Investigating the Magnetic Imprints of Major Solar Eruptions with SDO/HMI High-Cadence Vector Magnetograms
Xudong Sun, J. Todd Hoeksema, Yang Liu, Maria Kazachenko, Ruizhu Chen
DD RAFT VERSION M AY
16, 2018
Preprint typeset using L A TEX style AASTeX6 v. 1.0
INVESTIGATING THE MAGNETIC IMPRINTS OF MAJOR SOLAR ERUPTIONSWITH
SDO /HMI HIGH-CADENCE VECTOR MAGNETOGRAMS X UDONG S UN ( 孙 旭 东 ) , J. T ODD H OEKSEMA , Y ANG L IU ( 刘 扬 ) , M ARIA K AZACHENKO , AND R UIZHU C HEN ( 陈 瑞 竹 ) W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA; [email protected] Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA Department of Physics, Stanford University, Stanford, CA 94305, USA
ABSTRACTThe solar active region photospheric magnetic field evolves rapidly during major eruptive events, suggestingappreciable feedback from the corona. Previous studies of these “magnetic imprints” are mostly based on line-of-sight only or lower-cadence vector observations; a temporally resolved depiction of the vector field evolutionis hitherto lacking. Here, we introduce the high-cadence (90 s or 135 s) vector magnetogram dataset from theHelioseismic and Magnetic Imager (HMI), which is well suited for investigating the phenomenon. Theseobservations allow quantitative characterization of the permanent, step-like changes that are most pronouncedin the horizontal field component ( B h ). A highly structured pattern emerges from analysis of an archetypicalevent, SOL2011-02-15T01:56 , where B h near the main polarity inversion line increases significantly duringthe earlier phase of the associated flare with a time scale of several minutes, while B h in the periphery decreasesat later times with smaller magnitudes and a slightly longer time scale. The dataset also allows effectiveidentification of the “magnetic transient” artifact, where enhanced flare emission alters the Stokes profiles andthe inferred magnetic field becomes unreliable. Our results provide insights on the momentum processes insolar eruptions. The dataset may also be useful to the study of sunquakes and data-driven modeling of thecorona. Keywords:
Sun: flares — Sun: photosphere — Sun: magnetic fields INTRODUCTIONSolar active regions (ARs) harbor strong magnetic fieldsthat often carry significant electric currents. Processes suchas flux emergence and shearing motion gradually bring ex-cess magnetic energy into the low corona. During an erup-tion, the coronal magnetic field reorganizes rapidly, convert-ing part of the magnetic energy into intense emission as flares,or propelling plasma into interplanetary space as coronal massejections (CMEs). There are two distinctive time scales inthis “storage and release” picture (e.g. Schrijver 2009). Inthe plasma-dominated photosphere, the characteristic Alfv´enspeed ( v A ) is low. Magnetic evolution leading to an erup-tion occurs over hours or days. In the lower corona, how-ever, plasma β is low and v A can reach a thousand kilometersper second. Flare emission and CME acceleration occur on ashorter time scale, on the order of 10 minutes.Such a separation of time scales breaks down during ma-jor solar eruptions. There has been mounting evidence for therapid evolution of the photospheric magnetic field associatedwith intense flares and fast CMEs (for a recent review, seeWang & Liu 2015). For example, permanent and step-wisechanges have been observed in the line-of-sight (LoS) fieldcomponent ( B l ) for many large flares (e.g., Cameron & Sam-mis 1999; Kosovichev & Zharkova 2001; Sudol & Harvey2005; Petrie & Sudol 2010). Changes up to several hundred Gauss occur within mere minutes. In general, the LoS mag-netic flux on the disk-ward side of the AR decreases, while thelimb-ward flux increases, indicating a more horizontal mag-netic configuration near the polarity inversion line (PIL; Wanget al. 2002; Wang & Liu 2010). The pattern is consistent withthe observed darkening of the inner penumbrae and weaken-ing of the outer penumbrae in δ -sunspots (Liu et al. 2005).The step-wise changes of B l often start in the early phase ofa flare, well before the soft X-ray (SXR) peak (Cliver et al.2012; Johnstone et al. 2012; Burtseva et al. 2015).This picture is consistent with vector field observations,which showed that the horizontal field component ( B h ) andthe shear angle near the main PIL increases after a flare (Wang1992; Wang et al. 1994). In addition, B h has been found to de-crease in the peripheral areas of δ -sunspots (Wang et al. 2009).Since 2010, routine full-disk vector magnetograms from theHelioseismic and Magnetic Imager (HMI; Schou et al. 2012;Hoeksema et al. 2014) aboard the Solar Dynamics Observa-tory ( SDO ) have provided definitive evidence that the rapid,permanent photospheric field changes occur during most largeflares (e.g., Wang et al. 2012a,b; Sun et al. 2012; Petrie 2012,2013). A common scenario is that B h increases significantlynear the PIL, whereas the radial field component ( B r ) variesless and without a clear pattern. The field becomes strongerand more inclined in the AR core. a r X i v : . [ a s t r o - ph . S R ] A p r
100 150 200 250 300−300−250−200 G UT x y (arcsec) ( a r cs e c ) HMI 135 s (a) −1000 1000 B r ( G )
10 100 1000101001000 B B (G) ( G ) (b)
10 100 1000101001000 B l B l ; 720 (G) ; ( G ) (d)
