bottom applies to all of the helioseismic images that are normalized to unity for the mean quiet Sun. From Braun and Lindsey (1999 ).

5.2.5 Phase shifts and wave-speed perturbations

The scattering phase shifts induced by sunspots were first measured with Hankel analysis by Braun et al. (1992 ) and Braun (1995 ). The $m$ -averaged difference between incoming and outgoing p-mode phases is plotted in Figure 49 for sunspot AR 5254 observed in 1988 at the south pole (Braun, 1995 ). The f-mode phase shifts could not be determined accurately. The acoustic phase shifts are generaly positive and increase with frequency (or harmonic degree) to reach values in excess of $90o$ . Notice that the increase with frequency is not linear: The rate of increase is smaller at smaller frequencies. This could indicate that the origin of the scattering phase shifts is due to perturbations that are confined to shallow depths (Braun, 1995 ). The phase shifts are also observed to decrease with $|m |$ , suggesting that scattering occurs over a small area (Braun, 1995 ). Fan et al. (1995 ) estimate that the phase shifts are mostly happening in the region inside the outer edge of the penumbra. Braun (1995 ) find no significant phase shifts in plage regions. Both the $m$ and frequency dependence of the phase shifts have been modelled successfully by Cally et al. (2003 , Figure 49 ). This provides a strong confirmation of the central physical mechanism that they advocate: partial conversion of incoming waves into downward propagating slow magnetoacoustic waves. We note that organized flows in and around sunspots should also introduce small phase shifts.

Figure 49:

Phase shifts between outgoing and outgoing waves from Hankel analysis, as a function of frequency for several different radial orders $n$ . The data points with error bars are $m$ -averaged values for NOAA 5254 (Braun, 1995 ). The solid lines are from a model by Cally et al. (2003

). From Cally et al. (2003

Chen et al. (1998 ) used acoustic imaging to map phase shifts as well. They measured phase shifts between ingoing waves and outgoing waves and found a difference between quiet and active regions. Their maps correlate sharply with the surface magnetic field. According to Chou (2000 ), the phase shifts represent the phase perturbation accumulated along the wave path, which can be due to a change in the phase velocity, wave path, but also magnetic field and changes in the mode cavity. Figure 50

shows phase-shift maps focusing at the solar surface obtained with TON data (Chou et al., 1999

). The maps confirm the original findings obtained with Hankel analysis. The acoustic imaging technique is very similar to phase-sensitive holography based on the correlation between the egression and the ingression (Lindsey and Braun, 1997 ; Braun and Lindsey, 2000

, and Section 4.4). The two techniques give consistent results. Braun and Lindsey (2000

) report that the phase shifts (or reduced travel time perturbations) increase in amplitude like the logarithm of the surface magnetic flux density.

Figure 50:

Observed acoustic power maps, outgoing intensity maps, phase-shift maps, and envelope-shift maps focusing at the solar surface at $3 mHz$ (first row), $3.5 mHz$ (second row), $4 mHz$ (third row), $4.5 mHz$ (fourth row), and $5 mHz$ (fifth row). Gray scales at different frequencies are the same except in the envelope-shift map at $5 mHz$ , where the gray scale is 1.5 times larger. The envelope peak of the cross-correlation function provides information about wave travel time, associated with the group velocity along the wave path. The phase time of the cross-correlation function between ingoing and outgoing waves provides information about phase changes along the wave path, including the phase change at the boundaries of the mode cavity and flux tubes. From Chou et al. (1999 ).

The travel time perturbations below active regions was studied by Kosovichev et al. (2000

, 2001 ) using time-distance helioseismology. Mean travel times are usually interpreted in terms of wave speed. Kosovichev et al. (2000

) found that the absolute difference in wave-speed between a sunspot (AR 8131) and the quiet Sun is up to $1 km s- 1$ . For reference, the quiet Sun sound speed is about $20 km s-1$ at a depth of $4 Mm$ and $35 km s-1$ at $10 Mm$ . The relative change in the squared sound speed is about $2 2 dc /c -~ - 0.1$ at a depth of $4 Mm$ , which they say would correspond to a 10% temperature decrease. At greater depths ( $7 -15 Mm$ ), the sound-speed perturbation switches sign and becomes positive. This increase in sound-speed could be due to a temperature change or the direct effect of the magnetic field. The perturbations vanish at depths greater than $15 Mm$ , which may be an indication of the depth extent of active regions or perhaps of the poor resolution of the inversions there. Kosovichev et al. (2000

