1. Differential Emission Measure
Nanoflares
Differential Emission Measure
Samuel Lipschutz
Paolo Grigis

2. 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

3. 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

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

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

6. AIA 171 Å
6/10/2010
Zoomed in Event

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

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

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

10. 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

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

12. Channel 94 Å

13. 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

14. 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

15. 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

16. 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

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

18. 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]

19. The Response Functions

20. 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

21. 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

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

23. Ratio of Modeled Signal vs observed

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

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

26. Ratio of Modeled Signal vs observed

27. 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

28. 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

29. Ratio of Modeled Signal vs observed

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

31. Modeled With the MCMC DEM

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

33. 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

34. 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

35. 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

36. FIN
Thank you