Hello! We are Andre Hinds and Paul Lessard, assistants in Dr. Johnson’s astrophysics lab. Our project is working toward the goals of creating viable statistics to analyze galactic clustering, and of identify merging cluster systems in astronomical surveys, such as the Sloan Digital Sky Survey (SDSS). The long-term application of this project is to constrain the model for gravitational interactions on huge scales. We know, for example, how a ball will interact with the Earth if it is thrown off a cliff with a given speed, but the model that governs that interaction breaks down when applied to extremely large scales, such as those of merging galaxy clusters.

My (Paul) work on the project has revolved around the compiling of a list of known galaxy cluster mergers and obtaining relevant data (2-dimensional position and recessional velocity) for as many galaxies in these clusters as possible. This was done by means of a literature search. I started my search in the latest data release from SDSS, where I created a query to search through the entire database to find all galaxies within a radius referred to as R_{200} of a central galaxy. These central galaxies, called Brightest Cluster Galaxies (BCG’s), were all taken from another database called the MaxBCG catalog. I then ran a function in MATLAB to find all of the clusters that were within a certain distance from one another. However, while there were plenty of clusters that were within this radius of each other, they were almost exclusively understudied due to the observationally expensive nature of obtaining recessional velocities; most clusters had less than 5 galaxies with recorded recessional velocities.

From here I turned to the Merging Cluster Collaboration, a research group who study the evolution of galaxy cluster mergers. Using data published by their members has provided me with many more results. At the present, I have obtained data for 4000 galaxies across 19 merging clusters. From this data, I have calculated velocity dispersions for each cluster, a value which provides insight into the cluster’s mass. This is because a higher velocity dispersion correlates to higher velocities within the cluster, and if the velocities are higher, than there must be more mass within the cluster to keep everything bound.

My ongoing work involves graphically organizing this data into velocity histograms and bubble plots for use in preliminarily identifying the members of each merging sub-cluster within the mergers. Once this leg of the project has finished, my work will shift back to the velocity dispersions, as I will begin studying and modelling the mass functions of the galaxy clusters. Mass functions describe the number density of clusters above a threshold mass *M*, and can be used as a critical test of theories of structure formation in the universe.

My (Andre) work this summer has been centered on developing a mathematical statistic to determine clustering in data sets. The bases of the his statistic has been the nearest neighbor principle meaning that by comparing a data point to its neighboring two points, you can determine whether or not the point is close to its neighbors relative to the average spacing of the entire data set. In the simple case, position data can be projected on to the x or y-axis and observed for clustering. The complex case will take a xy-vector and project the data onto various axes to test for clustering in various cluster orientations. The statistic, once determined arithmetically, must then be programmed to accept simulated cluster data. The simulation data was put together by our collaborator from NASAs’ Goddard Flight Center and is representative of known cluster dynamics. The center is more densely populated than the edges and the primary galaxy interaction is gravitational as opposed to collisional. The simulation data is far more complete than what can be obtained observationally but with the additional information we have a complete understanding of the simulated merger. This is done so that the statistic can be shown to provide the correct interpretation of data that we already understand. The simulation from NASA also has a few different initial parameters such as the clusters mass and the incident of the collision. Currently my statistics functional form is being fine tuned for optimum sensitivity and minimum error while working with small samples of the larger simulated data set. We use a subset of our simulation because the entire simulated data set represents a perfectly sampled cluster, which is next to impossible to achieve observationally. Observational data also only has x and y position and redshift (z velocity), where as our data has x, y, and z positions and velocities. The simulation also allows us to look at the time evolution of mergers which can’t be done observationally because the time scales are far greater than observable (hundreds of millions of years long), but the statistic I’m developing should give some insight into what point in the evolution we are observing.

In the future, Paul’s work determining viable cluster data sets will be used in conjunction with the statistic that I’m working on to determine clustering (and axes thereof) in any rich data set. The stage of the clustering will also be determined by using the statistic, allowing us to have an idea of how clustering progresses over time.