Understanding Heating Frequency of Active Region Loops through - PowerPoint PPT Presentation

Understanding Heating Frequency of Active Region Loops through Forward Modeling and Machine Learning 2018 SDO Science Workshop — Ghent, Belgium 31 October 2018 Will Barnes 1 , Stephen Bradshaw 1 , Nicki Viall 2 , Stuart Mumford 3 1 Rice University, 2 NASA Goddard Space Flight Center, 3 University of She ffi eld

Connecting Observables to Heating Properties Multi-wavelength Observations Atomic Physics + Instrument 131 ˚ A Underlying Heating Mechanism Warren et al. (2012) Observables Viall and Klimchuk (2012)

Connecting Observables to Heating Properties Multi-wavelength Observations Atomic Physics + Instrument 131 ˚ A Underlying Heating Mechanism Warren et al. (2012) Observables Viall and Klimchuk (2012)

Forward Modeling Pipeline 1. Extrapolate field from magnetogram 2. Trace fieldlines through extrapolated volume 3. Run a hydrodynamic simulation for each fieldline 4. Use T(s,t), n(s,t) to compute emissivity and convolve with wavelength response function 5. Map back to field geometry 6. Integrate along LOS and convolve with PSF See also: Schrijver et al. (2004), Mok et al. (2005), Warren and Winebarger (2007), Winebarger et al. (2008), Lundquist et al. (2008a,b), Bradshaw and Viall (2016)

Building the Active Region “Skeleton” 1200 -20 � -10 � AIA 171 ˚ A HMI LOS Magnetogram 1000 -100.0 Helioprojective Latitude [arcsec] Number of Loops 800 600 -200.0 -20 � 400 200 -300.0 0 0 50 100 150 200 250 -400.0 -300.0 -200.0 -400.0 -300.0 -200.0 L [Mm] Helioprojective Longitude [arcsec] Trace 5000 loops through • NOAA 11158 observed by SDO/HMI and SDO/AIA on • extrapolated field 12 February 2011 Choose closed loops in • From catalogue of 15 active regions compiled by • range 20 Mm < L < 300 Warren et al. (2012); also Viall and Klimchuk (2017) Mm

Heating Model High Intermediate Low Model spatially-averaged loop dynamics with two- 0 . 025 Q [erg / cm 3 / s] fluid EBTEL model 0 . 015 Discrete events on each strand with frequency, 0 . 005 high frequency < 1, 8 ⟨ t wait ⟩ intermediate frequency ε = ∼ 1, 6 τ cool T [MK] low frequency > 1 4 Waiting time proportional to the heating rate, 2 t wait , i ∝ E i 1 . 5 n [10 9 cm − 3 ] Constrain total flux over whole AR to be 10 7 erg 1 . 0 cm -2 s -1 0 . 5 Simulate 3 × 10 4 s of evolution 0 . 0 0 5000 10000 15000 20000 25000 30000 t [s] Withbroe and Noyes (1977), Parker (1988), Cargill (2014), Barnes et al, 2016a

Synthesizing Intensities I c = 1 4 π ∫ LOS ∑ d h P ij R c ( λ ij ) { ij } P ij = n h Ab( X ) f X , k ( T e ) N j ( n e , T e ) A ij Δ E ij n e n e Mason and Monsignori Fossi (1994); Bradshaw and Raymond (2013)

Synthesizing Intensities I c = 1 4 π ∫ LOS ∑ AR Geometry d h P ij R c ( λ ij ) Instrument Boerner et al. (2012) Bradshaw and Klimchuk (2011) { ij } P ij = n h Ab( X ) f X , k ( T e ) N j ( n e , T e ) A ij Δ E ij n e n e CHIANTI EBTEL Model Nonequilibrium Dere et al. (1997) Klimchuk et al. (2008) Young et al. (2016) Cargill et al. (2012a,b) Ionization Barnes et al. (2016a) Bradshaw (2009) Mason and Monsignori Fossi (1994); Bradshaw and Raymond (2013)