) also detected the presence of narrow sound-speed anomalies (termed ‘fingers’) that connect internally the sunspot with two nearby pores (confirmed by Couvidat et al., 2004 ). Kosovichev and colleagues studied several other active regions, including AR 9393 which was seen on the disk for more than 3 months in 2001 (with a different name at each disk passage). The sound-speed perturbations under this giant active region are shown in Figure 51

(movie).

Figure 51:

Wave speed perturbation associated with the active region AR 9393. The positive values are shown in red and the negative ones in blue. The movie shows the evolution of the wave speed perturbation from March 25 until April 1, 2001. Courtesy of A.G. Kosovichev.

Surface Doppler velocity measurements are not always reliable in highly magnetized regions. Following a suggestion by Duvall Jr (1995 ), Duvall Jr and Kosovichev (2001

) have implemented a travel time averaging scheme to focus below a sunspot without using surface measurements directly inside the sunspot. This is achieved by considering all the rays that intersect at a target location in the solar interior (deep focusing technique). The standard and deep-focusing time-distance techniques seem to give consistent measurements of wave-speed perturbations (Duvall Jr and Kosovichev, 2001 ). Another way to avoid contamination is to perform sound-speed inversions of selected travel times that involve only data outside sunspots (Zhao and Kosovichev, 2003b ). Figure 52

shows a comparison of sound-speed inversions below a sunspot obtained with and without cropping the data in the sunspot (GONG data; Hughes et al., 2005

). The results are qualitatively similar in the two cases, i.e., the sign of the sound-speed perturbation as a function of depth is preserved. General agreement is also found between GONG and MDI for both travel times (Rajaguru et al., 2004 ) and inversion results (Hughes et al., 2005

Figure 52:

Horizontal slices through the inferred sound-speed perturbations under a sunspot using GONG data. From top to bottom the rows correspond to the depth ranges $1.7 -2.3 Mm$ , $3.6- 4.4 Mm$ , $6.2- 7.3 Mm$ , and $8.5 -9.8 Mm$ . The inversion results for uncropped (left column) and cropped data (right column) are qualitatively similar. From Hughes et al. (2005 ).

Kosovichev et al. (2000

) studied the emergence in time of an active region. Their results show that the wave-speed perturbations rise very fast across the upper $18 Mm$ of the convection zone. An analysis for $2 hr$ time steps suggests that the emerging magnetic flux travels the upper $10 Mm$ in less than $2 hr$ , implying a minimum speed of $1.3 km s- 1$ . Jensen et al. (2001 ) inferred the wave-speed structure beneath the same emerging active region using an inversion technique based on Fresnel-zone sensitivity kernels, as opposed to ray-based kernels. Their results are similar to those of Kosovichev et al. (2000

Using local mode frequency differences between active and quiet Sun regions measured with the ring-diagram technique (see, e.g., Hindman et al., 2000 ; Rajaguru et al., 2001 ), Basu et al. (2004 ) performed structure inversions to estimate the sound speed and adiabatic index in active regions. The results are for regions with horizontal size $o 15$ and $7$ -day averages. An attempt was made to remove the uncertainty in the modelisation of the surface layers (Section 4.2.3): inversions do not provide information for depths less than $1 Mm$ . The uncertainties in modeling the surface layers were ’removed’ in this process (Section 4.2.3), such that no reliable information at depths of less than $1 Mm$ could be extracted.

The relative difference of the sound speed between active and quiet regions is plotted in Figure 53 for 12 different active regions. For active regions with strong magnetic fields, a reduction in sound-speed is observed in the upper layers (for depths less than, say, $7 Mm$ ). At greater depths, the sound speed is increased relative to the quiet Sun. This is consistent with the work of Kosovichev et al. (2000 ) based on time-distance helioseismology. The amplitude of the perturbations are much smaller here than in the time-distance case simply because the magnetic region covers only a few percent of the area of ring-diagram analysis. Because the analysis of Basu et al. (2004 ) is based on the physics of normal modes, it provides an independent check of the results obtained using time-distance helioseismology.

