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

Understanding Heating Frequency of Active Region Loops through Forward Modeling and Machine Learning

Will Barnes1, Stephen Bradshaw1, Nicki Viall2, Stuart Mumford3

1Rice University, 2NASA Goddard Space Flight Center, 3University of Sheffield

2018 SDO Science Workshop — Ghent, Belgium

31 October 2018

Connecting Observables to Heating Properties

131 ˚ A

Observables Multi-wavelength Observations Underlying Heating Mechanism Atomic Physics + Instrument

Viall and Klimchuk (2012) Warren et al. (2012)

Connecting Observables to Heating Properties

131 ˚ A

Observables Multi-wavelength Observations Underlying Heating Mechanism Atomic Physics + Instrument

Viall and Klimchuk (2012) Warren et al. (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)

50 100 150 200 250

L [Mm]

200 400 600 800 1000 1200

Number of Loops

Building the Active Region “Skeleton”

• Trace 5000 loops through

extrapolated field

• Choose closed loops in

range 20 Mm < L < 300 Mm

• 400.0
• 300.0
• 200.0
• 100.0
• 200.0
• 300.0

Helioprojective Longitude [arcsec] Helioprojective Latitude [arcsec] HMI LOS Magnetogram

• 400.0
• 300.0
• 200.0
• 10
• 20
• 20

AIA 171 ˚ A

• NOAA 11158 observed by SDO/HMI and SDO/AIA on

12 February 2011

• From catalogue of 15 active regions compiled by

Warren et al. (2012); also Viall and Klimchuk (2017)

0.005 0.015 0.025

Q [erg/cm3/s]

High Intermediate Low 2 4 6 8

T [MK]

5000 10000 15000 20000 25000 30000

t [s]

0.0 0.5 1.0 1.5

n [109 cm−3]

Heating Model

Withbroe and Noyes (1977), Parker (1988), Cargill (2014), Barnes et al, 2016a

Waiting time proportional to the heating rate,

ε = ⟨twait⟩ τcool < 1, high frequency ∼ 1, intermediate frequency > 1 low frequency

Discrete events on each strand with frequency, twait,i ∝ Ei Constrain total flux over whole AR to be 107 erg cm-2 s-1 Model spatially-averaged loop dynamics with two- fluid EBTEL model Simulate 3×104 s of evolution

Synthesizing Intensities

Mason and Monsignori Fossi (1994); Bradshaw and Raymond (2013)

Pij = nh ne Ab(X)fX,k(Te)Nj(ne, Te)AijΔEijne

Ic = 1 4π ∫LOS dh ∑

{ij}

PijRc(λij)

Synthesizing Intensities

Mason and Monsignori Fossi (1994); Bradshaw and Raymond (2013)

Pij = nh ne Ab(X)fX,k(Te)Nj(ne, Te)AijΔEijne

Ic = 1 4π ∫LOS dh ∑

{ij}

PijRc(λij)

EBTEL Model CHIANTI Nonequilibrium Ionization

Klimchuk et al. (2008) Cargill et al. (2012a,b) Barnes et al. (2016a)

Bradshaw (2009) Dere et al. (1997) Young et al. (2016)

AR Geometry Instrument

Boerner et al. (2012) Bradshaw and Klimchuk (2011)

• 200.0
• 300.0

High

94 ˚ A 131 ˚ A 171 ˚ A 193 ˚ A 211 ˚ A 335 ˚ A

• 200.0
• 300.0

Helioprojective Latitude [arcsec]

Intermediate

• 300.0
• 200.0
• 300.0

Low

• 300.0

Helioprojective Longitude [arcsec]

• 300.0
• 300.0
• 300.0
• 300.0

Synthesizing Intensities

2 3 4 5

a

1000 2000 3000 4000 5000

Number of Pixels

High Intermediate Low

2 3 4 5

• 350.0
• 300.0
• 250.0
• 200.0
• 250.0

Helioprojective Longitude [arcsec] Helioprojective Latitude [arcsec] High Intermediate Low

Model: Emission Measure Slopes

• Compute EM(T) using method of

Hananh and Kontar (2012)

• Assume 20% uncertainty on time-

averaged intensities

• Use temperature bins 105.5 < T <

107.5 K with bin sizes of logT=0.1

• Compute EM(T) slope in every pixel,
• Fit on the “cool” side from 105.8 to

106.4 K

• Expected range: 2 < a < 5

EM(T) ∼ Ta

Jordan (1976); Bradshaw et al. (2012); Cargill (2014); Warren et al. (2012)

2000 4000 6000 8000 10000

t [s]

0.0 0.5 1.0

Ic/Ic,max

94 ˚ A 131 ˚ A 171 ˚ A 193 ˚ A 211 ˚ A 335 ˚ A −5000 −3000 −1000 1000 3000 5000

τ [s]

−0.2 0.2 0.6 1.0

CAB

94–335 211–131 193–171

Timelag Analysis

• Peaks in successively cooler channels as

plasma cools

• Timelag—offset which maximizes the cross-

correlation between channels

• By convention, order hot channel first, cooler

channel second such that positive timelags = cooling plasma

Viall and Klimchuk (2012), Bradshaw and Viall (2016), Viall and Klimchuk (2017)

−4000 −2000 2000 4000 94-335 ˚ A

High

• 200.0
• 300.0

Helioprojective Latitude [arcsec]

