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to bottom) from a 2D horizontal inversion, plotted at the depths corresponding |
to the mean depth of the respective averaging kernels. The one-sigma level of |
random noise in uzis equal to 10 m s 1by construction (horizontal black lines). |
Adapted from Jackiewicz, Gizon & Birch (2008).Local Helioseismology 43 |
Figure 13: (Left) Map of the average MDI/SOHO line-of-sight component of the |
magnetic eld in the Sun's photosphere for the 107 hr period starting 06:59 UT |
on 2003 January 6. (Middle) Map of phase travel time (Finsterle et al. 2004b) for |
magnetoacoustic waves with frequencies near 3 mHz based on contemporaneous, |
simultaneous Doppler velocity data of the full solar disk as viewed at 5890 A |
(Na) and 7699 A (K). (Right) Magnied views of two regions of the phase-travel- |
time map overlaid with an estimate of the location of the boundaries of the |
supergranular-scale convective cells as determined using a segmentation of the |
mean intensity image at 5890 A. Note that there is not a signicant travel-time |
signal in all of the observed plages, only in regions where the eld is highly |
inclined. This signal is noticeably larger than that in the boundaries of the |
supergranules. This is probably due to the larger magnetic lling factor in the |
plage. Figure and caption from Jeeries et al. (2006).44 Gizon, Birch & Spruit |
Figure 14: Eect of the Coriolis force on supergranulation |
ows. ( a) Vertical |
vorticity (curl) averaged over regions with positive horizontal divergence ( hcurli+, |
blue curve) and negative horizontal divergence ( hcurli , red curve) as functions |
of sin() |
()= |
eq, whereis the heliographic latitude and |
= |
eqis the local |
surface angular velocity relative to the equator. A vorticity of 1 M s 1corresponds |
to an angular velocity of 2 :5day 1or a typical tangential velocity of 10 m s 1. |
(b) Horizontal average hcurl diviversus sin() |
()= |
eq. Adapted from Gizon & |
Duvall (2003). |
Figure 15: Moat |
ow around the sunspot in AR 9787 (see Figure 2 ) using the |
same time-distance inversion as in Figure 12a. The background colors show the |
MDI line-of-sight component of the magnetic eld. The depth is 1 Mm and the |
observation time is T= 1 day. The random noise in each horizontal component |
of the |
ow is estimated to be 17 m s 1. Adapted from Gizon et al. (2009) by |
Jason Jackiewicz.Local Helioseismology 45 |
Figure 16: Wave-speed perturbations under sunspots relative to quiet Sun. The |
perturbations are measured along sunspot axes except for the case of (unresolved) |
ring-diagram analysis. The solid red line shows a phenomenological model based |
on the Fourier-Hankel analysis of the sunspot in active region NOAA 5254 dur- |
ing 27 { 30 November 1988 (Fan, Braun & Chou 1995). The dashed red curve |
shows the fast wave speed, cf= (c2+a2)1=2, in NOAA 5254 from the forward |
model of Crouch et al. (2005) that consists of nested magnetic cylinders. The |
green and solid blue lines give the wave-speed perturbations under the sunspot in |
active region NOAA 9787 inferred from ring-diagram analysis and time-distance |
helioseismology using phase-speed lters (Gizon et al. 2009). The same tracked |
patch (diameter 15) was analyzed in both cases. The sunspot is not spatially |
resolved in the ring analysis: a factor of ten is applied to improve the comparison. |
This active region, which includes a long-lived sunspot and surrounding plage, |
was observed by SOHO/MDI during 20-27 January 2002. The two analyses give |
inconsistent estimates of the subsurface wave-speed perturbations averaged over |
the 15patch. Possible explanations for this disagreement are described in the |
text. The dashed blue line is the fast wave speed of the semi-empirical model of |
Cameron et al. (2009, submitted), based on the umbral model of Maltby et al. |
(1986) and discussed in Figure 17 . The black curve is the fast wave speed from |
the radiative MHD numerical simulation of Rempel et al. (2009).46 Gizon, Birch & Spruit |
Figure 17: Sunspot time-distance helioseismology and forward numerical modeling. The |
top panel shows the observed covariance, C(r;t) =R |
dt0(t0)(r;t0+t), between the MDI |
Doppler velocity averaged over the red line ( L) atx= 40 Mm,(t0), and the Doppler |
velocity delayed by t= 130 min, (r;t0+t). The horizontal coordinates r= (x;y) are |
centered on the sunspot. The color scale is such that positive values of Care red and |
negative values are yellow. The two red circles indicate the boundaries of the umbra and |
penumbra of the sunspot in Active Region 9787. The Doppler observations were ltered |
to select only the p 1acoustic modes. To reduce noise, the cross-covariance was averaged |
over nine days (20{28 January 2002) and over angles using the azimuthal symmetry of |
the sunspot. The panel below shows the numerical simulation from Figure 11 , except |
that the vertical component of velocity, vz, is now shown. The initial conditions were |
chosen such that vzmatches the observed cross-covariance in the far eld. The observed |
Cand the simulated vzare averaged over 2:5 Mm< y < 2:5 Mm and plotted as |
function of x. The simulation provides a good match in phase and amplitude with the |
observations, for this particular model sunspot. The bottom panel shows the simulated |
vzin thex{zcut through the sunspot. The vertical scale is given in units of Mm and |
thea=clevel is shown by the blue curve. See Supplemental Movie 8 . A similar |
analysis was performed by Cameron, Gizon & Duvall (2008) for f-mode wave packets.Local Helioseismology 47 |
Figure 18: Synoptic map of local horizontal |
ows in the top 2 Mm below the |
solar surface, obtained with f-mode time-distance helioseismology. The horizontal |
and vertical axes give the longitude and the latitude in heliographic degrees. The |
data were averaged in time (7 days) in a frame of reference that co-rotates with |
the Sun (Carrington rotation rate). The |
ow maps were further processed to |
remove the average dierential rotation and meridional |
ow. The gray scale |
gives the relative change in f-mode travel times: reduced travel times correlate |
with magnetic activity. Adapted from Gizon, Duvall & Larsen (2001).48 Gizon, Birch & Spruit |
Figure 19: Daily averages of the horizontal |
ows around active region NOAA |
9433 from 23 April until 26 April 2001 (one column for each day) inferred from |
ring-diagram analysis (Haber et al. 2004). The depths shown are 2 Mm (top |
row), 7 Mm (middle row) and 14 Mm (lower row). The green and red shades are |
for the two polarities of the surface magnetic eld (MDI magnetograms). The |
transition between in |
ow and out |
ow occurs near 10 Mm depth.Local Helioseismology 49 |
Figure 20: Anti-symmetric component of the near-surface meridional |