Figure 53:

Relative differences of the squared sound speed between active and quiet regions obtained by inverting the frequency differences measured using ring-diagram analysis. The blue solid line shows the RLS inversion results, with the blue dotted lines showing the 1 $s$ error limit. The red points are the SOLA (Subtractive OLA) inversion results. The vertical error bars are the 1 $s$ error, and the horizontal error bars mark the distance between the quartile points of the averaging kernels and are a measure of the resolution of the inversions. The magnetic field strengh in each panel is a local magnetic activity index. From Basu et al. (2004

The wave-speed anomalies below sunspots could be caused by a variety of physical effects, for example thermal and magnetic perturbations. It has not been possible to disentangle these effects yet. The low sound-speed regions just below the surface have been attributed to a smaller temperature (Kosovichev et al., 2000 ; Basu et al., 2004

). On the other hand, the higher wave speeds measured at a depth of $10 Mm$ below sunspots are unlikely to be due only to the direct effect of the magnetic field (or it would imply very large field strengths of a several tens of $kG$ ). The likely cause is a combination of magnetic and structural/thermal effects (Brüggen and Spruit, 2000 ; Basu et al., 2004 ). Barnes and Cally (2001 ) and Cally et al. (2003 ), however, have questioned the interpretation of travel time anomalies in terms of linear perturbations to the wave speed. Their numerical simulations of wave propagation through a model sunspot have been able to reproduce the phase shifts measured by Hankel analysis without the need for a thermal perturbation. This stresses the need for a proper solution of the forward problem of time-distance helioseismology in sunspots.

Lindsey and Braun (2003 ) argued that strong magnetic fields near the photosphere introduce large phase shifts in waves passing upwards into the photosphere of active regions and termed this effect the “showerglass” effect. They argue that the showerglass makes measurements of local variations in the subsurface more difficult, and thus attempts should be made to correct for this effect before inverting for subphotospheric structure and flows. Measurements of the showerglass were made by Lindsey and Braun (2003 ), and in more detail by Lindsey and Braun (2005a ). In both cases the local egression and ingression control correlations (Section 4.4.3) were computed in active regions using MDI data. Maps of the phase and amplitude of the control correlations showed a clear relationship with the line-of-sight magnetograms, suggesting that the surface magnetic field was altering the amplitudes and phases of the waves used to compute the control correlation. Lindsey and Braun (2005b ) used the measurements of the phase shifts of Lindsey and Braun (2005a ) to correct the data before doing phase-sensitive holography (Section 4.4.5). They suggest that with the effect of near-surface magnetic field removed there is no clear evidence for sound-speed perturbations at depths greater than $5 Mm$ below a sunspot and that the effect of strong photospheric magnetic field on local helioseismic measurements should be studied further.

5.2.6 Far-side imaging

The first observational results from far-side helioseismic holography are due to Lindsey and Braun (2000b ). Their results showed that active regions on the far-side of the Sun introduce travel time deficits compared to the quiet Sun of order ten seconds. The demonstration by Lindsey and Braun (2000b ) that far-side imaging was practical is important for space weather predictions, as it allows about a week of warning before an active region will be seen at the East limb. Braun and Lindsey (2001 ) expanded the original idea presented by Lindsey and Braun (2000b ) to allow imaging not just of the central region of the far-side of the Sun, but also the regions nearer to the limb. Daily far-side images computed from MDI data are available from the web at http://soi.stanford.edu/data/farside/. Figure 55 shows far-side images computed by Braun and Lindsey (2001 ) for subsequent days together with magnetograms for the visible part of the disk. Active regions seen on the far-side can be seen in the synoptic magnetogram of the subsequent Carrington rotation. Figure 54 and the companion movie show simultaneously the front-side and farside of the Sun during the period March-June 2001 which saw the evolution of AR 9393.

