How do we convert velocity into distance?
Imagine an explosion in space. Since there is little friction in space, the explosion will expand freely from its center into a sphere of ever increasing size. What happens in a seemingly complex structure such as Cas-A is something very similar.
Cas-A exploded 400 years ago. Faster objects, during this 400 years, of course will travel further than slower objects. Therefore, via basic geometry, we can figure out a simple mathematical conversion we can use to convert velocity to distance!
Professor DeLaney applied this method to various elements in Cas-A. Here is a plot showing the conversion between velocity and distance in the elusive third dimension from the center of the explosion. The x-axis, ‘arcsec’ is an astronomer’s proxy for distance. Think of it as just another unit of distance akin to km or miles.
After building similar maps for other elements, we can finally convert the velocities in Cas-A images into distances in the third dimension. Finally we can take a look at this exploding star in all its three dimensional glory!