0 6 P r ob . den s . ( de x − G − ) −100 0 1000.000.06 B B − (G) O cc u rr en c e (c) −100 0 1000.000.060.12 B l B l ; 135 − ; 720 (G) (e) Figure 1 . Comparison of 135 s and 720 s magnetograms for AR 11158 at 2011-02-15T01:11:20 UT. (a) Background imageshows the 135 s radial field B r . Arrows show horizontal field B h . Contours show total field strength B at 300 G. The yellowbox outlines the field of view for Figures 2–5. (b) Two-dimensional distribution of B for 135 s ( B ) and 720 s ( B ) data.Logarithm scale highlights the low field values. Dotted line has a slope of unity. (c) Distribution of B − B for pixels with B , B > G. (d) Similar to (b), but using only the absolute values of B l when the two versions agree in sign. (e) Similarto (c), but for B l .The rapid appearance of these “magnetic imprints” suggeststhat they have a coronal origin, possibly as feedback fromthe eruption. In the “coronal implosion” conjecture (Hud-son 2000), the non-erupting AR loops must contract to com-pensate for the loss of magnetic energy, which is consistentwith the observed increase of field inclination. The impulsivecoronal Lorentz force, which accelerates CME plasma to highspeed, must act downward on the rest of the Sun due to mo-mentum conservation (Hudson et al. 2008; Fisher et al. 2012).This back reaction has been evoked to explain sunquakes(Zharkov et al. 2011; Alvarado-G´omez et al. 2012) and sud-den changes of sunspot rotation rate during flares (Wang et al.2014; Liu et al. 2016a). Flares without a CME seem to ex-hibit weaker magnetic imprints than its eruptive counterpart(Sun et al. 2015).Past observations have revealed much about the nature ofmagnetic imprints, but their LoS or lower-cadence natureleaves ambiguities in interpretation. For example, B l gener-ally contains a mixture of horizontal and radial field compo-nents, so the changes of B h and B r generally cannot be distin-guished. Furthermore, the default HMI vector magnetogramshave a cadence of 12 minutes and a wider, tapered temporalaveraging window of ∼ B l sign reversal, seem to correlate with white-light orhard X-ray flare emission and are thought to be artifacts in- duced by flare-altered line profiles (Qiu & Gary 2003; Abra-menko & Baranovsky 2004). For the 12-minute-cadence HMIvector data processing, potentially anomalous line profilesmay be averaged with normal ones, making diagnostics dif-ficult.To definitively characterize the rapid, vector field evolution,we have created a new high-cadence (90 s or 135 s) vectormagnetogram dataset from HMI and use it to examine anarchetypical event. Our intentions are twofold. Firstly, weprovide a reference for the dataset by describing the key pro-cessing procedures and new features. Secondly, we demon-strate that the dataset is well suited for studying the magneticimprints and transients in a quantitative and more temporallyresolved manner. The new observations reveal a highly struc-tured pattern of field evolution, which sheds light on the mo-mentum processes in solar eruptions. We discuss the potentialusage of the dataset for other studies. DATAHMI measures the Stokes parameters at six wavelengthsin the photospheric Fe I ( I, Q, U, V ) requires 135 s to com-plete. Since April 2016, HMI has been operating under a new“Mod-L” observing scheme, which combines the polarizationmeasurements from both cameras (Liu et al. 2016b; HMI Sci-ence Nugget IGH -C ADENCE V ECTOR M AGNETOGRAMS hmi.B 135s ). The 90 s cadence versionis under development. The dataset has the same format asthe standard 720 s version (Hoeksema et al. 2014) and is pro-cessed with identical pipeline options except the following.1. The filtergrams are interpolated linearly in time, and all con-tributing filtergrams are taken within 270 s (“quick-look”averaging scheme). This contrasts with the default, higher-order interpolation scheme and a wider temporal windowthat can produce artifacts when features are fast evolving(e.g., Mart´ınez Oliveros et al. 2011).2. A 50 G constant is added to the noise masks that are usedas weak-field threshold in the 180 ◦ azimuth ambiguity res-olution algorithm (Hoeksema et al. 2014) to account for thehigher noise (see below).3. Data will be processed for selective periods of significantactivity and by request only. The first release of ∼
290 hrdata covers about 30 events, most of which feature M- or X-class flares . The corresponding Stokes parameter dataset( hmi.S 135s ) is also available.The high-cadence data have higher noise due to shorter in-tegration time and are more susceptible to contamination by p -mode oscillation. We illustrate this by comparing 135 s and720 s data for AR 11158 at one instance (Figure 1(a)). Thedistribution of field strength B in the 135 s data ( B ) peaksat 129 G, while the 720 s data ( B ) peaks at 85 G (Fig-ure 1(b)). These are typical values in the quiet Sun where thepolarization degree is low, and the inferred B largely orig-inates from photon noise. For B l , the two frames are wellcorrelated down to the deca-Gauss range (Figure 1(d)), sug-gesting that most noise resides in the transverse component.We have carried out a similar comparison for 257 pairs of135 s and 720 s full-disk B image over 6.4 days in February2011. The median of B varies daily between about 155 and175 G, presumably induced by SDO ’s orbital velocity (Hoek-sema et al. 2014). It varies in phase with the median of B ,and is consistently ∼
50 G higher. We thus add 50 G to ournoise mask for azimuth disambiguation.In the example frame, the 135 s and 720 s data agree wellin the strong-field regions. For pixels with
B >
G, thedifferenced B ( ∆ B ) and B l ( ∆ B l ) have narrow distributionscentered around 0 (Figures 1(c) and (e)). The half width halfmaximum (HWHM) is 25 and 17 G for ∆ B and ∆ B l , re-spectively. For comparison, the median formal uncertainty offield strength σ B derived from spectral line inversion is 35and 28 G for the 135 s and 720 s data, respectively. Evolutionalso contributes to the difference. For available time intervals and more details on the dataset, see http://jsoc.stanford.edu/data/hmi/highcad.
