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Quantifying the likelihood of substructure in Coronal LoopsKathryn McKeough1Vinay Kashyap2 & Sean McKillop21 Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15289, USA2 Harvard-Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA 02138, USA

What can we see at very small spatial scales that help constrain the theories of coronal heating

Temperature range of CoronaTemperature of AIAHow far the sun is from earthWhat wavelength AIA we are looking at (HiC is same)Radius of the sun

1Coronal Heating500,000 - 3 million K1000 times hotter than surface of sunPower required = ~ 1kilowatt/ m2

http://apod.nasa.gov/apod/ap090726.htmlSurface area of the sun 6.09*10^12 km^2Corona, transition, chromosphere, photosphere.where energy is coming from how it is being deposited (understandable because corona is lower density)2Coronal LoopsMagnetic flux tube filled with hot plasma Connects regions of opposite polarityPotential location of coronal heating mechanisms

AIA 193 A 2012/07/11 18:53:44 (top)http://www.daviddarling.info (bottom)

3Coronal Heating -SolutionsSmall scaleSmall consecutive bursts of energy that contributes to heatingMagnetic reconnection induced by stresses from footpoint motions causing braids in flux tubesLarge scaleAlfven waves dissipate energy into plasma through turbulence Waves propagate along flux tubesNanoflaresAlfven Wavestwo types small scale v. large scaleNanoflares small compared to across the loopAlvfen Waves- long compared to the length of the loop-propogate from center, but can be reflected backNot all energy caused by turbulanceAW 0.08 mfootpoint= where loop enters chromosphere4GoalBy identifying the substructure of coronal loops, we determine dominant spatial scales and constrain theories of coronal heating.5

0.6 arc sec193 Increased Spatial Resolution

193 0.1 arc sec

Atmospheric Imaging Assembly (AIA)High-resolution Coronal Imager (Hi-C)

18:53:4418:53:44Model smooth variations of imageBeyesian multiscale method that uses MCMCAIA on SDO since 20106Increased Spatial ResolutionLow-Count Image Reconstruction and Analysis (LIRA)Bayes / Markov Chain Monte CarloTwo components1 smooth underlying baselineInferred multi-scale componentEsch et al. 2004Connors & van Dyk 2007

Atmospheric Imaging Assembly (AIA)0.6 arc sec193

High-resolution Coronal Imager (Hi-C)193 0.1 arc sec

LIRAModel smooth variations of imageArc second resolution of each AIA is 1.3 arc min (77 arc sec) acrossBeyesian multiscale method that uses MCMC----- Meeting Notes (8/13/14 12:06) -----Forward modeling process (start with source, push through instrument to compare to data)7

LIRASharpness ValueQuantify the prominence of the substructure

Wee & Paramesran 2008

Sharpness----- Meeting Notes (8/13/14 12:06) -----retitle LIRA on --> sharpnessqualitatively explain sharpness value8Gradient CorrectionLinear Regression in log-log spaceApply transformation to sharpness

Detecting too many edgesPivot data about horizontal using function of gradient & linear regression fit of sharpness v gradient in log-log space9Significance of SubstructureNull hypothesis = no substructure in coronal loopNull image = convolve observed image with PSFLIRA on Observed Corrected SharpnessLIRA on Null Image Corrected Sharpness

10p-Value Upper Bound5 Poisson realizations of double convolved imageCompare sharpness for the observed image (o) and the simulated images (n)

Stein et al. 2014 (draft)

g()p-value upper bound

QUESTIONAdjacent sharpness are correlatedP-value test is independent?Draw gamma_o curvewhat we chose for gamma_n (=0.05)11p-Value Upper BoundSignificant sharpness: < 0.06

AIA

p-valueUpper Bound12Hi-C Comparison

Hi-Cp-valueUpper Bound13

Hi-C Comparison

Hi-Cp-valueUpper BoundTrial 1Hi-Cp-valueUpper BoundTrial 6Regions of Interest

For each of the loops, we are able to see if there is substructureIf all loops come up with substructure strands everywhere (low lying, upper corona etc.)

Apply to different regions of the sun to determine where along the loops substructure exists and therefore where we expect to see these coronal heating phenomena.15Detected Loops

areaA1areaB1areaB3areaF1

Those that don't may have not been detectedthose that do have strong indication of substrandsMore likely to be heated by nanoflares in future

16SummaryDeveloped method to search for substructure in solar imagesFound evidence for substructure in AIA images that we observe in Hi-CSimilar evidence of substructure in AIA loops outside of Hi-C region: Loops with strands appear to be ubiquitous Supports nanoflare modelNot all loops found to have substructure unclear if statistical or physical explanationIsolated points possibly result of Poisson artifactsFuture WorkResults are preliminaryQuantify false positives and non-detectionsIncreasing power could expand detection regionsUnderstand implications of resultsRelation between bright points and detections compare significant pixel light curvesWhy some loop complexes show no detections

quantify= poisson artifactsPower = simulations18AcknowledgementsWe acknowledge support from AIA under contract SP02H1701R from Lockheed-Martin to SAO.

We acknowledge the High resolution Coronal Imager instrument team for making the flight data publicly available. MSFC/NASA led the mission and partners include the Smithsonian Astrophysical Observatory in Cambridge, Mass.; Lockheed Martin's Solar Astrophysical Laboratory in Palo Alto, Calif.; the University of Central Lancashire in Lancashire, England; and the Lebedev Physical Institute of the Russian Academy of Sciences in Moscow.

Vinay Kashyap acknowledges support from NASA Contract to Chandra X-ray Center NAS8-03060 and Smithsonian Competitive Grants Fund 40488100HH0043.

We thank David van Dyk and Nathan Stein for useful comments and help with understanding the output of LIRA.

BibliographyBrooks, D. et al. 2013, ApJ, 722L, 19BCargill, P., & Klimchuck, J. 2004, ApJ, 605, 911CConnors, A., & van Dyk, D. A. 2007, Statistical Challenges in Modern Astronomy IV, 371, 101Cranmer, S., et al. 2012, ApJ, 754, 92CCranmer, S., et al. 2007, ApJS, 171, 520CDeForest, C. E. 2007, ApJ, 661, 532DEsch, D. N., Connors, A., Karovska, M., & van Dyk, D. A. 2004, ApJ, 610, 1213 Pastourakos, S., & Klimchuk, J. 2005, ApJ, 628, 1023PRaymond, J. C., et al. 2014, ApJ, 788, 152RViall, N. M., & Klimchuck J. 2011, ApJ, 738, 24VWee, C. Y., & Paramesran, R. 2008, ICSP2008 Proceedings, 978-1-4244-2179-4/08Extra SlidesBaseline ModelBegin with maxCorrect using min curvature surface through convex hullIterate until surface lies below data

Correction never more than 5% ----- Meeting Notes (8/13/14 12:06) -----BYE BYE SLIDE22LIRA OperationsPoint Spread Function (PSF)Observed Image (2nx2n)Baseline ModelPrior & Starting ImageMCMC iterations of Multi-scale CountsPosterior distribution of departures from baselineDe-convolutionINPUTOUTPUTMulti-scale Representation

Sharpness Value

Image matrixNormalizationSubtract meanCovariance matrixSum of squared eigenvalues (diagonal of D)

Singular Value Decomposition----- Meeting Notes (8/13/14 12:06) -----EXTRA SLIDE25Sharpness & Structure Dependence

Random, X and randomized 26

Edge DetectionGradient steepest along edges edge detection

p-valueUpper Bound

AIAGradient Correction