How are photospheric flows related to solar flares?

1
How are photospheric flows related to solar
flares?

• Brian T. Welsch1,
• Yan Li1,
• Peter W. Schuck2,
• George H. Fisher1
• 1SSL, UC-Berkeley
• 2NASA-GSFC
• See also ApJ v. 705 p. 821

2
Preliminary Ideas

• We dont understand processes that produce flares
  and CMEs, but would like to.
• The coronal magnetic field BC powers flares and
  CMEs, but measurements of (vector) BC are rare
  and uncertain.
• The instantaneous state of the photospheric field
  BP provides limited information about the coronal
  field BC.
• Evolution of BP can reveal additional
  information about the coronal field BC.
• We used tracking methods (and other techniques)
  to quantitatively analyze photospheric magnetic
  evolution in a few dozen active regions (ARs).
• We found a proxy Poynting flux to be
  statistically related to flare activity. This
  association merits additional study.

3
Can the photospheric magnetic field BP be used to
empirically predict flares?

• Early idea big complex ARs are likely to
  produce flares. (Complex is tough to define
  objectively!)
• Kunzel 1960 d sunspots are more likely to flare
  than non-d sunspots.
• Hagyard et al., 1980s sheared fields along
  polarity inversion lines (PILs) are associated
  with flare activity
• Falconer et al., 2000s Both shear and flares are
  associated with strong gradient PILs

4
The instantaneous photospheric magnetic field
vector BP isnt very useful for predicting flares.

• Leka Barnes (2007) studied 1200 vector
  magnetograms, and considered many quantitative
  measures of AR field structure.
• They summarize nicely We conclude that the
  state of the photospheric magnetic field at any
  given time has limited bearing on whether that
  region will be flare productive.

5
Can we learn anything about solar flares from the
evolution of the photospheric magnetic field BP?

• The coronal magnetic field BC powers flares and
  CMEs, but measurements of (vector) BC are rare
  and uncertain.
• When not flaring, coronal magnetic evolution
  should be nearly ideal ? connectivity with
  photosphere is preserved.
• As BP evolves, changes in the coronal field BC
  are induced.
• Further, following active region (AR) fields in
  time can provide information about their history
  and development.

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Assuming BP evolves ideally (see Parker 1984),
then photospheric flow and magnetic fields are
coupled.

• The magnetic induction equations normal
  component relates apparent motion u to dBn/dt
  (Demoulin Berger 2003).
• ?Bn/?t ? x (v x B) n - ? ? (u Bn)
• Flows v along B do not affect ?Bn/?t, but v
  contaminates Doppler measurements, diminishing
  their utility.
• Many optical flow methods to estimate u have
  been developed, e.g., LCT (November Simon
  1988), FLCT (Welsch et al. 2004), DAVE (Schuck
  2006).

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The apparent motion of magnetic flux in
magnetograms is the flux transport velocity, uf.
Démoulin Berger (2003) In addition to
horizontal flows, vertical velocities can lead to
uf ?0. In this figure, vhor 0, but vn ?0, so uf
?0.

• uf is not equivalent to v rather, uf ? vhor -
  (vn/Bn)Bhor
• uf is the apparent velocity (2 components)
• v? is the actual plasma velocity (3 comps)
• (NB non-ideal effects can also cause flux
  transport!)

8
Aside Doppler shifts cannot fully determine v

• Generally, Doppler shifts cannot distinguish
  flows to B (red), perp. to B (blue), or in an
  intermediate direction (gray).
• With v? estimated another way projected onto
  the LOS, the Doppler shift determines v
  (Georgoulis LaBonte, 2006)
• Doppler shifts are only unambiguous along
  polarity inversion lines, where Bn changes sign
  (Chae et al. 2004, Lites 2005).

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Dopplergrams are sometimes consistent with
siphon flows moving along the magnetic field.