335-131 ˚ A 193-171 ˚ A

Intermediate

• 400.0
• 300.0
• 200.0

Helioprojective Longitude [arcsec] Low Random Cooling

Models: Timelags

2 3 4 5

a

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Number of Pixels (Normalized)

Observed High Intermediate Low

2 3 4 5

• 400.0
• 350.0
• 300.0
• 250.0
• 200.0
• 300.0

Helioprojective Longitude [arcsec] Helioprojective Latitude [arcsec]

Observations: Emission Measure Slopes

2 3 4 5

a

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Number of Pixels (Normalized)

Observed High Intermediate Low

2 3 4 5

• 400.0
• 350.0
• 300.0
• 250.0
• 200.0
• 300.0

Helioprojective Longitude [arcsec] Helioprojective Latitude [arcsec]

Observations: Emission Measure Slopes

Suggests range of frequencies across the entire active region

−4000 −2000 2000 4000 94-335 ˚ A 94-171 ˚ A 94-193 ˚ A 94-131 ˚ A 94-211 ˚ A

• 200.0
• 300.0

Helioprojective Latitude [arcsec]

335-131 ˚ A 335-193 ˚ A 335-211 ˚ A 335-171 ˚ A 211-131 ˚ A 211-171 ˚ A

• 400.0
• 300.0
• 200.0

Helioprojective Longitude [arcsec]

211-193 ˚ A 193-171 ˚ A 193-131 ˚ A 171-131 ˚ A

Observations: Timelags

Classifying Observations

Hastie et al. (2009); Breiman (2001); Pedregosa et al. (2011)

• Random forest—train many “weak” decision

trees on random samples of the training data and random subsets of the variables

• Train RF on labeled model timelags and max

cross-correlations for all 15 channel pairs

• ≈3×105 pixels from all 3 heating frequencies,

s0 s1 sn

frequency labels

Xmodel = τ00 … τ0N τ10 … τ1N τ20 … τ2N ⋮ ⋱ ⋮ τM0 … τMN}

}

# of channel pairs (x2)

Ymodel = f0 f1 f2 ⋮ fM} Xobserved = τ00 … τ0N τ10 … τ1N τ20 … τ2N ⋮ ⋱ ⋮ τM′0 … τM′N Yobserved = [?]

Total # of pixels

• 100 trees with maximum depth of 25
• ~3% misclassification error on test

data—not overfitting to model data

High Intermediate Low

• 400.0
• 300.0
• 200.0
• 200.0
• 300.0

Helioprojective Longitude [arcsec] Helioprojective Latitude [arcsec]

Classifying Observations

• 200.0
• 300.0

Helioprojective Latitude [arcsec] High Intermediate

• 200.0
• 400.0
• 300.0
• 200.0

Low Helioprojective Longitude [arcsec]

0.0 0.2 0.4 0.6 0.8 1.0

Summary

• Comparing modeled and observed emission measure slopes suggest
• bservations 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!

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” Acknowledgment:

• SDO Workshop SOC
• SPD/Metcalf Travel Award Committee

Supplementary Slides

Hydrodynamic Simulations

• Time-dependent coronal T,n for each strand using two-fluid ebtel++ model
• Efficiency allows for exploration of large parameter space, many loops in AR
• Uniform in field-aligned direction, but many overlapping structures along LOS

Klimchuk et al. (2008), Cargill et al. (2012a,b), Barnes et al. (2016a)

d dt ¯ pe = γ − 1 L (ψTR − (RTR + RC)) + kB¯ nνei( ¯ Ti − ¯ Te) + (γ − 1)Qe d dt ¯ pi = − γ − 1 L ψTR + kB¯ nνei( ¯ Te − ¯ Ti) + (γ − 1)Qi d dt ¯ n = c2(γ − 1) c3γLkB ¯ Te (ψTR − Fe − RTR)

10−29 10−27 10−25

94 ˚ A

O Mg Si S Ca Fe Ni

131 ˚ A 171 ˚ A

105 106 107

T [K]

10−29 10−27 10−25

Kc [DN cm5 s−1 pixel−1] 193 ˚ A

105 106 107

211 ˚ A

105 106 107

335 ˚ A

Effective AIA Response Functions

Non-equilibrium Ionization

Macneice et al. (1984), Bradshaw (2009)

If the heating timescale is less than the ionization timescale, need to account for time- dependent ionization,

∂Yi ∂t = Ri+1Yi+1 + Ii−1Yi−1 − RiYi − IiYi · Y = CY

This set of Z+1 equations can then be solved using an explicit scheme,

Yt+1 = Yt + Δt 2 ( · Yt+1 + · Yt) = Yt + Δt 2 (Ct+1Yt+1 + CtYt) Yt+1 = (𝕁 − Δt 2 Ct+1)

−1

(𝕁 + Δt 2 Ct) Yt

Computing Timelags

I′

c = Ic − ¯

Ic σc ,

Normalize time series in each channel in each pixel, Compute cross-correlation,

𝒟AB ≡ I′

A(t) ⋆ I′ B(t) = I′ A(−t) * I′ B(t),

And by the convolution theorem,

ℱ{𝒟AB} = ℱ{I′

A(−t) * I′ B(t)} = ℱ{I′ A(−t)}ℱ{I′ B(t)},

𝒟AB = ℱ−1{ℱ{I′

A(−t)}ℱ{I′ B(t)}} .

Select temporal offset that maximizes the cross-correlation,

τAB = arg max

τ (𝒟AB(τ))