SH13A-2243: Evolution of the Photospheric Vector Magnetic Field in HMI Data

by Brian T. Welsch & George H. FisherSpace Sciences Lab, UC-Berkeley

We discuss aspects of magnetic field structure and evolution in HMI data, including artifacts of the observation procedure and data reduction, and characterization of noise in the magnetic variables and their rates of change.

We analyzed vector magnetograms of AR 11158, from the first “test” data released by the HMI Team.

Left: full-disk line-of-sight (LOS) magnetogram. Right, clockwise from top left: BLOS, vDoppler, Bx, and By.

We discuss two artifacts: (1) Flipping azimuths and (2) convective blueshifts. Topic #1 first:

The direction of the magnetic vector Btrs transverse to the LOS --- its azimuth --- is ambiguous by 180o.

– An algorithm is used by the HMI Team to resolve this “180o

ambiguity” in field azimuth. – Ambiguities are resolved for each vector magnetogram

independently of previous and subsequent m’grams.

– Among other factors, the algorithm minimizes current by favoring field alignment in neighboring pixels.

– The algorithm is non-local: azimuths in neighborhoods are coupled.

We identified and “fixed” back-and-forth flips in azimuth, which are likely due to errors in resolving the 180o ambiguity.

From left to right, 1st column: 100 x 100 pixel patches of transverse-field azimuths (color wheel in top panel) from seven successive vector magnetograms (separated by 12 minutes), starting at 10:00UT on 2011/02/14. Time increases down. 2nd column: Difference in azimuth between current and previous maps (note different color wheel in top panel). Initial difference map is arbitrarily set to zero. 3rd column: Filtered versions of the azimuth maps (see below) in the 1st column, in which continuity in azimuths has been imposed (color wheel in top panel). 4th column: Difference in azimuth between current and previous filtered maps (color wheel in top panel). Back-and-forth flips in many pixels have been removed --- including in weaker-field areas at left edges.

Our method to identify & “fix” suspicious (not necess. wrong!) azimuth flips minimizes azimuth differences in time.

• But we first tried a few approaches that didn’t work, so here we describe what worked well for us.

• First, we identify large jumps in azimuth over one step that are followed by reversals to the pre-jump level over the next step. – “large” is a free parameter: we use 120o

• Next, we compared means of two azimuth differences: – (1) unsigned azimuth differences between frame i and ±2 frames – (2) the same differences, but with all pixels’ azimuths in frame i reversed

• Pixels for which flipping would decrease the mean, unsigned, frame-to-frame azimuth differences were then flipped.

• NB: Flipped azimuths are then used in subsequent computations of azimuths differences between successive frames (in frames -1 & -2).

A simple noise model, consistent with the observations, can be used to predict two-peaked histograms of Bx & By values.

Left: Distributions of observed of BLOS and Btrs are well fit by Gaussians.Right: A Gaussian in Btrs (displaced from zero, since Btrs is a magnitude) & random azimuths yields a distribution of Bx is double-humped.

For reasons we do not yet understand, our “corrections” systematically affect the distributions of Bx & By.

Left: As in the simplistic model, “uncorrected” distributions of Bx & By are double-peaked. Right: After “correcting” flipped azimuths, however, the distributions of Bx & By become single-peaked (or nearly so).

Conclusions, Topic #1• We found suspicious flips in azimuths in HMI data.

• When using the time rate of change of vertical current to estimate the photospheric electric field (e.g., Fisher et al. 2010), spurious changes in field azimuth will cause problems!

• We developed a straightforward automated procedure to identify and “correct” suspicious flips.– This changes numerous azimuths in weak-field pixels.

• These “corrections” affect the distributions of Bx & By; we’ still trying to understand why, and the implications of this fact.

Now Topic #2: The convective blueshift affects velocities in Dopplergrams!

Because rising plasma is (1) brighter (it’s hotter), and (2) occupies more area, there’s an intensity-blueshift correlation (talk to P. Scherrer!)

S. Couvidat: line center for HMI is derived from the median of Doppler velocities in the central 90% of the solar disk --- hence, this bias is likely present!

