The Einstein Cross

by Theodore R. Frimet

How to measure a Gravitational Lens

The daily commute to backfill, in Norristown, sometimes has me waiting in the off-ramp. Car is idle, and I spy a bird on the left shoulder. She sits atop a tree. Looks like a bad version of a Blue Spruce. Not the bird, the tree. I wonder at her, as she lofts from the tree, and off into the brush, nearer to my gas guzzling, carbon spewing, iron chariot. Ok, not so much a guzzler. Sure, there is a carbon footprint – yet my car is mostly light steel, aluminum and plastic. The bird flies away. Ironic.

You’ve read the preamble, and you are confused. So am I. How did this experience ever spew intelligence onto the light bending affects of gravitational lensing? I dunno. No clue.

Here is what did follow, as I stepped onto the accelerator;

[which by now you should all know that this isn’t your fathers gas pedal – it is a link to actuate, via micro-controller, your mass flow air sensors, and aggregate accoutrements.]

was a brief time foray into a meager graphic analysis of how I could measure density differences of a gravitational lens.

Here it is briefly. It is brief because I choose not to augment my mind-scape with mathematics. I leave that to you, all. Calculus, anyone? Ok. My bad. It is simply because I can’t possibly drink another cup of coffee, without offending someone, or something. Sigh. I could probably use a dose of polynomial mathematics, where each band of the Cross is represented by a separate variable and coefficient – and the answer is the total mass of the lens. “What?” – Lil John.

Borrow, beg or steal three Hubble images. They need to be representative of a gravitational lensing effect. No time? No worries. I’ve done this for you in a past essay. We’ll repost the three images. Here is the link: Ring Around The Rosies

Caveat Emptor. I dug these out on my own, and they aren’t the BEST images of gravitational lensing effects, ever. Whomsoever, they will do. ‘That’ll do, pig. That’ll do.’

The best ever would show an Einstein Cross. So, for now, use your imagination. Take the composite image, and put it into a graphics program. Or print it out, in full color, and put it onto the table before you. No matter. (Hey, maybe that’s a pun- ‘no matter’ – hehe).

Construct a Cartesian plane onto your image. You know? Four quadrants. Cool beans. Find a matching element, from one of the mirror image galaxies, that was smeared across the page. Measure it, coordinate – to – matching coordinate. You are going to see if there was any subtle movement, in any mirror image.

Or more easily enough, look at my composite. I have stacked three Grayscale images, and enabled them as RED, GREEN and BLUE, in a graphics program. They appear to you, in the above link, as ‘black and white’, separately, and color (RGB) when combined. Where-ever you find subtle color shifts, in different quadrants, please know that the grayscale values shifted, over time. Remember that each image used in the composite was taken at a different time. You would imagine that there would be shift in the image. However, I would expect that each mirror image would shift the same. It does not. Did it? You tell me. After all, it’s your Universe.

In an Einstein Cross, the images that swirl, up and down, left and right, have some variance in position. If you deconstruct the images, and their effect, perhaps by means of a reverse-Gaussian algorithm, you might come to one of two of my conclusions. Either space-time was severely constrained, or warped, differently in each of the quadrants. Or the massive galaxies that make up the galactic lens have an obvious geometry and structure that can be recreated by studying an Einstein Cross’.

Yes, the geometry and structure of the massive galaxies warp space-time, and create the lens. Yes, I think that you can at the very least, know which quadrant has a more “dense” allocation of gravity bending space-time matter. Above we hint at the structure, and function of what is behind the eye of this Cosmological Camera obscura.

If you have access to more advanced channels of Cosmology, may I recommend a cup of Quasars, detected in the background, and to meter the differences in their absorption spectrum? This notion, I must admit, was borrowed from the article, “Gas filaments of the cosmic web located around active galaxies in a protocluster”, Science, 4 October 2019, Col 366, Issue 6461, pp 97-100.

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