• Left MDI Dopplergram at 1912 UT on 2003
  October 29 superposed with the magnetic neutral
  line. Right Evolution of the vertical shear flow
  speed calculated in the box region of the left
  panel. The two vertical dashed lines mark the
  beginning and end of the X10 flare. (From Deng
  et al. 2006)

10
Photospheric electric fields can affect
flare-related magnetic structure in the corona.

• Since E -(v x B)/c, the fluxes of magnetic
  energy helicity across the photosphere depend
  upon v.
• ?tU c ? dA (E x B) n / 4p
• ?tH c ? dA (E x A) n / 4p
• BC ? BP coupling means the surface v provides an
  essential boundary condition for data-driven MHD
  simulations of BC. (Abbett et al., in progress).
• Studying v could also improve evolutionary models
  of BP , e.g., flux transport models.

11
We studied flows u from MDI line-of-sight (LOS)
magnetograms from NAR 46 active regions (ARs).

• ARs were mostly bipolar ? NOT a random sample!
• The radial field BR was estimated via BR
  BLOS/cos(T)
• Magnetograms were reprojected to compensate for
  distortion by foreshortening.
• We tracked gt 2500 MDI full-disk, 96-minute
  cadence magnetograms from 1996-1998, using both
  FLCT and DAVE separately.

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Fourier local correlation tracking (FLCT) finds
v( x, y) by correlating subregions, to find local
shifts.




4) ?x(xi, yi) is inter- polated max. of
correlation funct
1) for ea. (xi, yi) above Bthreshold
2) apply Gaussian mask at (xi, yi)
3) truncate and cross-correlate
13
FLCT and DAVE flow estimates are correlated, but
differ significantly.
When weighted by the estimated radial field
BR, the FLCT-DAVE correlations of flow
components were gt 0.7.
14
For both FLCT and DAVE flows, speeds u were not
strongly correlated with BR --- rank-order
correlations were 0.07 and -0.02, respectively.
The highest speeds were found in weak-field
pixels, but a range of speeds were found at each
BR.
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To baseline the importance of field evolution to
previous results, we also analyzed properties of
BR.

• Total unsigned flux, ? S BR da2
• ? is strongly correlated with flaring (Leka
  Barnes 2007)
• Total unsigned flux R near strong-field polarity
  inversion lines (PILs), where BR changes sign
• Schrijver (2007) found R to be correlated with
  flaring
• (R to the LSG measure from Falconer et al.
  2003, 2006)
• Total of field squared, S BR2
• and many, many more properties of BR!

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We then quantified field evolution in many ways,
e.g.

• Changes in flux, d?/dt.
• Change in R with time, dR/dt
• Means variances of speed u summed speed, S u.
• Mean and total (?h u ) ( z ?h ? u)
• A proxy Poynting flux, SR S u BR2
• Measures of shearing converging flows near PILs

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For some ARs in our sample, we auto-correlated
ux, uy, and BR, for both FLCT and DAVE flows.
tcorr 6 hr.
BLACK shows autocorrelation for BR thick is
current-to-previous, thin is current-to-initial.
BLUE shows autocorrelation for ux thick is
current-to-previous, thin is current-to-initial.
RED shows autocorrelation for uy thick is
current-to-previous, thin is current-to-initial.
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Parametrization of Flare Productivity

• We binned flares in five time intervals, t
• time to cross the region within 45o of disk
  center (few days)
• 6C/24C the 6 24 hr windows (Longcope et al.
  2005, Schrijver et al. 2005) centered each flow
  estimate
• 6N/24N the next 6 24 hr windows after 6C/24C
• Following Abramenko (2005), we computed an
  average GOES flare flux µW/m2/day for each time
  interval
• F (100 S(X) 10 S(M) 1.0 S(C) )/ t
• exponents are summed in-class GOES significands
• Our flare sample 154 C-flares, 15 M-flares, and
  2 X-flares

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Correlation analysis showed several variables
associated with flare flux F. This plot is for
disk-passage averaged properties.