Synthesizing Intensities 94 ˚ 131 ˚ 171 ˚ 193 ˚ 211 ˚ 335 ˚ A A A A A A -200.0 High -300.0 Helioprojective Latitude [arcsec] -200.0 Intermediate -300.0 -200.0 Low -300.0 -300.0 -300.0 -300.0 -300.0 -300.0 -300.0 Helioprojective Longitude [arcsec]

Model: Emission Measure Slopes High Intermediate Low Helioprojective Latitude [arcsec] • Compute EM( T ) using method of Hananh and Kontar (2012) -200.0 • Assume 20% uncertainty on time- -250.0 averaged intensities -350.0 -300.0 -250.0 Helioprojective Longitude [arcsec] • Use temperature bins 10 5.5 < T < 10 7.5 K with bin sizes of log T =0.1 2 3 4 5 5000 High • Compute EM( T ) slope in every pixel, Intermediate Number of Pixels 4000 Low EM( T ) ∼ T a 3000 • Fit on the “cool” side from 10 5.8 to 2000 10 6.4 K 1000 • Expected range: 2 < a < 5 2 3 4 5 Jordan (1976); Bradshaw et al. (2012); Cargill (2014); Warren et al. (2012) a

Timelag Analysis • Peaks in successively cooler channels as 1 . 0 94 ˚ A plasma cools 131 ˚ A 171 ˚ A I c /I c,max 193 ˚ A • Timelag —o ff set which maximizes the cross- 0 . 5 211 ˚ A 335 ˚ A correlation between channels • By convention, order hot channel first, cooler 0 . 0 0 2000 4000 6000 8000 10000 channel second such that positive timelags = t [s] cooling plasma 1 . 0 94–335 211–131 193–171 0 . 6 C AB 0 . 2 − 0 . 2 − 5000 − 3000 − 1000 1000 3000 5000 Viall and Klimchuk (2012), Bradshaw and Viall (2016), Viall and Klimchuk (2017) τ [s]

Models: Timelags High Intermediate Low Random Cooling 94-335 ˚ A 4000 Helioprojective Latitude [arcsec] 2000 335-131 ˚ A -200.0 0 -300.0 193-171 ˚ A − 2000 − 4000 -400.0 -300.0 -200.0 Helioprojective Longitude [arcsec]

Observations: Emission Measure Slopes 2 3 4 5 2 . 00 Number of Pixels (Normalized) Observed 1 . 75 High Intermediate 1 . 50 Helioprojective Latitude [arcsec] Low -200.0 1 . 25 1 . 00 0 . 75 0 . 50 0 . 25 2 3 4 5 -300.0 a -400.0 -350.0 -300.0 -250.0 Helioprojective Longitude [arcsec]

Observations: Emission Measure Slopes 2 3 4 5 2 . 00 Number of Pixels (Normalized) Observed 1 . 75 High Intermediate 1 . 50 Helioprojective Latitude [arcsec] Low -200.0 1 . 25 1 . 00 0 . 75 0 . 50 0 . 25 2 3 4 5 -300.0 a Suggests range of frequencies across the entire active region -400.0 -350.0 -300.0 -250.0 Helioprojective Longitude [arcsec]

Observations: Timelags 94-335 ˚ 94-171 ˚ 94-193 ˚ 94-131 ˚ 94-211 ˚ A A A A A 4000 Helioprojective Latitude [arcsec] 2000 335-131 ˚ 335-193 ˚ 335-211 ˚ 335-171 ˚ 211-131 ˚ A A A A A -200.0 0 -300.0 211-171 ˚ 211-193 ˚ 193-171 ˚ 193-131 ˚ 171-131 ˚ A A A A A − 2000 − 4000 -400.0 -300.0 -200.0 Helioprojective Longitude [arcsec]