In this study, we focus on a 2 hr interval around an X-classflare on 2011 February 15, during which 54 frames of 135 scadence data are available. We keep the images in the nativeHelioprojective-Cartesian coordinate, re-project the field vec-tors into a Heliocentric-spherical coordinate, and propagatethe formal uncertainties (Sun 2013). We co-align the framesby cross-correlating continuum images obtained from inver-sion. The final dataset consists of cubes with a (cid:48)(cid:48) × (cid:48)(cid:48) field of view at a . (cid:48)(cid:48) pixel scale. RESULTSAR 11158 generated the first X-class flare of Cycle 24,
SOL2011-02-15T01:56 . An X2 flare and a fast CME orig-inated from the central bipole in this quadrupolar AR, lo-cated at W20S10 (Schrijver et al. 2011; Sun et al. 2012). Theflare ribbons exhibited an archetypical “double-J” morphol-ogy (Figure 2(a)), which then extended both along and awayfrom the main PIL. The
GOES
SXR flare started, peaked, andended at 01:44, 01:56, and 02:06, respectively. The
RHESSI B h and B r , and defer analysis of other variables such as azimuth andelectric current to future studies. We utilize a new databasefor flare ribbons (Kazachenko et al. 2017) observed in 1600 ˚Aby the Atmospheric Imaging Assembly (AIA). It corrects forspurious intensities associated with strong flare emission andprovides easy access to the evolving ribbon morphology.3.1. Example of Magnetic Imprint
The co-aligned, high-cadence data now allow us to performmeaningful temporal analysis on single pixels. Following Su-dol & Harvey (2005), we use a step-like function to model themagnetic imprint in a time sequence of field component B i , B i ( t ) = a + bt + c (cid:26) π arctan[ n ( t − t m )] (cid:27) , (1)where a , b , c , n , and t m are free parameters. The term a + bt accounts for linear evolution; ∆ B i = 2 c measures the mag-netic field change; t m corresponds to the mid-time of change; τ = πn − characterizes the time scale of change; t s = t m − τ / is the start time of change; and dB i /dt = ∆ B i /τ is the change rate. We employ a least-square Monte Carlomethod for fitting, and quote the median and 1 σ confidenceinterval when needed. To reduce the effect of noise, we con-sider only strong-field pixels, where B >
G. Additionaldetails of modeling are presented in Section 3.3.A base-difference map of B h (Figure 2(a)) shows clear,structured patterns of field change. In particular, B h increases
180 200 220 240−240−220
I D Q UT − 01:40:35 UT x y (arcsec) ( a r cs e c ) Differenced B h (a) −600 600 B h ∆ ( G ) I Increase (b) D Decrease01:30 02:00 02:306008001000 Q Quiescent Time ( UT ) B h ( G )
180 200 220 240−240−220
I D Q UT − 01:40:35 UT x y (arcsec) ( a r cs e c ) Differenced B r (c) −600 600 B r ∆ ( G ) −800−600−400 I (d) −600−400−200 D Q Time ( UT ) B r ( G ) Figure 2 . Rapid magnetic field evolution. (a) Base-differenced B h map. Gray regions have B <
G. Green shades outlineflare ribbons in AIA 1600 ˚A at 01:47:54. Contours are for B r at ± and ± G. Symbols “I”, “D”, and “Q” mark thesample pixels, where B h exhibits significant increase, decrease, or little change (quiescent), respectively. (b) Temporal evolutionof B h at sample pixels. Here and after, symbols show observations; horizontal error bars show the temporal averaging windowof filtergrams; vertical error bars show formal uncertainty from spectral line inversion. Curves show a fitted step-like function.Vertical gray band indicates GOES flare time; vertical dotted line indicates SXR flare peak. (c)–(d) Similar to (a)–(b), but for B r .(An animation of this figure is available.)significantly near the main PIL between the flare ribbons, inagreement with previous findings (Wang et al. 2012a; Sunet al. 2012; Gosain 2012; Petrie 2013). An equally importantaspect is the wide-spread, though somewhat weaker decreaseof B h further away from the PIL. A closer look at the temporalevolution of two representative pixels reveals clear, step-likechanges that are well-resolved temporally (Figure 2(b)). Thefit parameters (∆ B h , t m , τ ) are (468 +35 − , . +0 . − . , . +2 . − . ) and ( − +75 − , . +1 . − . , . +12 . − . ) for the two examplepixels (in units of G, minute since flare start, and minute),respectively. The increase is stronger, occurs earlier, andevolves faster compared to the decrease. In contrast, the ex-ample quiescent profile is not well fitted by the step-like func-tion.To assess the significance of ∆ B h , we evaluate the secu-lar evolution by differencing pairs of B h maps both before orboth after the flare. We choose a time lag of 11.25 minute (5frames), which is close to the median of τ (see Section 3.3),i.e., typical magnetic imprint time scale. For 15 pre-flare and19 post-flare pairs, the root mean square (rms) ∆ B h is 64 G, and the rms formal uncertainty of ∆ B h is 68 G. We takethe quadrature sum 93 G as the quiescent background. Thechanges at the two example pixels are thus at . +0 . − . σ and − . +0 . − . σ , respectively.In comparison, the variation of B r is less pronounced andless structured (Figure 2(c)). There appear to be patchychanges along the flare ribbons of both increase and decrease.The quiescent background of ∆ B r is 76 G. Neither examplepixels with step-like B h change exhibit significant B r change(Figure 2(d)). 3.2. Magnetic Transients
Magnetic transients have been reported for
SOL2011-02-15T01:56 using HMI 45 s LoS data. They are associatedwith continuum enhancement and Doppler-velocity transients(Kosovichev 2011). The observed left- and right-circular-polarization profiles appear to be distorted (Raja Bayannaet al. 2014). HMI high-cadence Stokes data have been usedto study magnetic transients too. For this event, transientchanges occur in all Stokes parameters (Maurya et al. 2012).
