#### Student Major/Year in School

Mathematics/Physics, Third Year

#### Faculty Mentor Information

Lado Samushia, Physics, College of Arts & Sciences

#### Abstract

Today, it is believed that approximately 80 percent of the matter that comprises the universe takes the form of dark matter--a theorized substance that interacts with “normal” baryonic matter mostly through gravitational force. Through gravitation, dark matter creates potential wells that determine the motion of stars inside galaxies and galaxies inside galaxy clusters. Dark matter accumulates and forms roughly spherical structures called “dark halos”. Most galaxies and groups of galaxies are located inside such halos. Visible matter tends to cluster inside these halos because of the higher accumulation of dark matter and deeper gravitational wells. The power spectrum is obtained from a Fourier transform of the “galaxy correlation function” which is simply the degree of clustering over a certain scale. The power spectrum is useful for the analysis of clustering and density fluctuations as it gives the variation power as a function of the spatial scale--thereby enumerating the magnitude of small fluctuations in density that through gravity, are amplified and give rise to large-scale universal structure. Theoretical predictions are easy to make for distributions of galaxies in a cube. Real observations, however, have a more complicated geometry. There are usually upper and lower cuts in the distance, and the angular mask is very sophisticated. The purpose of this project is to calculate and determine how the power spectrum of halos is influenced by the implementation of a window function representative of limited visibility. To be able to use our theoretical predictions, we should be able to predict what happens to the power spectrum when an observational mask is applied to galaxies. Using the data from the Dark Sky Simulations Collaboration, we will develop numeric codes for applying the effect to the data. We can then observe how the statistical properties of halos vary based on the observational window applied and how they are related to the properties of their progenitor dark matter.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

#### Recommended Citation

Coria, David
(2019).
"Dark Halos: The Windowed Power Spectrum,"
*Kansas State University Undergraduate Research Conference*.
https://newprairiepress.org/ksuugradresearch/2019/posters/38

Dark Halos: The Windowed Power Spectrum

Today, it is believed that approximately 80 percent of the matter that comprises the universe takes the form of dark matter--a theorized substance that interacts with “normal” baryonic matter mostly through gravitational force. Through gravitation, dark matter creates potential wells that determine the motion of stars inside galaxies and galaxies inside galaxy clusters. Dark matter accumulates and forms roughly spherical structures called “dark halos”. Most galaxies and groups of galaxies are located inside such halos. Visible matter tends to cluster inside these halos because of the higher accumulation of dark matter and deeper gravitational wells. The power spectrum is obtained from a Fourier transform of the “galaxy correlation function” which is simply the degree of clustering over a certain scale. The power spectrum is useful for the analysis of clustering and density fluctuations as it gives the variation power as a function of the spatial scale--thereby enumerating the magnitude of small fluctuations in density that through gravity, are amplified and give rise to large-scale universal structure. Theoretical predictions are easy to make for distributions of galaxies in a cube. Real observations, however, have a more complicated geometry. There are usually upper and lower cuts in the distance, and the angular mask is very sophisticated. The purpose of this project is to calculate and determine how the power spectrum of halos is influenced by the implementation of a window function representative of limited visibility. To be able to use our theoretical predictions, we should be able to predict what happens to the power spectrum when an observational mask is applied to galaxies. Using the data from the Dark Sky Simulations Collaboration, we will develop numeric codes for applying the effect to the data. We can then observe how the statistical properties of halos vary based on the observational window applied and how they are related to the properties of their progenitor dark matter.