• Field and flow properties are ranked by distance
  from (0,0), the point of complete lack of
  correlation.
• Only the highest-ranked properties tested are
  shown.
• The more FLCT and DAVE correlations agree, the
  closer they lie to the diagonal line (not a fit).

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We also used discriminant analysis (DA) to
identify the strongest predictors of GOES flares
gt C1.0 class.

• Given one input variable, DA finds the optimal
  point between the flaring and quiet populations.
• (Linear DA assumes Gaussian distributions and
  dichotomous pop-ulations --- not very accurate
  here!)

Standardized proxy Poynting flux, SR S u BR2
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The distributions of other variables and their
correponding discriminant results look different!

• The Gaussian assumption seems even less
  applicable here!
• We are exploring non-parametric methods for
  quantifying correlations between magnetic
  variables and flare activity.

Standardized Strong-field PIL Flux R
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Reliability plots characterize the accuracy of
forecasts based upon a discriminant function.

• Such plots compare the predicted and observed
  event frequencies.
• A good model will follow the 45o line.
• Underpredictions (failed all clear
  predictions) lie above the dotted line.
• This underpredicts in low and high probability
  ranges.

Proxy Poynting flux, SR S u BR2
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Reliability plots for discrimination using the
strong-field PIL flux R also show imperfect
forecasting.

• This model under-predicts (makes failed at all
  clear forecasts) in the low-probability range,
  and over predicts in the high-probability range.

Strong-field PIL Flux, R
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Given two input variables, DA finds an optimal
dividing line between the flaring and quiet
populations.

• The angle of the dividing line can indicate
  which variable discriminates most strongly.
• Blue circles are means of the flaring and quiet
  populations.
• (With N input variables, DA finds an N-1
  dim-ensional surface to partition the
  N-dimen-sional space.)

Standardized Strong-field PIL Flux R
Standardized proxy Poynting flux, SR S u BR2
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Many of the variables correlated with average
flare SXR flux were correlated with each other.

• Such correlations had already been found by many
  authors.
• Leka Barnes (2003a,b) used linear discriminant
  analysis to find variables most strongly
  associated with flaring.

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We used discriminant analysis to pair field/ flow
properties head to head to identify the
strongest flare associations.

• For all time windows, regardless of whether FLCT
  or DAVE flows were used, DA consistently ranked S
  u BR2 among the two most powerful discriminators.

28
Total unsigned AR flux ? is correlated with
average flare SXR flux.

• Some studies relating magnetic properties with
  flares have not taken this underlying correlation
  into account.

29
Is rapid magnetic evolution correlated with flare
activity?

• We computed the current- to- initial frame
  autocorrelation coefficients for all ARs in our
  sample, and fit their decay rates.

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We found that rapid magnetic evolution is
anti-correlated with ? --- but ? is correlated
with flares!

• Hence, rapid magnetic evolution, by itself, is
  anti-correlated with flare activity.

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We made head to head comparisons of SRS u BR2
with other variables using two-variable
discriminant functions.
For most time windows, SRS u BR2 had the
greatest power to discriminate between flaring
and quiet populations.

• The strong-field PIL flux R was also a powerful
  predictor it was the strongest in a few time
  windows.
• The areas that contributed most strongly to the
  sum S u BR2 are away from PILs suggesting u BR2
  and R are physically distinct.

Grayscale u BR2. Contours BR
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Conclusions

• We found SRS u BR2 and R to be strongly
  associated with
• average flare soft X-ray flux and flare
  occurrence.
• - both can discriminate flaring/ quiet regions
  independently
• - their spatial distributions differ.
• S u BR2 seems to be a robust predictor
• - speed u was only weakly correlated with BR
• - S BR2 was independently tested
• - using u from either DAVE or FLCT gave similar
  results.
• The association with S u BR2 suggests that ARs
  that are both rapidly evolving and large are
  flare-prone.
• This study suffers from low statistics further
  study is needed. (You might soon review a
  proposal to extend this work!)