Figure 54:

Movie showing far-side and front-side images of the Sun from March to June 2001. The large activity complex AR 9393 is seen for several rotation periods. The horizontal axis spans all longitudes measured in the Carrington frame of reference. The fuzzy image shows shorter wave travel times (in red) caused by active regions located on the far-side of the Sun. The Earth-side image of the Sun shows continuum intensity (active regions appear as red/dark shades).

Figure 55:

Composite images of SOHO/MDI magnetograms and far-side images made using SOHO/MDI Doppler data. The magnetograms have a higher spatial resolution. The boundary in the far-side images is where the algorithm is switched from two-skip/two-skip imaging, used to image in center of the far-side, to three-skip/one-skip imaging used further from the antipode of the visible disk. See Figure 27

for a diagram of the geometry. The color scale for the far-side images shows the time delay between the egression and the ingression. The sign of the signal in active regions is of the sense of faster propagation time underneath active regions. The top four panels show the far-side images for 1999 April 22-25. The bottom panels shows the magnetogram for Carrington rotation 1999 May 1-28. From Braun and Lindsey (2001 ).

The sign of the travel time perturbation associated with active regions seen by far-side imaging is consistent with increased wave speeds or shorter paths traveled by the waves. This is consistent with the results of phase-sensitive holography of plage regions on the visible disk (see, e.g., Braun and Lindsey, 2000 ) and may be related to the observed solar cycle variation of normal mode frequencies (see, e.g., Lindsey and Braun, 2000b , and references therein).

5.2.7 Excitation of waves by flares

Kosovichev and Zharkova (1998 ) used data from the SOHO/MDI instrument (Scherrer et al., 1995 ) to make the first clear observations of a helioseismic wave produced by a flare. A roughly circular wave front, though with not insignificant quadrupole component, was seen emerging from the location of the now famous Bastille Day flare, an X-class flare of 1996. The wave packet was seen out to a distance of $120 Mm$ from the source and took about $55 min$ to travel that distance (see Figure 56 ). Earlier attempts using ring diagrams (Haber et al., 1987 ) and Hankel analysis (Braun and Duvall, 1990 ) reported small, but not significant, variations of the p-mode signal in flaring regions.

Later, Donea et al. (1999 ) used acoustic power holography (see Section 4.4.4) of SOHO/MDI data to investigate the same flare as was studied by Kosovichev and Zharkova (1998 ). The acoustic power holography showed that the wave source was strongest around $3 mHz$ , though the signal-to-noise ratio was higher around $6 mHz$ . The signal in the $6 mHz$ band appeared about $4 min$ after the signal in the $3 mHz$ band. Donea and Lindsey (2004 ) found significant acoustic power signatures associated with two other flares and showed a possible connection between the fine-scale spatial structure of the acoustic power maps and motions of the footpoints of the flaring loops. We note that detection of flare-induced acoustic waves using ring-diagram analysis has been claimed by Ambastha et al. (2003 ).

The basic mechanism by which a flare excites helioseismic waves is not entirely clear. Wolff (1972 ) suggested that the energy released in the flare heats the atmosphere, the expansion of which in turn causes a downward propagating wave. Zharkova and Kosovichev (1998 ) argue, on the basis of the momentum needed to explain the observed Bastille Day flare wave amplitude, that the shock wave created by chromospheric evaporation may not be the complete explanation and suggested that perhaps momentum transfer by electron or proton beams impacting directly on the photosphere may be important. Zharkova and Kosovichev (2001 ) argued that electron beams can carry sufficient momentum to explain the observed amplitude of the helioseismic wave caused by the Bastille Day flare.

A separate issue is the mechanism that leads to the initiation of solar flares. The contribution of local helioseismology to this problem has been rather poor so far. We note that Dzifčáková et al. (2003 ) have searched for a relationship between the evolution of subsurface flows and flaring activity.

Figure 56:

Remapped and filtered MDI Dopplergram $25 min$ after the Bastille Day flare. The flare signal was extracted, enhanced by a factor of 4, and then superimposed on the Dopplergrams. The movie shows the temporal evolution of the signal. From Kosovichev and Zharkova (1998 ).