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Flare-Associated Magnetic Field Changes Observed with HMI by Brian T. Welsch & George H. Fisher Space Sciences Lab, UC-Berkeley Permanent changes in photospheric magnetic fields have been observed to occur during solar flares (e.g., Sudol & Harvey 2005, Wang & Liu 2010, Petrie & Sudol 2010). For the X2.2 flare in AR 11158, we present preliminary results regarding the timescales over which these field changes occur.

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Topic 1: What is the time scale over which flare- associated field changes occur? Background: Magnetic fields tend to become more horizontal during a flare (Hudson 2000; Hudson, Fisher, & Welsch 2008; Wang et al., ApJ 716 L195, 2010). These changes δB imply a radial Lorentz force (e.g., Hudson, Fisher, & Welsch 2008), This force could be related to CME acceleration (Fisher, Bercik, Welsch, & Hudson 2012).

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This X2.2 flare resulted in a peak upward force of 4x10 22 dynes acting on the outer atmosphere (and an equal & opposite downward force on the solar interior).

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This “Lorentz impulse” has implications for observations of CME momenta. Acting over δt, the impulse increases CME radial velocity from zero to δv r : Escape velocity v e = (2GM /R ) 1/2 = 620 km/sec is the min. ballistic CME speed, so this enables a testable prediction:

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A key unknown is the time scale of field changes, which should match the duration δt of the Lorentz impulse. Typical area-integrated forces are δF r ~ 10 22 dynes. Assuming δt ~ 10 3 sec gives M max ~ 10 18 g --- and all CMEs fall well below this constraint! Wang, Liu, & Wang (ApJ 757 L5, 2012) note that if the duration of Lorentz impulses δt is ~ 10 sec, then CME momenta are consistent with Lorentz impulses. Is this 10 sec. time scale realistic?

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Data: HMI’s cameras record filtergrams with rapid cadence. Each of 2 cameras records an image every 3.75 sec. Tunable filter for 6 wavelengths (WL) – Internal labels: 465, 467, 469, 471, 473, 475 Measures 6 polarization states (PS) – Internal labels: – 258/258 (LCP/RCP) – 250-253 (I,Q,U,V) Front cam: B LOS (LCP – RCP)* 6 WL repeats in 45 sec. Side cam: B full-Stokes cycle is 90 sec (4 PS *6 WL) Schou et al., Sol. Phys. 275 229 (2012 )

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Timing of filtergrams are magnetic observations with both high cadence and high duty cycle (to catch flares). Single-WL LCP or RCP series have 45 sec. resolution. Intensity variations δI associated with δB can be identified in Stokes’ V in individual WL series. Time shift between WLs series are multiples of 7.5 sec. Hence, comparisons in timing between WL series can determine timing of field changes to within 7.5 sec!

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Single-WL Stokes V intensity I(x,y) clearly shows magnetic structure at a given time.

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Intensity changes δI(x,y,t) in single-WL Stokes V clearly shows structure associated with flare-related field changes, δB.

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Sudol & Harvey (2005) (and subsequent researchers) fitted time profiles of sudden changes in B i (t) in single pixels via: B i (t) = a + bt + c { 1 + 2 π -1 tan -1 [n(t – t 0 )] } B i represents one component of B(x 0,y 0,t) a, b give background level + linear evolution in magnetic field c gives the amplitude of the field change t 0 is center of interval of change π n -1 parametrizes time scale of field change We also investigated fitting tanh[n(t – t 0 )], w/similar results.

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We also fitted time profiles of pixels in single-WL images this way, but also included a term prop. to t 2. Our time series was 90 min. long, w/flare at midpoint. Like Sudol & Harvey, we used a Levenberg-Markwardt fitting algorithm.

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Among single-WL fits, the distribution of fitted timescales is consistent with field changes over a few sec.

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Future Work: Next, we must compare fitted δt & t 0 in individual pixels between different WL series. If changes are step-wise at the 45-sec. resolution of each WL series ==> δt = (π n -1 ) << 45 sec. Some WL might “catch” field at midpoint of change δB /2, implying δt = (π n -1 ) ~ 45 sec. Hence, differences in fits for δt can constrain field changes. Perhaps changes in different pixels have different physical timescales? (Are fits to t 0 robust, in the sense of consistent with time lags between observations in each WL?)

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Summary Flares can cause changes in the photospheric magnetic field δB resulting in an upward “Lorentz impulse” δF r on the outer solar atmosphere. Observable predition: the Lorentz impulse should impart momentum to CMEs; these quantities should be related. The duration δt over which the Lorentz impulse acts on the CME is unknown; this should directly affect the CME momentum. Measurements of CME momenta have been interpreted to imply impulse timescales of ~ 10 sec. Single-WL HMI filtergrams w/ 45 sec. cadence are consistent with changes on this short time scale. Comparing filtergrams in different WLs should enable resolving time scales of a few seconds --- but we haven’t investigated this yet! 14

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Acknowledgements This work was supported by the NASA Heliophysics Theory Program (NNX11AJ65G), the NASA LWS TR&T Program (NNX11AQ56G), and the NSF AGS program (AGS 1048318).

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