IGH -C ADENCE V ECTOR M AGNETOGRAMS
180 200 220 240−240−220 T Differenced I UT − 01:47:20 UT x y (arcsec) ( a r cs e c ) (a) −0.15 0.15 II ∆ / C
180 200 220 240−240−220 T Differenced B r UT − 01:47:20 UT x y (arcsec) ( a r cs e c ) (b) −300 300 B r ∆ ( G ) T II / C (c) B h ( G ) −2400−2000−1600 B r ( G ) σ B ( G ) Time ( UT ) UT UT T II / C (d) −0.0050.0000.005 Q I / C −0.016−0.0080.000 U I / C −200 −100 0 100 200−0.050.000.05 V I / C λ∆ (mÅ) Figure 3 . Flare-induced artifact as “magnetic transient”. (a) Differenced map of Stokes I ( ∆ λ = +172 m ˚A offset from linecenter) near the flare peak, normalized to the quiet-Sun mean continuum I c . Symbol “T” marks the sample pixel. (b) Differenced B r map. (c) Temporal evolution of the sample pixel. Red symbols show the frames affected by flare emission. Green curvesshow the fitted step-like function for B h and B r and a fitted third-order polynomial for σ B ; green bands show the σ fittingconfidence interval. Larger fitting uncertainty during flare time is due to the fact that we exclude magnetic transients. (d) Stokesprofiles of the sample pixel at two instances, near (red) and before (gray) the flare peak. Error bars are derived assuming Poissonstatistics.For an M7.9 flare SOL2012-03-13T17:41 , transient changesin linear polarization appear to be consistent with genuinefield evolution (Harker & Pevtsov 2013).We search for transient signals first by inspecting run-ning difference image sequences. In two elongated patchesthat resemble UV ribbons, Stokes I increases across the lineprofile by as much as 15 % of the nearby mean quiet-Suncontinuum value ( I c ) during the flare impulsive phase (Fig-ure 3(a)). Transient field changes appear in both B h and B r (Figure 3(b)), and are approximately co-spatial with Stokes I enhancement. We do not find obvious sign reversals in B r .Time profile of an example pixel (Figure 3(c)) exhibitsa resolved transient change in both B h and B r during theflare, superposed on a step-like, permanent change. Thissuggests that the magnetic transient can occur in conjunc-tion with the magnetic imprint. The increase starts early inthe flare and reaches maximum slightly before the SXR peak.We find that the formal uncertainty of inferred field strength σ B increases significantly during this period, nearly triplingthe background. The Stokes profiles deviate from the pre-flare conditions (Figure 3(d)); polarization generally becomesweaker except for U near the line core. These observations suggest that the Stokes profiles are distorted by flare emissionand are not adequately modeled under the default settings ofthe spectral line inversion algorithm (Centeno et al. 2014).The inferred magnetic fields become less reliable.To identify and characterize the magnetic transients, we ap-ply the following four criteria with respective empirical iden-tification schemes (Figures 3(c) and 4(a)).1. The observation is made during the GOES flare time.2. The pixel resides in the flare ribbons. The UV ribbons ateach instant are expected to be much more extended thanthe white-light sources, and thus should safely encompassthe impacted photospheric region. Our new AIA 1600 ˚Aflare ribbon database provides co-aligned masks of ribbonlocations at a 24 s cadence (Kazachenko et al. 2017), whichwe further dilate by ∼ t , we create a “ribbon mask” that includes allpixels in the AIA masks within t ± minute.3. The formal uncertainty of field strength, σ B significantlyexceeds the non-flaring background in a single-pixel timesequence. We mask out the time steps during the flare andfit a third-order polynomial to the rest, assuming there is
180 200 220 240−240−220 x y (arcsec) ( a r cs e c ) (a) Mask 01:54:05 UT σ B B Ribbon
180 200 220 240 x (arcsec) (b) Evolution T i m e ( U T ) Figure 4 . Identification and evolution of magnetic transients. (a) Masks for the 01:54:05 UT frame. AIA 1600 ˚A instantaneousflare ribbon mask is shown in green; mask for transient values in B r or B h time sequence is shown in red; mask for transientvalues in σ B is shown in blue. Pixels where all three masks overlap are colored white and used as our final mask. (b) Evolutionof the transient mask color-coded by time, overplotted on a pre-eruption I map. (An animation of this figure is available.)no sudden change in measurement quality during quiescenttimes. We mark those flare-time measurements that exceedthe fit by more than three times the rms residual. For a sin-gle time step, all marked locations constitute a “ σ B mask”.4. The measured magnetic field B h or B r is an outlier in asingle-pixel time sequence. We mask out all measurementsof suspect quality identified in the previous step, and fit therest with both a step-like function and a third-order polyno-mial. Using the better of the two models (smaller reducedchi-square χ r ), we mark those flare-time measurements thatdeviate from the fit by more than three times the rms resid-ual, and create a “ B mask” for each time step.The σ B mask (blue in Figure 4(a)) and B mask (red) re-side almost completely inside the ribbon mask (green), sug-gesting that the transient variations of the field measurementand its quality are indeed correlated with UV flare emission.The σ B and B masks often overlap. However, there are caseswhere the quality of inversion is suspect but no transient sig-nal is found in the inferred magnetic field (cyan). There arealso cases where the field changes transiently but the qual-ity of inversion remains similar (yellow), so there is no evi-dence against genuine field evolution. A detailed analysis ofthe Stokes parameters and the inversion result at these loca-tions is necessary, but is out of the scope of this work.Here, we narrowly define