Differential Emission Measure Nanoflares Differential Emission Measure Samuel Lipschutz Paolo Grigis

Nanoflare Definition Properties: Selection criteria Small scale brightening Localized Selection criteria Selected manually Occurred in the quiet sun Give a definition small scale brightening averages were results not selection criterion Short duration averaging ~ 8 minutes Small scale brightening Small in area averaging ~ 11 pixels

Why Look at Nanoflares There are a variety of different events occurring on the sun that release energy Large infrequent events: Flares Small frequent events: Nanoflares As the more frequent small scale events provide a larger data set to work with, we have the the ability to perform significant statistical studies We can look at the properties of these events and determine if they are similar to larger scale events Which would indicate that the mechanism behind the events were similar Are they powered by the same mechanism See if the properties of the small events are similar to the large events Vice versa if the properties are similar we can use the larger number of them to our advantage

SDO AIA AIA Wavelengths Extreme Ultra Violet 94 Å 131 Å 171 Å 193 Å 211 Å 304 Å 335 Å

AIA 171 Å 6/10/210 AIA 171 Å 6/10/2010 512 Pix 307’’ Plot the 512X 512 box Say the 171

AIA 171 Å 6/10/2010 Zoomed in Event

Close Up AIA 171 Å 6/10/2010 21 Pix 13 ‘’

Movie of the Event AIA 171 Å 6/10/2010

Movie of the Event AIA 193 Å 6/10/2010

Light Curve Channel 171 Å Point out the size of the event The duration The various lines that were plotted First show without lines Use a zoomed in image

Channel 335 Å Talk about the analysis techniques. The selection of data and so on.

Channel 94 Å

Excluding 304 Å In the calculations the 304 Å pass band was ignored In searching for a Differential Emission Measure function it is only meaningful to consider light that was emitted from a volume of plasma not just a surface Since 304 is an optically thick line we are only receiving information about the emitting surface, which is not relevant for the DEM

What is an EM Formally: But assuming a constant density However, since the observations available are over and area we measure This gives EM units of cm-5

What I was Looking For DEM Energetics Differential Emission Measure as a function of temperature The amount of emitting plasma per temperature bin Energetics The total thermal energy associated with these events

Basic Principle The signal can be measured The response is the product of the plasma emission model and the effective area of the instrument So we have: Split the R in to the effective area Asubi Spectral part does not depend on channel

AIA Effective Area Three things Effective area the amount of plasma the likeyhood a transition occuring that would produce light at that wave length

Response Functions Response Functions are determined in part by atomic physicists The Plasma Emission Model The expected emission lines and continuum for a plasma of particular abundances at a particular temperature The effective area The sensitivity of the telescope to incoming photon flux at various wavelengths Conveniently, the response is given in terms of DN/S/Pix/EM [cm-5]

The Response Functions

Methods Producing a DEM meant fitting a function that satisfied this relation in each channel With our first attempt we used a piece iterative fitting software (XRT_DEM_Iterative2) Which produced non-physical results The revised attempt implemented a Markov Chain Monte Carlo (MCMC) method Explain the iterative method thing

XRT Fitting Too Hot Uses splines (which makes the smooth curve) That is why the MCMC ones are different XRT DEM produces fit with a high temperature peak ~40 million K

Error Distribution 100 iterations of the the fitting with a ∓5% error added to data

Ratio of Modeled Signal vs observed

XRT Fitting Looks Reasonable For this event the fitting does not produce the second hot peak

Error Distribution The error in the fitting though is high at the higher temperatures

Ratio of Modeled Signal vs observed

Energetics From XRT Iterative DEM Though we know that the DEMS aren’t necessarily accurate they produce reasonable results for the thermal energy released in these events Event Total Thermal Energy ERGS 1.55e 24 1 2.46e 24 2 1.00e 24 3 2.22e 25 4 1.40e 25 5 1.58e 24 6 9.81e 23 7 1.59e 25

High error but reproduces the observed signal well MCMC DEM Event: 1 94 was used as a limiting variable High error but reproduces the observed signal well

Ratio of Modeled Signal vs observed

MCMC DEM Event: 6 Again has significant error but reproduces the observed data well

Modeled With the MCMC DEM

Comparing the Two DEMS For this instance the two fits seem to coincide relatively well. Both having a peak at a reasonable temperature

Comparison of the two models Event Total Thermal Energy From XRT fit (ERGS) Total Thermal Energy From MCMC fit (ERGS) Percent Difference 1 2.46e 24 1.46e 24 51.0 % 6 9.81e 23 1.50e 24 41.8 % 3 2.22e 25 1.18e 24 179 % 4 1.40e 25 2.71e 24 135 % Even though the XRT DEMS showed some non- physical attributes the energies derived from them mostly coincide with MCMC results

Conclusions By looking at a handful of events we attempted to understand the basic properties associated with nanoflares Despite the troublesome results obtained for the DEMS, we were able to reproduce the data relatively well From this the energetics determined for the events were in an acceptable range of magnitude

Outlook The first step would be to better understand why the XRT DEM functions produced the second peak Lower the error on the MCMC DEM functions Attempt another method for producing the DEM functions Create a way to automatically identity and study these events on a large scale

FIN Thank you