Stellar Evolutionary Tracks

Unsupervised classification looks for patterns in the data set, patterns that can be associated with “classes”. There are basically two kinds of patterns: clumps and tracks. Clumps exist because of similarity between objects, and tracks are formed by relationships. Most of the diversity in the Universe is due to evolution. Astronomical objects, such as stars, globular clusters or galaxies, evolve continuously according to physical laws governing their internal physics and chemistry, and also through interactions with their environment. Evolution in astrophysics is a continuous transformation, even during violent events. Apart from identifying classes of similar objects for synthetic purpose, astronomers are much interested between the evolutionary pathways.

A perfect and relatively simple example of these two tasks are the evolution of stars. The physics of stars is, to a first approximation, simple and depends on only two initial properties: mass and chemical composition (summarized as the metallicity). As a result, the classification of stars, based mainly on two observables (luminosity and temperature) and depicted on the Hertzsprung-Russell (HR) diagram, identifies the main evolutionary stages of stars as main classes (Main Sequence, red giants, white dwarfs…). The evolution of a given stars is relatively easily computed (again at first approximation). Stars go through most of these classes depending on their mass, the starting point  each  evolutionary track being defined by mass and metallicity.

In the figure below, I show the evolutionary tracks of nine stars with three values of metallicities and three masses. The main sequence from which these computed tracks start is on the leftmost side of each track.

The goal is to reconstruct such evolutionary tracks from data. Statistical clustering techniques look for clumps and are thus obviously not adapted.

At first glance, stellar evolution does not seem to be a good case for a phylogenetic study. On one hand, the evolution of a star depends on only two parameters (mass and metallicity), so that a lineage can be easily defined as the evolutionary path of stars having initially the same two parameters. But on the other hand, the branching pattern is not obvious since there is no interaction between stars. However, i) there is an indirect physical relationship between the lineages through the explosions of the most massive stars the gas of which forms the new stars (transmission with modification), and ii) the link could be merely conceived mathematically as a change of the parameters in the continuum of possible values.

A few years ago, with my colleague Marc Thuillard, we wrote a paper explaining the use of Maximum Parsimony on data coming from simulations of stellar evolution. We also compared to k-means, which fail, and Minimum Spanning Tree which gives a result nearly as good as Maximum Parsimony. The paper was refused for publication because no application on real data was included, but it can be found on HAL. At least I got here probably the best proof that phylogenetic tools are useful in astrophysics.
It was only a year ago when I met Sergi Blanco-Cuaresma that I could find both real data and a topical issue of stellar astrophysics.This is called chemical tagging that aims are reassembling the stars that were born together by using their chemical signatures. This is a multivariate problem that clustering techniques such as k-means cannot solve as Sergi and collaborators showed in a earlier paper.  We show that Maximum Parsimony, and Neighbor Joining Tree Estimation as well, succeeds in reconstruct the members of the open clusters of our sample.
In the figure below, you see the tree, and gray boxes showing obvious structures. The x-axis gives the index of the 35 open clusters in our sample in order of the available population. The four largest clusters have about 20 members, while the other ones have less than eight stars, many having only one or two! If we concentrate on the largest one, the families are well reconstructed. Note that the cluster 3 (IC4651) is mixed up with cluster 1 (M67). Interestingly, these two clusters are known to have very similar chemical composition.
Since stellar physics is much simpler than that for galaxies, I think that phylogenetic tools will be understood more easily and find many applications in the study of our Milky Way and its history.
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