magnetic transients as measure-ments that satisfy all four criteria above (white in Figure 4(a)).By definition, they appear where the magnetic field cannotbe reliably derived from flare-impacted Stokes observations.They cover about 6 % of strong-field pixels in AR 11158.Our empirical scheme appears to work effectively at separat-ing transients from magnetic imprints and secular evolution(Figure 3(c)). Interestingly, the location and evolution of theidentified transients (Figure 4(b)) closely resemble that of thewhite-light sources in Hinode continuum observations (Kerr& Fletcher 2014), even though we have not explicitly usedHMI Stokes I or continuum in our scheme. This further sug-gests that the photospheric impact of flare emission is a nec-essary condition for magnetic transients. Transients identified in HMI LoS observations are similarin nature, as the essential assumption of a Gaussian line pro-file may break down. Additional artifacts may also come fromour observing scheme. For example, the slightly different ob-servation times of the Stokes parameters at different wave-lengths can cause an undesirable aliasing effect (Mart´ınezOliveros et al. 2014).3.3. Statistics of Magnetic Imprints
We now study the statistical behavior of magnetic imprints.After excluding the identified transient measurements, we fitthe time sequence at each pixel with both a step-like function(for magnetic imprints) and a third-order polynomial (for sec-ular evolution). Only pixels that favor the magnetic imprintmodel, that is, having a smaller χ r for the step-like functionfit, are included in our analysis. About 5 % of pixels with thepoorest fit ( χ r ≥ . ) are discarded.We further apply several empirical selection criteria. Toensure that the profile is temporally resolved, we includeonly pixels where the time scale is longer than the cadence( τ ≥ s) and the mid-change time is no earlier than thefirst observation since flare start ( t m ≥ . minute) . Weadditionally require that the change starts after the flare onset( t s ≥ ), but no too long after ( t m < minute and τ < hr).The rate of field change of the magnetic imprint should alsoexceed that of the linear evolution | dB/dt | > | b | (see Equa-tion 1).For B h , 15 % (about 4200) strong-field pixels are finallyselected (Figure 5). In particular, we compare two subregions(Box “I” and “D”), which contain about 250 well fitted pixelseach. Our analysis indicates the following.1. Magnetic imprints appear over the entire AR. Most im-printed pixels are located in the inner or the outer penumbraof the central sunspot pair. The former resides along the PILbetween the flare ribbons; the latter brackets the ribbons. In practice, fitting is performed within the following limits to ensure aphysically meaningful imprint model: . ≤ t m ≤ . minute (from01:45:05 to 02:21:05) and . ≤ τ ≤ . minute (from 1 to 9 π timesteps). Fits hitting any limit (e.g., t m = 1 . or τ = 2 . ) are excluded. IGH -C ADENCE V ECTOR M AGNETOGRAMS ID
180 200 220 240−240−220 x y (arcsec) ( a r cs e c ) Change of B h (a) −600 600 B h ∆ ( G ) σ σ ID −400 0 400 8000.00.10.2 B h ∆ (G) O cc u rr en c e (b)
180 200 220 240−240−220 x y (arcsec) ( a r cs e c ) Mid−time of change (c)
0 16 t m ( m i n s i n c e f l a r e s t a r t ) GO ES pea k t m (min since flare start) O cc u rr en c e (d)
180 200 220 240−240−220 x y (arcsec) ( a r cs e c ) Start time of change (e)
0 16 t s ( m i n s i n c e f l a r e s t a r t ) GO ES pea k t s (min since flare start) O cc u rr en c e (f)
180 200 220 240−240−220 x y (arcsec) ( a r cs e c ) Time scale (g)
0 30 τ ( m i n ) τ (min) O cc u rr en c e (h) Figure 5 . Characteristics of the field evolution derived from the step-like function fit after correcting for magnetic transients. (a)Horizontal field change ∆ B h , overlaid on a pre-eruption I map. Only pixels with reasonable fits are included (see the text fordetails). The two subregions marked as “I” and “D” are selected for comparison. (b) Histogram of ∆ B h in subregions “I” and“D”. Darker and lighter gray bands indicate σ and σ quiescent background, respectively. (c)–(d) Similar to (a)–(b), but for themid-time of change t m . Vertical dotted lines in (d) indicates GOES
SXR peak time. (e)–(f) Similar to (a)–(b), but for the starttime of change t s . (g)–(h) Similar to (a)–(b), but for the time scale of change τ .2. The magnitude of change ∆ B h is almost exclusively posi-tive in Box “I” and negative in Box “D” (Figures 5(a) and(b)). Box “I” has a median increase of 441 G ( . σ , thequiescent background). Box “D” shows a weaker decreasewith a median of − G ( . σ ). While ∆ B h may not besignificant at individual pixels, the wide-spread, coherentpattern of change is striking. A two-sample Kolmogorov- Smirnov (K-S) test on ∆ B h in Box “D” confirms that thechanges during the eruption are very different from quies-cent evolution. We compare the distribution of ∆ B h in a difference B h map spanningthe eruption (Figure 2(a)) with seven difference maps before the eruption.The K-S test median K is . , and in all cases p (cid:28) − . We thus rejectthe null hypothesis that ∆ B h of magnetic imprints and quiescent evolutionare drawn from the same distribution. UT (a) AR 11166 UT (b) AR 11283 UT (c) AR 11429 UT (d) AR 11890 UT (e) AR 12017 UT (f) AR 12205 UT (g) AR 12242 UT (h) AR 12297 UT (i) Figure 6 . Overview of magnetic imprints in nine arbitrarily selected events with X-class flares from the first data release. Eachpanel shows base-differenced B h map scaled between ±
