1. Searching for Small-Scale Anisotropies in the Arrival Directions of Ultra-High Energy Cosmic Rays with the Information Dimension Eli Visbal (Carnegie Mellon University) Advisor: Dr. Stefan Westerhoff

2. Overview Cosmic Rays and HiRes Potential Anisotropies Information Dimension Clusters Lines Voids Limitations of the Information Dimension HiRes Data Summary and Conclusions

3. Cosmic Rays Cosmic Rays are very energetic particles These particles can have energies over 10 20 eV When these particles enter the atmosphere they produce a shower of lower energy secondary particles The origin of those with highest energies remains a mystery This is in part due to magnetic deflection GZK cutoff prevents particles above 6x10 19 eV from traveling more than roughly 150 million light years

4. HiRes Cosmic Rays are studied by observing nitrogen fluorescence light caused by relativistic electrons created in a shower It is in Dugway, Utah Works on clear moonless nights

5. HiRes Skymap

6. Anisotropies Studying arrival directions may help to identify origins Potential Anisotropies  Clustering  Lines  Voids Can we use one test to identify all of these anisotropies?

7. Information Dimension Analogous to equation for entropy Measures how “clumpy” a data set is The information dimension is a case of the more general fractal dimensionality Fractal dimensionality is a measure of scaling symmetry in a structure where P is the probability of finding an event in bin i with edge size

8. Information Dimension HEALPix (Hierarchical Equal Area isoLatitude Pixelization) was used A pixelization of over 3,000,000 was used Probability values are assigned to each pixel based on Gaussian functions centered around each event

9. Information Dimension Example of a distribution used to generate statistical significance Distribution of D I Values with Isotropic Data for 55 Events

10. Information Dimension On the left we have an example of the maximum information dimension value

11. Comparison Compared anisotropy-specific tests to the information dimension What is the best test for a particular anisotropy? Sets of 55 and 271 events were produced

12. Clusters Points were placed accord to a Gaussian with 0.5 degree standard deviation Clusters can be identified with the 2-pt correlation technique In this technique the distance between each pair is examined and those below a certain threshold are counted and compared to isotropic simulated data A threshold of 4 degrees was used

13. Clusters

15. Lines If a group of particles with different energies is being emitted from the same source those with lower energies would follow a similar path but be deflected more This could leave lines on the sky We generated data sets with 3-pt lines 4 degrees long and 4-pt lines 6 degrees long The triangle test was developed to detect lines

16. Triangle Test Cuts of 8 degrees and 0.0005 steradians were used

17. Lines

19. Voids Could be caused by less sources in a region or magnetic deflection 15, 10 and 5 degree voids were produced artificially The void probability function method was investigated

20. Void Probability Function Dots-Isotropic Squares-Data with Artificial Voids

21. Voids-Information Dimension

22. Limitations Cannot resolve anisotropies much larger than the uncertainty used in assigning the P values to each pixel

23. HiRes Energy Scan

24. Conclusions In one test the information dimension searches for many types of small scale anisotropy simultaneously No arbitrary thresholds are necessary It is quite effective comparatively