alx-ai/arxiv_papers · Datasets at Hugging Face

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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 s1by 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 s1corresponds
to an angular velocity of 2 :5day1or a typical tangential velocity of 10 m s1.
(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 s1. 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

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 s1by 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 s1corresponds

to an angular velocity of 2 :5day1or a typical tangential velocity of 10 m s1.

(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 s1. 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