Using HMI to Understand
Flux Cancellation
by Brian Welsch1, George Fisher1, Yan Li1, and Xudong Sun2
Cancellation of magnetic flux in magnetograms has been defined in observational terms as "the
mutual apparent loss of magnetic flux in closely spaced features of opposite polarity."
Physically, this removal of flux could correspond to one of three mechanisms: (i) the emergence of
U-shaped magnetic loops, (ii) the submergence of Omega-shaped loops, or (iii) reconnection in the
magnetogram layer.
Evidence has been reported for all three of these mechanisms, but does one predominate?
We can investigate cancellation mechanisms at work in an active region's magnetic fields using timeaveraged Doppler shifts along polarity inversion lines (PILs) of the line-of-sight (LOS) magnetic field
near disk center. Along these PILs, the LOS component of the magnetic field vanishes, so LOS flows
inferred from Doppler shifts are perpendicular to the magnetic field. If the evolution is ideal, such
flows imply the transport of magnetic flux across the atmospheric layer imaged in the
magnetogram.
As a preliminary step in our study, we present an innovative method to remove biases in the
measured Doppler velocities due to offset in the line-center position, which might arise from a wellknown correlation between brightness and blueshifts in the convecting photospheric plasma
1Space
Sciences Lab, UC-Berkeley, 2Stanford University
Q: How is flux removed from the photosphere?
• Each 11-year cycle, c. 3000 active regions,
each with c. 1022 Mx, emerge.
• What processes remove all this flux?
• The short answer is CANCELLATION --- the
“mutual apparent loss of flux in closely spaced
magnetogram features of opposite polarity”
(Livi et al. 1985)
Q: But what is cancellation?
Cancellation could be any of three processes:
Doppler shifts on PILs can distinguish between these!
Q: Which process predominates in active regions?
Which model more accurately describes the Sun?
Changes in LOS flux are quantitatively related to PIL
Doppler shifts multiplied by transverse field strengths.
From LOS m’gram:
LOS
   x 2 [BLOS (t f )  BLOS (t i )] (Eqn. 1)
t
near PIL
From Faraday’s law,


 c  da (  E)  nˆ 
t
 da ( (v  B)) nˆ
Since flux can only emerge or submerge at a PIL,

PIL
  lˆ  (v LOS  B transverse )
t
PIL
(Eqn. 2)
Summed Dopplergram and transverse field
along PIL pixels.
Inthe absence of errors, ΔΦLOS/Δt =ΔΦPIL/Δt.
Let’s test the method with HMI data!
An automated method (Welsch & Li 2008) identified PILs in a
subregion of AR 11117. Note predominance of redshifts.
Problem: We must remove the convective blueshift!
HMI’s Doppler shifts are not absolutely
calibrated! (Helioseismology uses time
differences in Doppler shifts.)
There’s a well-known intensity-blueshift
correlation, because rising plasma
(which is hotter) is brighter (see, e.g.,
Gray 2009; Hamilton and Lester 1999; or
talk to P. Scherrer).
Because magnetic fields suppress
convection, lines are redshifted in
magnetized regions.
From Gray (2009): Bisectors for 13 spectral
lines on the Sun are shown on an absolute
velocity scale. The dots indicate the lowest
point on the bisectors. (The dashed
bisector is for λ6256.)
Lines formed deeper in the atmosphere,
where convective upflows are present, are
blue-shifted.
So we must calibrate the bias in the zero-velocity v0 in
estimated Doppler shifts before we can study cancellation.
From Eqn. 2, a bias velocity v0 implies
apparent PIL v 0 PIL



 v 0 (lˆ  Btransverse )  ˆl
t
t
t
t
PIL
BL
:= “magnetic length” of PIL
But ΔΦLOS should match ΔΦPIL, so we can solve for v0:
apparent  
bias
LOS
v0 

t BL
t BL
(Eqn. 3)
NB: v0 should be the SAME for ALL PILs ==> solve statistically!
We have solved for v0 using data from > 100 PILs in
three successive magnetogram triplets from Fig. 3.
Incorporating error bars on estimates of ΔΦ’s is still a work in
progress; ideally, we’d estimate v0 using total least squares.
The inferred offset velocity v0 can be used to
correct Doppler shifts along PILs.
Conclusions
• We have demonstrated a method to correct
the bias velocity v0 in HMI’s Doppler velocities
from convective-blueshifts.
• Using v0-corrected Doppler data, we can study
flux cancellation in active regions, to
determine which physical process underlies
cancellation.
Future Work
• Incorporate error bars on estimates of ΔΦ’s and
magnetic lengths, and investigate estimation of v0
via total least squares.
– Errors are present in both magnetic lengths and ΔΦ’s.
• Actually investigate cancellation!
– Investigate statistics of cancellation mechanisms in
both active regions (and quiet sun).
– Extrapolate flux submergence rates over solar cycle
(and quiet Sun flux turnover time) to constrain flux
recycling in solar cycle (and quiet sun) dynamo.