Searching for Small-Scale Anisotropies in the Arrival Directions of Ultra-High Energy Cosmic Rays with the Information DimensionEli Visbal (Carnegie Mellon University)

Advisor: Dr. Stefan Westerhoff

Overview

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

Cosmic Rays

Cosmic Rays are very energetic particles These particles can have energies over 1020 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 6x1019 eV from

traveling more than roughly 150 million light years

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

HiRes Skymap

Anisotropies

Studying arrival directions may help to identify origins

Potential AnisotropiesClusteringLines Voids

Can we use one test to identify all of these anisotropies?

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

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

Information Dimension

Example of a distribution used to generate statistical significance

Distribution of DI Values with Isotropic Data for 55 Events

Information Dimension

On the left we have an example of the maximum information dimension value

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

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

Clusters

Clusters

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

Triangle Test

Cuts of 8 degrees and 0.0005 steradians were used

Lines

Lines

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

Void Probability Function

Dots-Isotropic

Squares-Data with Artificial Voids

Voids-Information Dimension

Limitations

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

HiRes Energy Scan

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