TheSkySearchers

fascinating this effect , thx .

This part confused me:

In addition, the lensed supernova image predicted to appear in 2037 lags behind the other images of the same supernova because its light travels directly through the middle of the cluster, where the densest amount of dark matter resides. The immense mass of the cluster bends the light, producing the longer time delay. "This is the last one to arrive because it's like the train that has to go deep down into a valley and climb back out again. That's the slowest kind of trip for light," Rodney explained.

I would expect based on my simple grasp of trigonometry that the only variable in determining time lag is the length of the optical path. The images that appear first would be those skirting the edge of the cluster nearest to the unobstructed LOS between the object and the observer. Later arriving images would be those following longer and more sharply bent paths around the more distant edges of the cluster.

I would then expect the path through the center to be more red-shifted due to the greater mass along that path, or more scattered by dust and gas, or both. I don't see where a delay comes in here.

Did I miss something or did the writers get it wrong?

GCoyote wrote: ↑Tue Sep 14, 2021 2:24 pm This part confused me:

In addition, the lensed supernova image predicted to appear in 2037 lags behind the other images of the same supernova because its light travels directly through the middle of the cluster, where the densest amount of dark matter resides. The immense mass of the cluster bends the light, producing the longer time delay. "This is the last one to arrive because it's like the train that has to go deep down into a valley and climb back out again. That's the slowest kind of trip for light," Rodney explained.

I would expect based on my simple grasp of trigonometry that the only variable in determining time lag is the length of the optical path. The images that appear first would be those skirting the edge of the cluster nearest to the unobstructed LOS between the object and the observer. Later arriving images would be those following longer and more sharply bent paths around the more distant edges of the cluster.

I would then expect the path through the center to be more red-shifted due to the greater mass along that path, or more scattered by dust and gas, or both. I don't see where a delay comes in here.

Did I miss something or did the writers get it wrong?

It's an interesting question. Your initial premise about the longest time delay being the longest optical path is, of course, correct. But trigonometry alone won't find the longest optical path.. You have to take into account the "index of refraction" along the candidate paths. That's where it gets tricky. Regions with higher density of matter have a larger deviation from unity (+/- 1 depending on whether you use the East or West Coast convention for the metric tensor). It turns out that these larger deviations from 1 can be modeled as an index of refraction. So the optical path length is actually larger through the center of the mass distribution. That's the source of the greater delay.

About greater red shift, remember that the light falling into the cluster gets shifted blue first, then on the way out is shifted red. I expect that this will be a small effect. We have a delay of a few decades over several billion years of travel time so that's the order of magnitude of the red shift.

Another way to think of this is using the slowing down of clocks in a gravitational field. Where the mass density is highest, clocks run slower. So the propagation of light through the intervening cluster is slower for a beam through the middle.

Okay, treating it as a higher optical density so the light rays are now moving below nominal c. Feels a little odd to apply those concepts on the scale of a galaxy cluster but it makes sense in terms of optics.

Thanks as always!

GCoyote wrote: ↑Tue Sep 14, 2021 10:51 pm Okay, treating it as a higher optical density so the light rays are now moving below nominal c. Feels a little odd to apply those concepts on the scale of a galaxy cluster but it makes sense in terms of optics.

Thanks as always!

Oh, I agree it's seemingly odd! I was playing around with using an eikonal equation approach (valid at the boundary between ray and wave optics) when I was in school. However some folks have found it useful. You can see the local "cartesian grid speed of light" written in terms of the gravitational potential and the index of refraction in equations 6 & 7 of the following charming little nugget.

https://www.pas.rochester.edu/assets/pd ... ensing.pdf

Now why an East Coast institution should be using the West Coast metric convention (a minus on the time-time component of the metric tensor) is interesting. The religious wars over that sign convention must be easing.

Thanks nFA. Just think of all the things that are in the massive amount of data we have waiting to be found.