Tuesday, April 14, 2020

The Most Misunderstood Hubble image

There is a beautiful set of images from the Hubble Space Telescope (HST) that are almost always described as an explosion. Here's a video assembled from those images. It is strikingly beautiful and it certainly LOOKS like an explosion.


But it isn't. The first clue that there is something "funny" going on here is the time scale involved. Let's take a look at the first four individual images used to make that video.




Taking into account the distance to this star, between the first and last of these four images that size of that "ring" has grown from 4 to 7 light-years. Growing 3 light years in 7 months raises (or at least should raise) some very large red flags. So what's going on here?

This is what is known as a light echo. So, what is that? Imagine a huge diffuse cloud of dust with a very bright flash bulb nearby. When the bulb goes off it will send light in all directions. The light that goes towards the observer will get there first and be seen as a bright dot. What happens to light that goes in other directions? It will illuminate the dust in a spherical shell moving off at the speed of light. At anytime after the flash, until the light moves past the dust cloud, the light will scatter in all directions. Some of that light will scatter towards the observer. That light forms a light echo. This has been seen in before astronomical settings but none have been so beautifully imaged as this series of images from HST.

The shape and development of a light echo depends on the distribution of dust around the light source. Taking into account the way light is scattered by the very small particles typical of interstellar dust the likely distribution of dust for this light echo has been modeled and found to be a plane of dust in front of the star.

To get an idea of what that will look like let's consider a very simple situation. A thin sheet of dust in front of a source a bright flash. Imagine looking at this from another vantage point. If the flash is a the center of the field and the original vantage point is far away to the left. That's shown in the animation below. The sheet of dust looks like a line and it's brightly light where the shell of light intersects it.



From the original vantage we'll see an expanding ring at the intersections of the shell of light and the sheet of dust. Since the light from the flash is farther to the left it gets to the observer before the light from the ring. So what's seen is a flash followed by a ring expanding away at a very high speed.

This is enough to understand why we a roughly circular bright ring growing very quickly. In detail the situation is more complicated. Proceed with CAUTION.

Again we look at the star with the original observer far away to the left. What would happen to a light beam that went directly away from the observer and traveled for a distance h before it hit some dust and then was scattered back to the observer as shown in the diagram below?



This would arrive at a time t=2hc, after that flash. What other beams would reach the observer at the same time? Here's an animation that shows this in action.




So what shape is traced out by all these point? If the object is far enough away the light from anywhere in the same telescope field will be travelling parallel so we can see that these points will be the ones that are the same distance from the source as they are from a plane at a distance 2hc behind the star. If you remember your conic section geometry you'll recognize that this defines a parabola. For every time after the flash the locations of the points that can scatter light back so that they reach the observer at the same time are on a parabola. Here's an animation that shows how that changes over time.


The time evolution of the apparent image will depend on the dust density along this paraboloid and the way that dusts scatters at the angles involved.