This project opens several interesting questions we can ask about neutrino oscillations in matter. At this point we can ask precisely how sensitive the oscillation probability is to changing these parameters. To do this we plan to integrate the probability as a function of zenith angle and energy over energy increments of 10 MeV to obtain the average probability as a function of zenith angle. We can then develop an error band in which we adjust the density parameter. It is clear from the plots above that there is poor resolution below 10 MeV, so we will examine the differences between low and high energy neutrinos.
Once we understand how sensitive an experiment could be, this work can be generalized to account for neutrino observation for a detector at different latitudes at any time of year. Also, a more detailed model including more Earth layers could give a slightly more accurate probability function.
Studying solar neutrinos not only gives us insight into the composition of the Earth. We also learn more about the properties of neutrinos themselves, which will thus give insight into the origins of cosmic neutrinos and the universe.
Dziewonski, Adam M.; Anderson, Don L. (June 1981). "Preliminary reference Earth model". Physics of the Earth and Planetary Interiors 25 (4): 297–356.
Background:
http://www.nasa.gov/sites/default/files/thumbnails/image/20150715_062759_n7eua_171.jpg
This material is based upon work supported by the National Science Foundation under Grant No. AST-1359462, a Research Experiences for Undergraduates (REU) grant awarded to CIERA at Northwestern University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
I would like to thank graduate students Kevin Kelly and Jeff Berryman for the great deal of input, advice, and encouragement they offered.
I would also like to thank Noah Rivera for his invaluable programming advice.