600 G with B r contours at ± ± B r maps scaled between ± σ and 6 σ (quiet-Sun rms) around flare peak as possiblesunquake sources (Chen & Zhao 2016). Scale bars are 20 (cid:48)(cid:48) in all panels.3. The increases in Box “I” occur early during the flare, withmedian t m and t s of 8.6 and 3.8 minutes (since flare start;Figures 5(c)–(f)), respectively. These are much earlier thanthe SXR peak at 12 minutes and the HXR peak at 10 min-utes. The decreases in Box “D” occur slightly later. Param-eters t m and t s have a wider distribution and median of 13.1and 6.5 minute, respectively. Almost all pixels (99 % ) startchanging during the flare ( t s < minute).4. The median time scale of change τ is 8.9 minute for Box“I” and 10.1 minute for Box “D” (Figures 5(g) and (h)).The decreases occur more slowly, as about 22 % of pixelshave τ > minute.These results and our selection criteria deserve some dis-cussion. Firstly, the magnetic imprints appear to be spatially separated from the magnetic transients despite some overlap(see Figures 5(a) and 4(b)). About 40 % of transient pixelsare co-spatial with imprints, while only 9 % of imprints aremarked for transients. Secondly, our requirement that thefield change must occur after the flare onset is purely empir-ical, which aims to establish some causal relations betweenthe imprint and the flare. However, many excluded pixels(28 % of the final selection) satisfy all other criteria but have − ≤ t s < minute. Given the measurement uncertainties, itis possible that they are genuine magnetic imprints. It is alsopossible that magnetic evolution can indeed precede flare on-set. Thirdly, a significant number of excluded pixels (89 % ofthe final selection) have a small τ ; their step-like changes arenot resolved at HMI’s cadence. This is compatible to B l ob-servations, where ∼ % (Sudol & Harvey 2005) and ∼ % IGH -C ADENCE V ECTOR M AGNETOGRAMS t m (Figure 5(c)) suggests that the B h changes “propagate” acrossthe AR from the main PIL, similar to the findings in Sudol &Harvey (2005) using B l observations.We apply the same procedures on B r and find many pixelswith clear step-wise changes significantly above the quiescentbackground (for a marked example, see Figure 3(c)). Never-theless, the changes appear much less structured spatially andtemporally. We do not attempt to make further conclusions. DISCUSSION AND OUTLOOKThe new high-cadence vector dataset allows us to quantita-tively depict a scenario where flare-associated magnetic im-prints, mainly appearing as step-wise, persistent changes in B h , occur over the entire AR with a spatially and temporallystructured pattern. Along the main PIL, B h increases rapidlyduring the early phase of the flare, whereas in the AR pe-riphery B h decreases more slowly and at later times. Thefield change is typically a few hundred Gauss, well above thequiescent background evolution, and stronger for the increasethan decrease. The time scale of temporally resolved changesis about 10 minutes; a significant portion is still unresolved atHMI’s 135 s cadence.We note that detailed temporal analysis has hitherto beenlimited to B l . Depending on the AR’s location, B l can in-clude large contributions from the less varying B r , so the pat-tern of field change may not be obvious. Moreover, althoughthe contrasting behaviors of B h in the AR core and the periph-ery were previously noticed in differenced vector data (Wanget al. 2009), the crucial temporal information was missing.Our new dataset is capable of removing certain ambigui-ties arising from LoS only or lower-cadence vector observa-tions. For example, Petrie & Sudol (2010) suggested that theobserved step-wise B l changes mainly result from the hori-zontal field changes based on the fact that the LoS flux variesmore when the AR is closer to the limb. HMI 720 s vectordata support the claim (Wang et al. 2012b; Petrie 2012), butlack the temporal information to reproduce the step-shapedprofiles seen in the 1-minute-cadence B l data. This can nowbe verified by decomposing the 135 s field vectors and com-paring the more temporally resolved behaviors of B l and B h .The high cadence and the information returned from spectralline inversion also allow us to effectively separate magneticimprints from transient signals. We can thus comment on thegenuineness of the flare-related field changes.Is the picture above universal? Preliminary inspection ofnine ARs hosting X-class flares suggests a positive answer(Figure 6). Many other aspects of magnetic imprints beside B h are worth exploring too. Are imprint characteristics cor-related to the flare (Wang et al. 2012b) and CME properties(Sun et al. 2015)? How do the azimuth (Petrie 2013; Harker &Pevtsov 2013), electric current (Janvier et al. 2014), and mag-netic topology (Zhao et al. 2014) evolve? Follow-up surveys are straightforward and are poised to address these questions.New advances on magnetic imprint and transient study maycome from high-spectral-resolution observations or more so-phisticated magnetic field inference techniques. Kleint (2017)reported step-wise changes in chromospheric B l for an X1flare ( SOL2014-03-29T17:48 ) using DST/IBIS Ca II B l (for ∆ B h , see Figure 6(f)).Kuckein et al. (2015) studied the photospheric and chromo-spheric responses in an M3 flare ( SOL2013-05-17T08:57 )using Si I I I Stokes shows that thefield strength decreases temporarily during the flare but re-covers afterwards. These results illustrate a more complicatedpicture than that proposed above, which warrants further in-vestigation. Upcoming NST and DKIST telescope magneticfield observations will contribute to this topic.The origin of the magnetic imprints is not entirely clear.The coronal implosion conjecture (Hudson 2000) is oftencited to explain the increase in horizontal photospheric field.We note that the model mainly concerns the contracting coro-nal structure; it is not guaranteed