Classifying Observations • Random forest —train many “weak” decision frequency labels f 0 Total # of pixels f M } τ 00 … τ 0 N trees on random samples of the training data and τ MN } f 1 τ 10 … τ 1 N random subsets of the variables τ 20 … τ 2 N Y model = X model = f 2 ⋮ ⋱ ⋮ ⋮ τ M 0 … • Train RF on labeled model timelags and max } cross-correlations for all 15 channel pairs # of channel pairs (x2) τ 00 … τ 0 N • ≈ 3 × 10 5 pixels from all 3 heating frequencies, … τ 10 τ 1 N τ 20 … τ 2 N Y observed = [?] X observed = ⋮ ⋱ ⋮ s 0 s 1 s n τ M ′ � 0 … τ M ′ � N • 100 trees with maximum depth of 25 • ~3% misclassification error on test data—not overfitting to model data Hastie et al. (2009); Breiman (2001); Pedregosa et al. (2011)

Classifying Observations 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 High Intermediate Low Helioprojective Latitude [arcsec] High Intermediate -200.0 Helioprojective Latitude [arcsec] -200.0 -300.0 Low -300.0 -400.0 -300.0 -200.0 -200.0 -400.0 -300.0 -200.0 Helioprojective Longitude [arcsec] Helioprojective Longitude [arcsec]

Summary • Comparing modeled and observed emission measure slopes suggest observations consistent with multiple heating frequencies • Timelag maps increasingly coherent with decreasing frequency • Systematic classification of observations shows range of frequencies across the active region

Thank You! Acknowledgment: • SDO Workshop SOC • SPD/Metcalf Travel Award Committee Two publications in preparation: • W.T. Barnes , S.J. Bradshaw, N.M. Viall, in prep., “Understanding the Heating Frequency in AR Cores through Synthetic Observables I. Modeling” • W.T. Barnes, S.J. Bradshaw, N.M. Viall, in prep., “Understanding the Heating Frequency in AR Cores through Synthetic Observables II. Classifying Observations”

Supplementary Slides

Hydrodynamic Simulations • Time-dependent coronal T,n for each strand using two-fluid ebtel++ model • E ffi ciency allows for exploration of large parameter space, many loops in AR • Uniform in field-aligned direction, but many overlapping structures along LOS p e = γ − 1 d n ν ei ( ¯ T i − ¯ ( ψ TR − ( R TR + R C )) + k B ¯ T e ) + ( γ − 1) Q e dt ¯ L p i = − γ − 1 d n ν ei ( ¯ T e − ¯ T i ) + ( γ − 1) Q i dt ¯ ψ TR + k B ¯ L n = c 2 ( γ − 1) d ( ψ TR − F e − R TR ) dt ¯ c 3 γ Lk B ¯ T e Klimchuk et al. (2008), Cargill et al. (2012a,b), Barnes et al. (2016a)

E ff ective AIA Response Functions O Mg Si S Ca Fe Ni 94 ˚ 131 ˚ 171 ˚ A A A 10 − 25 10 − 27 10 − 29 K c [DN cm 5 s − 1 pixel − 1 ] 193 ˚ 211 ˚ A A 335 ˚ A 10 − 25 10 − 27 10 − 29 10 5 10 6 10 7 10 5 10 6 10 7 10 5 10 6 10 7 T [K]

Non-equilibrium Ionization If the heating timescale is less than the ionization timescale, need to account for time- dependent ionization, ∂ Y i ∂ t = R i +1 Y i +1 + I i − 1 Y i − 1 − R i Y i − I i Y i · Y = CY This set of Z+1 equations can then be solved using an explicit scheme, Y t +1 = Y t + Δ t 2 ( · Y t +1 + · Y t ) = Y t + Δ t 2 ( C t +1 Y t +1 + C t Y t ) Y t +1 = ( 𝕁 − Δ t − 1 2 C t +1 ) ( 𝕁 + Δ t 2 C t ) Y t Macneice et al. (1984), Bradshaw (2009)