Transcript Searching for Small-Scale Anisotropies in the Arrival Directions of Ultra-High Energy

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
Overview
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Cosmic Rays and HiRes
Potential Anisotropies
Information Dimension
Clusters
Lines
Voids
Limitations of the Information Dimension
HiRes Data
Summary and Conclusions
Cosmic Rays
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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
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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 Anisotropies
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 Clustering
 Lines
 Voids
Can we use one test to identify all of
these anisotropies?
Information Dimension
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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
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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
Distribution of DI Values with Isotropic
Data for 55 Events
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Example of a
distribution used
to generate
statistical
significance
Information Dimension
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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
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Clusters
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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
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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
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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
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Void Probability Function
Dots-Isotropic
Squares-Data with Artificial Voids
Voids-Information Dimension
Limitations
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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
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