that the photosphere re-sponds in a similar fashion. As mentioned above, even thechromospheric and photospheric field evolution seems to bedissociated (Kleint 2017). Numerical models that reproducethe implosion phenomenon may help address the issue (Zuc-carello et al. 2017).Below, we discuss a couple of implications from our results.The first point is also an attempt to explain the observation interms of momentum conservation.Firstly, we note that the total Lorentz force inside a vol-ume can be expressed as a surface integral of the Maxwellstress tensor on its boundaries, fully determined by the localmagnetic field (Fisher et al. 2012). If we choose a volumein the solar atmosphere that encloses the entire CME ejecta,place its lower boundary in the photosphere, and assume thatthe contribution from the side and top boundaries is negligi-ble or largely invariant, the impulsive Lorentz force thoughtto provide the upward momentum of a CME must manifest asthe photospheric field changes. The increases of B h near thePIL will lead to a positive increase of the total vertical force F r ∝ (cid:80) ( B h − B r ) , which presumably drives the ejecta. Itshould be canceled later by a decrease of B h in the peripheryif the volume is to return to force equilibrium. In other words,the observed rapid magnetic imprint that evolves on a coronalAlfv´enic time scale is a natural consequence of momentumconservation. In reality, gravitational force and thermal dy-namics responses of the dense lower atmosphere complicatethe situation (Sun et al. 2016). We note that this putative up-ward Lorentz force inside the volume should not be confusedwith the downward force exerted on the rest of the Sun bythe selected volume. The latter is thought to be one possiblemechanism for sunquakes (see below).Secondly, numerical simulations of solar eruptions can be0used to verify the arguments above. We have investigated themagnetic field evolution in the lowest layers of two publishedMHD models (T¨or¨ok & Kliem 2005; Lynch et al. 2009). Pre-liminary analysis (Sun et al. 2016; Lynch et al. 2017) showsthat both display clear magnetic imprints similar to that ofAR 11158, that is, B h increases in the AR core and decreasesin the periphery, despite very different magnetic topology anderuption mechanisms. An earlier study of a third MHD model(Fan 2010) showed similar signatures (Li et al. 2011). Noneof these three models make assumptions that are known toproduce magnetic imprints, and the agreement is unlikely amere coincidence. We thus conjecture that the magnetic im-print may be a fundamental aspect of solar eruption.We finally point out that the high-cadence vector magne-tograms can be useful to the study of sunquakes and data-driven modeling of the solar corona, among other topics.Sunquakes, a helioseismic response to the flare impact inthe solar photosphere, have been thought to originate fromhigh-energy electrons, protons, or radiative back-warming(e.g., Kosovichev & Zharkova 1998; Donea & Lindsey 2005;Zharkova & Zharkov 2007). Magnetic force was recently pro-posed as an alternative mechanism (Hudson et al. 2008; Fisheret al. 2012). The new explanation is particularly appealing forthe sunquake observed in AR 11158, because the disturbanceis observed before significant HXR emission, thus disfavor-ing a high-energy particle origin (Kosovichev 2011), and thesources appear to be co-spatial with two ends of the erupt-ing flux rope (Figure 6(a); Zharkov et al. 2011). Neverthe-less, studies of individual events have not reached a consen-sus (e.g., Alvarado-G´omez et al. 2012; Judge et al. 2014). Tothis end, a survey of sunquakes in the context of magneticfield variations will be helpful. A preliminary analysis (Chen& Zhao 2016) detects sunquake signals in five of the nine X-class flares illustrated here (Figure 6). The location, strength,and timing of the sources can now be compared with the mag-netic evolution. Predictions from theoretical and numericalstudies (e.g., Lindsey et al. 2014; Russell et al. 2016) regard-ing the role of specific magnetic configuration can also betested.Knowledge of the coronal magnetic field is vital to ourunderstanding of solar eruptions and our capability to pre-dict major space weather events. New-generation data-drivenmodels (e.g., Cheung & DeRosa 2012; Inoue et al. 2014;Fisher et al. 2015; Galsgaard et al. 2015; Jiang et al. 2016)aim to take advantage of the observed evolution of the mag-netic and velocity fields and model the evolution of the coro-nal field with sufficient accuracy and efficiency. Leake et al.(2017) have investigated the effect of the driving time scale,i.e., the input data cadence, on the modeling accuracy usingtheir newly developed, data-driven MHD framework. Theydrive the new model with photospheric conditions sampledfrom a “ground-truth” flux-emergence MHD simulation (e.g.,Leake et al. 2013) and compare the outcomes with the knownground-truth. Rapid evolution of the sub-AR magnetic field cannot be recreated from a 12-minute-cadence driver. Con-trarily, a 1.2-minute-cadence driver reduces the relative errorin magnetic free energy by almost two orders of magnitude,down to less than 10 % . The test demonstrates that the high-cadence vector data are more suited for data-driven modeling,although the higher noise can be a concern.We thank S´ebastien Couvidat, Rebecca Centeno, Mon-ica Bobra, Jeneen Sommers, and Hao Thai for assistancewith data processing. This work is supported by NASAcontract NAS5-02139 (HMI), NASA awards NNX13AK39G(CGEM) and NNH14ZDA001N-HGI, and NSF SHINEaward AGS1622495. The SDO data are courtesy of NASAand the
SDO /HMI science team. Function fitting is performedwith MPFIT (http://purl.com/net/mpfit).
