Astronomy/The object inside the circle is GRB 090423, the earliest supernova explosion observed as of April 23, 2009.
The fact that we see this object at all must mean it has receded from us on average at less than the speed of light since the light left it correct? Also, the fact that it was presumably fairly close at the time (although we don't really know how far away it was or how big the universe was?) but took 13by to reach us implies the 96% recession that you state in the article.
I'm trying to understand how in 13 billion years it could have receded from us by another 50 billion light years as you seem to estimate in your article - that must mean it's recession has since surpassed the speed of light?
Before starting, I should note that the numbers on the webpage in question (http://cseligman.com/text/galaxies/lighttravel.htm
) were taken from the press release issued at the time of GRB 090423's discovery, and were not estimated by me (at the time I did not have easy access to a cosmological distance calculator). I now use Ned Wright's Cosmological Calculator (at http://www.astro.ucla.edu/~wright/CosmoCalc.html
) for such purposes, and it produces results that depend upon the assumptions used in entering data into the calculator. The team that published the research paper must have used different assumptions than I do, as the numbers produced by the calculator are somewhat different; but the important thing is the ideas involved, which are not affected by the exact values of the numbers.
The critical piece of information here is that the redshift measured for GRB 090423, which at the time was the largest ever measured (but is now only the second largest), was 8.2. That means that due to the expansion of the space that the light traversed during its journey toward us, it was stretched to 8.2 times its original wavelengths. This number is called z, and does not represent the speed that the object was going away from us at the time (or more accurately, the rate of expansion of the intervening space at that time). It represents the increase in the size of the intervening space during the light's journey. So however far away the object was when its light was emitted, the space that the light had to traverse was 8.2 times further.
In using the calculator, to get the age specified for the Universe at the time of the gamma-ray burst requires a value of 71 km/Mpc for the Hubble constant H. Assuming a "flat" average shape for the Universe (as is the preference among cosmologists at the this time), the amount of mass in the Universe has to be set at 27 to 30 percent of the "critical" mass, and the amount of "dark energy" has to be the remaining 70 to 73 percent. Note that every number in this paragraph is based on an assumption. Some of those assumptions are probably close to being correct, but some could be further off, and there is no way to know which is which. And for very large values of z, any error in those assumptions can produce a large difference in the results of the calculation. Hence the differences in the numbers below from those in the original press release.
At any rate, using the value of 8.2 for z and the other numbers as stated in the preceding paragraph, we find that the supernova that produced GRB 090423 must have exploded about 13 billion years ago, about 600 million years after the Big Bang, and at that time it was about 3200 million light years away, and the space between us and it was expanding at about 96% of the speed of light (any given part of that space at only a small fraction of that speed, constant throughout the 3200 million light year distance, but in sum, a total expansion rate of 96% of the speed of light).
Obviously, if the object was at a distance of 3200 million light years from us only 600 million years after the Big Bang, the space between it and us must have expanded at a rate much faster than the speed of light at some earlier date (that is a basic premise of the Inflationary Model of the Big Bang theory -- that at the instant of the Universe's formation, it was expanding much faster than the speed of light). However, due to the mass contained within the 600 million light years or so of space, the original very fast expansion had slowed down considerably, so that objects at that distance were no longer moving away from us even as fast as the speed of light. And for about the next 6 or so billion years the expansion slowed still more, as gravity tried to pull things back together. However, as time went on the mass spread out more and more, and by 6 or so billion years ago the mass of the Universe could no longer make any significant difference in the rate of expansion, and since then the Universe has been slowly speeding up (how much depends upon the "shape" assumed for space).
What Wright's calculator indicates is that (given our assumptions) at the time the star went supernova the object was about 3200 million light years away from us and the space between it and us was expanding at about 96% of the speed of light, so that covering that 3200 million light years took a lot longer than it would have if the space had not been expanding; and in fact it took about 4 times as long (namely 13000 million years) for the light to reach us, during which time the space it traversed expanded to 8.2 times its original size, stretching the light by that ratio. During the earliest parts of that journey, while the light was still far away, and the space between us and it was expanding at a large fraction of the speed of light, the light made very little headway; but during the latter parts of the journey, while passing through regions much closer to us, which are not expanding away from us as fast, the light made much greater headway. So most of its journey was spent at larger distances, and only a fraction of its journey was spent at shorter distances. On the average, it moved toward us at about 25% of the speed of light (the ratio of the 3.2 billion light years it originally had to cover to the 13 billion years it took to get here). Nearer its origin it made less headway, and nearer us it made more headway, so the average is only that -- an average -- and does not reflect the net motion of the light toward us at any given moment.
