Structural Analysis of the Milky Way Galaxy

Chapter 1)
Introduction - Welcome to the Milky Way!

Not For Tourists Guide to the Milky Way – An Introduction

What Greek and Roman mythologies describe as a splash of milk on the night sky, coming from the Gods, the Milky Way is the home galaxy of our Solar System. The “milky” part of its name was given due to its “misty patch” appearance as seen from Earth at night – the region of the sky containing the galactic plane (which in projection on our celestial sphere approximates a big circle) is seen as a dim glowing ring in powerful contrast with its dark surroundings, for which the human eye is unable to resolve individual stars.
Understanding our galaxy and our place in the universe has been a long pursued challenge for humans across the world – there are different legends describing the creation of the Milky Way in multiple cultures, and scientists worldwide have long been fascinated with the study of our galaxy. Through his telescopic observations, Galileo Galilei first suggested that the Milky Way is a large composite of individual stars, which can be observed even with the naked eye by looking at the night sky at an angle of approximately \(62.6\degree\) above the celestial equator. Immanuel Kant and Thomas Wright have later argued that our galaxy is a disk-shaped stellar collection, and that our Sun and Solar System lie inside the plane of this disk. William Herschel first created a map of the Milky Way in \(1785\) (see Fig. [1]), by counting all the stars and analyzing their spatial distribution as he could observe from Earth, to conclude that stars are located in a big disk formation. The 20th century then brought additional discoveries to the field of astronomy, with Edward Shapley calculating our location inside the Milky Way in \(1920\). By using Cepheid variable stars as distance indicators and applying the Period-Luminosity Law discovered by Henrietta Leavitt, Edward Shapley estimated distances to nearby globular clusters, which he has tracked in 683 regions of the sky. By plotting the found distances, he calculated that the Sun lies approximately two-thirds of the way out from the galactic center.

Map of the Milky Way Galaxy, as designed by William Herschel (Yerkes Observatory)

Today we believe the Milky Way is 13.21 billion years old, and that we are located at a distance of  8kpc (calculated using different methods, see summary in Table [1] below) from the Galactic Center. A wealth of new techniques and data analysis methods for space exploration have been developed since the early scientific efforts mentioned previously, yet we still do not have a precise 3D map of our galaxy. There are multiple advantages to building one, ranging from the large spatial resolution of observations conducted in our galactic neighborhood (which allows us to collect detailed information about specific types of objects), to the possibility of discovering and testing theories on the Milky Way which we could expand for the future study of other galaxies.

RR Lyrae Variables 8.0 0.5
Globular Clusters 8.0 0.8
Miras 7.9 1.0
Cepheids 8.0 0.5
OB Stars 9.1 1.0
HI and HII regions 8.1 0.5
H2O proper motion 7.2 0.7
OH/ IR stars 8.1 1.1
Nearby stars/ Oort constants 8.9 1.0
X-Ray Sources 7.4 1.0
Planetary Nebulae 7.6 0.7
Red Giants 7.9 1.0
Sgr A* Proper Motions 7.7 0.9
Weighted Average 8.0 0.5

Chapter 5)

Minimum Spanning Trees - Diagnosis

We analyze the images obtained in Chapter 4) and perform tree diagnostics on the MSTs corresponding to the 10 found filaments by (Zucker 2015). By analyzing these MSTs and deciding what are the parameters which describe them and which set them apart from other MSTs in the image, we want to be able to automatically distinguish minimum spanning trees of CO molecular clouds which match the location of bones of the galaxy. Ultimately, we have the goal of performing tree diagnostics on the entire minimum spanning forest that results from running Prim’s algorithm on the Peretto & Fuller catalog, such that we identify potential areas of interest for the exploration of additional bones of the Milky Way. Once we identify potential regions of interest in the catalog and additional bone candidates, we can proceed with performing data analytics in these areas by using previous methods as well, such as the visual method in l-b-v space suggested by (Zucker 2015). The MST approach is thus valuable since it can give us a better intuition with regards to locations on the sky where we are most likely to find additional bones, and eventually map the entire skeleton of the galaxy. For purposes of performing tree diagnostics, we suggest using the parameters below in order to describe the shape of a given tree and its likelihood for identifying a bone of the galaxy. We motivate choosing these parameters not only based on common properties of already identified filaments, but also based on the study of social networking graphs and of community detection algorithms.

  • Number of nodes – total number of vertices in a tree, or in our case total number of clouds connected inside a filament

  • Tree Size – total number of edges in a tree, always equal to N-1, where N is the total number of nodes

  • Tree Total Length – sum of weights of all edges inside a given tree

  • Longest Path Between Two Vertices – sum of weights along the longest path connecting two nodes inside a given tree

  • Average Degree – average connectivity degree of nodes inside a tree. In graph theory, the degree of a node is the total number of edges incident on that node.

  • Average Clustering Coefficient – measuring the degree to which nodes inside a graph are clustering together. Always zero for the case of a spanning tree (inside which there are no cycles)

  • Density of Tree – the density of undirected graphs is calculated using the formula ρ= 2m/(n ( n-1) ), where m is the number of edges, and n is the number of nodes.

  • Length on x-axis – spanning degree in longitude, calculated using∆x=x_(max )- x_min, where x is the longitude coordinate of a given node inside the tree.

  • Length on y-axis – spanning degree in latitude, calculated using ∆y=y_(max )- y_min, where y is the latitude coordinate of a given node inside the tree.

  • Length Ratio - ∆x/∆y, showing how features are more elongated on the x-axis than on the y-axis

  • Average Inclination Angle – average value of the slope calculated for each tree edge