Facility:
SDO
REFERENCES
Abramenko, V. I., & Baranovsky, E. A. 2004, Sol. Phys., 220, 81Alvarado-G´omez, J. D., Buitrago-Casas, J. C., Mart´ınez-Oliveros, J. C.,et al. 2012, Sol. Phys., 280, 335Burtseva, O., Mart´ınez-Oliveros, J. C., Petrie, G. J. D., & Pevtsov, A. A.2015, ApJ, 806, 173Cameron, R., & Sammis, I. 1999, ApJL, 525, L61Centeno, R., Schou, J., Hayashi, K., et al. 2014, Sol. Phys., 289, 3531Chen, R., & Zhao, J. 2016, AGU Fall Meeting Abstracts, SH43E-03Cheung, M. C. M., & DeRosa, M. L. 2012, ApJ, 757, 147Cliver, E. W., Petrie, G. J. D., & Ling, A. G. 2012, ApJ, 756, 144Donea, A.-C., & Lindsey, C. 2005, ApJ, 630, 1168Fan, Y. 2010, ApJ, 719, 728Fisher, G. H., Bercik, D. J., Welsch, B. T., & Hudson, H. S. 2012, Sol. Phys.,277, 59Fisher, G. H., Abbett, W. P., Bercik, D. J., et al. 2015, Space Weather, 13,369Galsgaard, K., Madjarska, M. S., Vanninathan, K., Huang, Z., & Presmann,M. 2015, A&A, 584, A39Gosain, S. 2012, ApJ, 749, 85Harker, B. J., & Pevtsov, A. A. 2013, ApJ, 778, 175Hoeksema, J. T., Liu, Y., Hayashi, K., et al. 2014, Sol. Phys., 289, 3483Hudson, H. S. 2000, ApJL, 531, L75Hudson, H. S., Fisher, G. H., & Welsch, B. T. 2008, in Astronomical Societyof the Pacific Conference Series, Vol. 383, Subsurface and AtmosphericInfluences on Solar Activity, ed. R. Howe, R. W. Komm, K. S.Balasubramaniam, & G. J. D. Petrie, 221Inoue, S., Hayashi, K., Magara, T., Choe, G. S., & Park, Y. D. 2014, ApJ,788, 182Janvier, M., Aulanier, G., Bommier, V., et al. 2014, ApJ, 788, 60Jiang, C., Wu, S. T., Feng, X., & Hu, Q. 2016, Nature Communications, 7,11522Johnstone, B. M., Petrie, G. J. D., & Sudol, J. J. 2012, ApJ, 760, 29Judge, P. G., Kleint, L., Donea, A., Sainz Dalda, A., & Fletcher, L. 2014,ApJ, 796, 85Kazachenko, M. D., Lynch, B. J., Welsch, B., Sun, X., & DeRosa, M. L.2017, ApJ, submittedKerr, G. S., & Fletcher, L. 2014, ApJ, 783, 98Kleint, L. 2017, ApJ, 834, 26Kosovichev, A. G. 2011, ApJL, 734, L15Kosovichev, A. G., & Zharkova, V. V. 1998, Nature, 393, 317—. 2001, ApJL, 550, L105Kuckein, C., Collados, M., & Manso Sainz, R. 2015, ApJL, 799, L25
IGH -C ADENCE V ECTOR M AGNETOGRAMS Leake, J. E., Linton, M. G., & Schuck, P. W. 2017, ApJ, 838, 113Leake, J. E., Linton, M. G., & T¨or¨ok, T. 2013, ApJ, 778, 99Li, Y., Jing, J., Fan, Y., & Wang, H. 2011, ApJL, 727, L19Lindsey, C., Donea, A.-C., Mart´ınez Oliveros, J. C., & Hudson, H. S. 2014,Sol. Phys., 289, 1457Liu, C., Deng, N., Liu, Y., et al. 2005, Appl. Phys.j, 622, 722Liu, C., Xu, Y., Cao, W., et al. 2016a, Nature Communications, 7, 13104Liu, Y., Baldner, C., Bogart, R. S., et al. 2016b, in AAS/Solar PhysicsDivision Meeting, Vol. 47, AAS/Solar Physics Division Meeting, 8.10Lynch, B. J., Antiochos, S. K., Li, Y., Luhmann, J. G., & DeVore, C. R.2009, ApJ, 697, 1918Lynch, B. J., Sun, X., T¨or¨ok, T., & Li, Y. 2017, ApJ, in prep.Mart´ınez Oliveros, J. C., Couvidat, S., Schou, J., et al. 2011, Sol. Phys., 269,269Mart´ınez Oliveros, J. C., Lindsey, C., Hudson, H. S., & Buitrago Casas, J. C.2014, Sol. Phys., 289, 809Maurya, R. A., Vemareddy, P., & Ambastha, A. 2012, ApJ, 747, 134Petrie, G. J. D. 2012, ApJ, 759, 50—. 2013, Sol. Phys., 287, 415Petrie, G. J. D., & Sudol, J. J. 2010, ApJ, 724, 1218Qiu, J., & Gary, D. E. 2003, ApJ, 599, 615Raja Bayanna, A., Kumar, B., Venkatakrishnan, P., et al. 2014, Research inAstronomy and Astrophysics, 14, 207Russell, A. J. B., Mooney, M. K., Leake, J. E., & Hudson, H. S. 2016, ApJ,831, 42Schou, J., Scherrer, P. H., Bush, R. I., et al. 2012, Sol. Phys., 275, 229 Schrijver, C. J. 2009, Advances in Space Research, 43, 739Schrijver, C. J., Aulanier, G., Title, A. M., Pariat, E., & Delann´ee, C. 2011,ApJ, 738, 167Sudol, J. J., & Harvey, J. W. 2005, ApJ, 635, 647Sun, X. 2013, ArXiv e-prints, arXiv:1309.2392 [astro-ph.SR]arXiv:1309.2392 [astro-ph.SR]