Dendrostar is an interactive applet for exploring dendrogram representations of spectral line data cubes. You can run it directly from a Java-enabled web browser without having to install any additional software.
Table of Contents
The DendroStar visualization applet for L1448, directly runnable from a Java-enabled web browser.
A two minute screencast about the DendroStar applet.
Dendrograms and Spectral Line Data Cubes
A “dendrogram” is a tree diagram used to illustrate the arrangement of the clusters produced by a clustering algorithm. Researchers affiliated with the Initiative in Innovative Computing and the Harvard-Smithsonian Center for Astrophysics have recently adopted dendrograms as a method for visualizing and analyzing the structure of “spectral line data cubes”, which are used to study star-forming regions. These data cubes represent the intensity of radio emission coming from a specific gas molecule at different points in the sky. Each xy coordinate of the data cube represents a point in the sky, and each z coordinate represents a velocity towards us or away from us. The value of the data cube at each xyz location in the data cube represents the intensity of radio emission at the given position-position-velocity coordinate.
Integrated Intensity Images
Since a spectral line data cube is a function of three variables, it can be difficult to visualize. Graphing it as a function would require four axes, which is problematic.
One way of representing the data cube with fewer than four axes is to make an “integrated intensity image”. Such an image is a 2D grey-scale image, for which each xy value is the sum of all the values with the same xy coordinates in the data cube. The result is more or less what you might see if you looked at that area of the sky, if only your eyes could see radio frequencies. Astronomers use integrated intensity images all the time, even though a lot of information is lost with them.
An integrated intensity image of CO emissions from the L1448 star forming region is shown to the right. It depicts a region to be discussed by Kauffmann et al. (in prep.). The data is a subset of the one presented by Ridge et al. 2006.
To represent the data cube using three axes, one can plot isosurfaces, which are the 3D analogue of the isocontours that appear on a contour map, but such plots can be difficult to generate. They can also be somewhat difficult to understand, as surfaces that are inside other surfaces will be visually obscured. An example of such a plot for L1448 can be seen in the figure to the right. (Putative self-gravitating gas cores have been labeled with billiard balls in this figure.)
Dendrograms can help with this situation, as they represent the nesting structure of the isosurfaces.
The figure to the right illustrates how to derive the dendrogram for a function given the function. The leaf nodes of the dendrogram represent local maxima of the function. The inner nodes represent where isocontours merge. (The inner nodes do not, as it might appear at first glance, only represent local minima, though isocontours do merge at local minima.)
The goal of this project was to provide an applet to let astronomers explore the relationship between the integrated image representation of a data cube, the dendrogram representation for it, and isosurface “shadows” projected onto the integrated intensity image.
The screenshot below shows the DendroStar applet in action.
Features we might add:
3D representation of the isosurfaces in addition to the 2D image and the isosurface “shadows” currently displayed.
- In the current implementation of the applet, a node of the dendrogram can only carry one of the three provided tints. This is not quite correct for reasons that are a bit too subtle to explain clearly here. Each dendrogram node should really be able to carry any combination of the three tints.
- Allowing the user to load different data cubes and dendrograms into the applet.
- Allowing the user to create their own tint palette and to adjust the brightness and contrast of the image.
- Allowing the user to slide up and down a vertical line on the dendrogram in order to specify a specific isosurface value, rather than only being able to use the predetermined values. This, however, is very difficult to implement as a real-time feature.
- Preservation of the tint state across sessions.
- Indicators on the dendrogram for self-gravitating regions.
Project Lead: Douglas Alan (IIC)
All programming for the visualization and the visualization design was done by Douglas Alan. All of the data and the figures were provided by the above contributors. The project was proposed by Michael Halle, Alyssa Goodman, Michelle Borkin, and Jens Kauffmann. Science consulting by Jens Kauffmann and Michelle Borkin.