PowerPoint Presentation
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.
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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