Galactic jet lag

In class, we discussed the implications and mechanics of light travel time. A major takeaway was the concept that because of the incredibly fast yet undeniably limited speed of light we are able to see VERY distant objects as they were VERY long ago.

If you are like me, you might try to see what this looks like at the extremes. So, I found myself asking a question. If we consider angles, would the diameter of an object not have an impact on the image if the center would get to us before the edges? Yes! the size of an object will have an effect on what we see, but the impact is much smaller than one might think. Let’s look at some scenarios:

relative size of milky way and distance to Adromeda not to scale

1. You are one light year away from 100,000 light year wide, face-on galaxy. Wow! This implies that the center of the galaxy is only one year behind us while the edges are 50,000 years in the past. That means that not only are these edge stars ancient, but they have also moved 50,000 years of traveling from where we see they are. The practical representation of this is our own galaxy, The Milky Way.
2. You are 70,000 light years away from a 10,000 light year wide, face-on galaxy. So, if you draw the triangles and use some basic trigonometry, you would find that the light-travel time-difference between Earth and the center and Earth and the edges is about 170 years which is about how long it took mankind to determine the universe has accelerate expansion after figuring out how to use stellar parallax which is rather profound. This describes our nearest galaxy, the Sagittarius Dwarf Galaxy.
3. Now consider a galaxy that is 2,500,000 light years away and 100,000 light years in diameter. In this scenario, the light-travel time-difference is approximately 500 light years between the edges and the center. Which is about the time it took mankind to discover water on Mars after Copernicus proved the Earth orbited the Sun.

First, I will address 2 and 3. In these scenarios I have described hundreds of years of difference in the position of the center and edges of galaxies. Could this describe why galaxies look spirally? In short, no. The spiraling effect this would have would be minimal and constant unlike the drastic and ever changing winding that takes place in spiral galaxies. This is understood when you consider the scale and speed of these galaxies. If our solar system and galaxy are typical then the average star orbits a galaxy at 0.0000004% of a rotation per year which means that for case 2 the position of the edge stars are only a mere 0.00007% percent of the full circle from where they should be, and for case 3, the number only rises to 0.0002%.

Okay, so lets do the same thing for case 1. The number only changes such that the furthest star in our own galaxy is 0.02% of it’s orbit behind where we expect it to be.

If anything this is a testament to how immense the universe is. That the time difference between two images can be so large and the macrostructure of galaxies appear unaffected is amazing.

If you want to see how dark matter affects the winding of galaxies, here is a video.