(Helioseismology uses time evolution of Doppler shifts, so such a bias doesn’t matter for that application.)

From

Dra

vins

et a

l. (1

981)

Line “bisector”

Because magnetic fields suppress convection, there are pseudo-redshifts in magnetized regions.

An automated method (Welsch & Li 2008) identified polarity inversion lines (PILs) of BLOS in AR 11158, color-coded by Doppler shift. Grayscale image shows BLOS, with PIL pixels color-coded by Doppler velocity. Grayscale saturation is set to ±100 Mx cm−2, and the velocity saturation is set to ±250 m sec−1. Note the predominance of redhsifted PILs.

11

The pseudo-redshift bias is evident in scatter plots of Doppler shift vs. |BLOS |.

• P. Scherrer (private communication) suggested the redshift was of the order of 1 m/s/G, based upon Wilcox Solar Observatory data (with poorer spatial resolution than HMI).

• HMI exhibits weaker trends.

12

Schuck (2010) also found the pseudo-redshift bias in MDI data.

Schuck’s trend of redshift with|BLOS |is also roughly ~0.2 m/s/G, but the net bias is much stronger in HMI, which reports higher field strengths.

Welsch & Fisher (2012) present a method to estimate the pseudo-redshift in active regions.

Flux only emerges (or submerges) along PILs. Here, flux (red field lines) is emerging along a PIL (dashed black line) due to an upflow along the PIL (green). By Faraday’s law changes in flux through the plane imply an electric field (from v x B) parallel to the PIL (blue).

• Ideally, changes in LOS flux and the rate of transport of transverse flux by Doppler velocites should agree.

• Any discrepancy could imply a bias in the Doppler velocity.

• This can be exploited to estimate the bias.

Welsch & Fisher (2012) also present a simpler method to estimate the pseudo-redshift: the median Doppler velocity on all PILs.

The solid black jagged line shows an empirical estimate of the bias velocity: the median of Doppler velocity along all PIL pixels (in regions above a 50 Mx cm−2 threshold), which ignores the flux-matching constraint discussed above. The dashed sinusoidal line shows 1/10th of the radial component of the spacecraft Doppler velocity, offset by +250 m s−1 to fit on the plot.

This simple estimate falls within the range of estimates derived using the flux-matching constraint.

Conclusions, Topic #2• We found evidence of the convective blueshift in HMI

Dopplergrams.

• When using Doppler velocities to improve estimates of the photospheric electric field (e.g., Fisher et al. 2012), such biases will cause problems!

• We developed two approaches to estimate the bias in HMI Doppler velocities, and correct for it.

• This work is described in Welsch & Fisher (2012), available at: http://arxiv.org/abs/1201.2451

And now for something completely different: Research by Masha Kazachenko et al. (2013, in prep.)

Masha used poloidal-toroidal decomposition (PTD, Fisher et al. 2010) to estimate photospheric electric fields in AR 11158.

- ∆B/∆t in HMI magneograms is used to infer E via Faraday’s law- (E∙B) = 0 is also assumed, from the ideal Ohm’s, cE = -(v x B)

Inferred electric fields can be used to compute the Poynting flux of magnetic energy into the corona.

Electric fields can also be used to drive time-dependent coronal magnetic field models (e.g., Cheung & DeRosa 2012).

Despite having teased you this these topics, I don’t want to steal either Masha’s or Mark’s thunder by focusing on these results!

Some other fun results: What are the noise levels on HMI’s measured B?

In preparing our data, we changed it: we flipped azimuths and spatially interpolated the data to reproject it onto a uniform Cartesian grid.

Consequently, we opted to empirically estimate uncertainties in the data from the distributions of final magnetic field values.

By quantitatively characterizing to the observed distributions’ widths, we derived uncertainties of 100 G in the horizontal field components and 30 G in the vertical field.

Photospheric vertical current appears to decrease after the X2.2 flare early on Feb. 15. Before:

Magnetic field vectors prior to the X2.2 flare.

At flare peak:

Magnetic field vectors during the X2.2 flare.

Difference:

Change in magnetic field vectors. Note: sense of curl is to “unwind” the field.