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.

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).

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).

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:

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 ~ dynes. Assuming δt ~ 10 3 sec gives M max ~ 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?

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) – (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 (2012 )

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!

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

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

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 { 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.

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.

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

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?)

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

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 ).