(In case anyone reading this is now completely lost, let me summarize: The object emitted the gamma radiation when it was 3200 million light years away, about 600 million years after the Big Bang. If the Universe had not been expanding throughout the time it took the light to get here, the light would have reached us only 3200 million years later, which is nearly 10 billion years ago; but since the intervening space was expanding (very rapidly for very large distances, but more slowly for smaller distances), the light had to struggle through 13 billion light years' worth of expanding space, and took 13 billion years to get here. As a result of that struggle, it was stretched out to 8.2 times its original wavelength.)
So far we have heard of two distances: (1) The original distance between "us" and GRB 090423, or 3200 million light years, and (2) the distance the light had to struggle through to reach us (13000 million light years, corresponding to the 13000 million years it took to get here). However, nothing has been said about what happened to the star (and galaxy that contained that star) that blew up, and thereby produced the light we observed.
Throughout the time the light was struggling to reach us, the star was being carried away by the expansion of the intervening space (at 96% of the speed of light at the time of its explosion, but at faster and faster speeds later on, as discussed in the following). The rate at which it was carried away from us increased over time, because as it was carried away there was more space between it and us, and the more space there was the faster the overall expansion of that space, even if the expansion of any given part of that space remained the same. And as stated earlier, the rate of expansion of the space did not remain the same, but slowly decreased at first, then (starting a few billion years ago) began to slowly increase (this is where the "shape" of space becomes important, as it determines how the calculations have to handle the initial slowing and subsequent speeding up).
Deliberately ignoring the complexity of the situation, and merely assuming that things were more constant than not, as the star moved further away from us, its motion away from us gradually increased. By the time it was a few percent further away the expansion of the intervening space would have exceeded the speed of light, so we shall never be able to see what happened to it after that, no matter how long we wait, or how powerful future telescopes become. We will only be able to observe it during the period between the supernova and the time that it became far enough away for the expansion of the intervening space to exceed the speed of light. We can calculate (though not necessarily exactly, since there are assumptions involved) how far away it is now, or will be at some point in the future, but we will never be able to actually see it or verify the accuracy (or lack thereof) of the calculations. However, if the calculations are correct, the star is now 30 to 50 billion light years away, moving away from us at 2 1/2 to 4 times the speed of light (it is not actually moving away from us at all; but the space between us and it is expanding at these rates, depending upon how much space that is).
In the press release, it was indicated that the object is now 50 billion light years away. That is based on assumptions about the shape of space and the rate of change of the expansion of space. Wright's calculator yields a current distance of only 30 billion light years, presumably because I used numbers that correspond to different assumptions about the shape of space and its rate of change of size. Either way, the object is now much further away than at the time of the supernova, and the space between us and it is now expanding (just a little bit in any given region, but cumulatively) much faster than the speed of light. And in fact, since the original expansion rate of the intervening space was very close to the speed of light, the object must have reached a (cumulative) recessional velocity equal to the speed of light not long after the light by which we saw it was emitted, and been moved away from us by the expansion of the intervening space at more than the speed of light for almost all of the 13 billion years since then (off the top of my head, I'd guess for at least 12 billion years).
Summary: At the time the star that produced GRB 090423 exploded, producing the gamma-ray burst with that designation, it was only 600 million years after the Big Bang, but the star (and its galaxy) were already 3200 million light years away, even though moving away at only (the reduced rate of) 96% the speed of light. Due to the expansion of the space between it and us during the time since then, the light had to traverse 13 billion light years of expanding space to cover that 3200 million light years, and took 13 billion years to reach us. During that time the star and its galaxy were moved away from us at a gradually increasing speed (due to their gradually increasing distance), and are now 30 to 50 billion light years away, moving away from us at 2.5 to 4 times the speed of light, so that we will never be able to tell what happened to them within the last 12 or so billion years.
This is obviously a mind-bending topic, and if there is any part of this that you would like me to try to explain in a clearer way, just let me know and I'll try to do so. And thanks for the question. It's been so long since I wrote that page that I'd forgotten it even existed, and odds are that it could use a good edit; so I'll be putting it on my list of things to do.