Photospheric Flows and Solar Flares

1
Photospheric Flows and Solar Flares

• Brian T. Welsch1,
• Yan Li1,
• Peter W. Schuck2,
• George H. Fisher1
• 1Space Sciences Lab,
• UC-Berkeley
• 2Naval Research Lab, Washington, D.C.

2
Why investigate correlations between photospheric
magnetic field flares/CMEs?

• Its the coronal field that drives flares/CMEs
• but, when not flaring, coronal magnetic
  evolution is nearly ideal ? connectivity is
  preserved.
• Coronal Bc is thus coupled to the photospheric
  Bp.
• So Does Bp have anything to do with
  flares/CMEs?
• Leka Barnes (2007) 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.

3
Magnetic evolution at the photosphere is
apparently steady.

• Magnetograms of AR 8210 from MDI over 24 hr. on
  01 May 1998 show no drastic field changes.
• Proper motions are 1 km/s.

4
Meanwhile, in the corona

• an M-class flare halo CME occurred.
• Q What can we learn from photospheric evolution?

5
The evolution of the photospheric field is
expected to be correlated with flares/CMEs.

• Observations theory suggest converging and/ or
  shearing flows along polarity inversion lines
  (PILs) are relevant to flares/CMEs.
• Flux emergence is also likely to dramatically
  affect coronal evlution.
• Falconer et al. (2006) and Schrijver (2007)
  argue that the presence of strong-field PILs
  (SPILs) is related to flares/CMEs. Does
  flare/CME likelihood increase as SPILs form?

6
Also, photospheric flows can be used to drive
time-dependent models of the coronal field.

• The magnetic induction equations z-component
  relates footpoint motion u to dBz/dt (Demoulin
  Berger 2003).
• ?Bz/?t ? x (v x B) z - ? ? (u Bz)
• Flows v along B do not affect ?Bn/?t, but v
  contam-inates 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).

7
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
8
We studied flows u from MDI magnetograms and
flares from GOES for a few dozen active region
(ARs).

• NAR 46 ARs were selected.
• ARs were selected for easy tracking usu. not
  complex, mostly bipolar -- NOT a random sample!
• gt 2500 MDI full-disk, 96-minute cadence
  magnetograms from 1996-1998 were tracked, using
  both FLCT and DAVE separately.
• GOES catalog was used to determine source ARs for
  flares at and above C1.0 level.

9
Magnetogram Data Handling

• Pixels gt 45o from disk center were not tracked.
• To estimate the radial field, cosine corrections
  were used, BR BLOS/cos(T)
• Mercator projections were used to conformally
  map the irregularly gridded BR(?,f) to a
  regularly gridded BR(x,y).
• Corrections for scale distortion were applied.

10
FLCT and DAVE flow estimates were correlated, but
differed substantially.
11
FLCT and DAVE flow estimates were correlated, but
differed substantially.
12
To baseline the importance of field evolution, we
computed intensive and extensive properties of
BR.

• Intensive properties do not intrinsically grow
  with AR size
• - 4 statistical moments of average unsigned
  field BR, (mean, variance, skew, kurtosis),
  denoted M(BR)
• - 4 moments of M( BR2 )
• Extensive properties scale with the physical size
  of an AR
• - total unsigned flux, ? S BR da2 this
  scales as area A (Fisher et al. 1998)
• - total unsigned flux near strong-field PILs, R
• (Schrijver 2007), should scale as length L
• - sum of field squared, S BR2

13
We then quantified field evolution in many ways,
e.g.

• Un- and signed changes in flux, d?/dt, d?/dt.
• Change in R with time, dR/dt
• Changes in center-of-flux separation, d(?x)/dt,
  with
• ?x ? x-x-, and
• x ? ?da (x) BR ? ?da BR
• We computed intensive and extensive flow
  properties, too
• Moments of speed M(u), and summed speed, S u.
• M(?h u ) M( z ?h ? u), and their sums
• M(?h ( u BR)) M(z ?h ? ( u BR)), and their
  sums
• The sum of proxy Poynting flux, S u BR2
• Measures of shearing converging flows near PILs

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.
15
For some ARs in our sample, we auto-correlated
ux, uy, and BR, for both FLCT and DAVE flows.
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.
16
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.
17
Parametrization of Flare Productivity

• We binned flares in five time intervals, t
• time to cross the region within 45o of disk
  center
• 6C/24C the 6 24 hr windows 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
  window
• F (100 S(X) 10 S(M) 1.0 S(C) )/ t
• exponents are summed in-class GOES significands
• Our sample 154 C-flares, 15 M-flares, and 2
  X-flares

18
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), 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).
• No purely intensive quantities appear --- all
  contain extensive properties.

19
With 2-variable discriminant analysis (DA), we
paired S u BR2 head to head with each other
field/ flow property.

• 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.

20
Conclusions

• We found S u BR2 and R to be strongly associated
  with avg. flare flux and flare occurrence.
• S u BR2 seems to be a robust predictor
• - speed u was only weakly correlated with BR
• - S BR2 was also tested
• - using u from either DAVE or FLCT gave the same
  result.
• This study suffers from low statistics, so
  further study is needed. (A proposal to extend
  this work is being written!)
• The study of photospheric magnetic evolution is
  still very much a research topic. FLCT
  however

21
v. 1.01 of FLCT (Fisher Welsch 2008) is capable
of matching HMIs 10-minute magnetogram cadence.

• HMI magnetograms have Npix 40962 (p/4) pix.
• It takes 3 min. to track all 12 Mpix, skipping
  every fourth pixel, with windowing parameter s
  15 pix
• If we only track pixels within 60o of disk center
  and
• Br gt Bthresh 20 G, then tracking should
  take 1 min.
• We are working with the HMI Team at Stanford to
  port the FLCT codes C-version to the HMI / JSOC
  pipeline.
• http//solarmuri.ssl.berkeley.edu/fisher/public/
  software/FLCT/