searching for small-scale anisotropies in the arrival directions of ultra-high energy cosmic rays...
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![Page 1: Searching for Small-Scale Anisotropies in the Arrival Directions of Ultra-High Energy Cosmic Rays with the Information Dimension Eli Visbal (Carnegie Mellon](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d415503460f94a1b27e/html5/thumbnails/1.jpg)
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
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Overview
Cosmic Rays and HiRes Potential Anisotropies Information Dimension Clusters Lines Voids Limitations of the Information Dimension HiRes Data Summary and Conclusions
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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
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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
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HiRes Skymap
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Anisotropies
Studying arrival directions may help to identify origins
Potential AnisotropiesClusteringLines Voids
Can we use one test to identify all of these anisotropies?
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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
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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
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Information Dimension
Example of a distribution used to generate statistical significance
Distribution of DI Values with Isotropic Data for 55 Events
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Information Dimension
On the left we have an example of the maximum information dimension value
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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
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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
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Clusters
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Clusters
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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
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Triangle Test
Cuts of 8 degrees and 0.0005 steradians were used
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Lines
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Lines
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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
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Void Probability Function
Dots-Isotropic
Squares-Data with Artificial Voids
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Voids-Information Dimension
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Limitations
Cannot resolve anisotropies much larger than the uncertainty used in assigning the P values to each pixel
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HiRes Energy Scan
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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