searching for small-scale anisotropies in the arrival directions of ultra-high energy cosmic rays...
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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