Do you mean the claim that quasars are 100x brighter than a galaxy? It’s in the quasar Wikipedia article.
Note that the last link says it’s 75 times typical quasar power.
Don’t these numbers not add up? If mass is 1000x luminosity, and quasars are 100x galaxy, then how is the ratio 75x? Seems like a random order of magnitude missing.
I tentatively think this resolves the 1 and 1000x questions, but leaves open the 1/1000 question. Will leave this up for rebuttal for a week before concluding that. By default it probably gets 1⁄2 credit if unrebutted.
For 1/1000, you have about the same amount of power as a galaxy, and you could only make a very dim quasar, so it seems like you’d need a different line of analysis. (E.g. that we’d notice something as bright as a galaxy with a weird spectrum.)
Don’t these numbers not add up? If mass is 1000x luminosity, and quasars are 100x galaxy, then how is the ratio 75x?
The ratio for the sun is actually 1480 to be exact, plus the rest of the galaxy is apparently dimmer per unit mass than the sun is.
For 1/1000x, I think if you put most of the energy into the radio spectrum, perhaps a single frequency or a few frequencies that you predict others will survey for, it should be easily noticeable. I’ll look for details when I get home, unless someone beats me to it.
If you put 1/1000 the mass of a galaxy into radio signals over 10 GHz bandwidth over 10 billion years, you get 2.7e28 W/Hz power spectral density. According to this paper table 2, at redshift z=2.083 (about 10 billion light years away) a radio source of 10^25.78 W/Hz was detected on Earth at a flux density of 3.54 mJy so 2.7e28 W/Hz should translate to 1580 mJy on Earth. According to this paper, NVSS has cataloged all objects of flux density >2.5 mJy over 82% of the sky so it likely has detected and cataloged the alien beacon. Unfortunately according to section 2.1.1 of this paper, “However, the large beam size does not allow one to determine precise structure of sources or to determine positions accurate enough to establish optical counterparts.” so we may not have noticed it as an anomalous object.
Back to the visible spectrum, according to this article:
The most recent phase, SDSS-III, began in 2008 and includes the Baryon Oscillation Spectroscopic Survey (BOSS), a part of SDSS-III aimed at mapping the cosmos. Its goal is to map the physical locations of all major galaxies back to seven billion years ago, and bright quasars back to 12 billion years ago – two billion years after the Big Bang.
So if the alien beacon is brighter than a major galaxy (not sure what that means exactly) and within 7 billion LY, then it would have been cataloged, and SDSS captures images at 5 color bands so it would be easy to use color to stand out. (SDSS runs a bunch of algorithmic filters to try to classify each light source based on color, and if none of the filters fit, the source is classified as OTHER and a human looks at it.) 1/1000 the mass of Milky Way over 10 billion years translates to 54 times the luminosity of Milky Way so it should have been noticed by SDSS. But SDSS only covers 35% of the sky, and it doesn’t seem like there’s another survey that’s comparable, so I guess there’s still a pretty good chance it wouldn’t have been noticed after all.
1580 is much more than 2.5, and even there are only a million things in their survey, surely we would notice such a bright source and inspect it in detail? It seems like there is basically nothing in the sky that bright at that redshift.
Just realized, if you combine colonization and radio beacons, 1/1000x galaxy mass would be enough to make an artificial pattern of >2.5mJy sources over an area of the sky that’s bigger than NVSS’s beam size, and that may have been noticed by someone as an anomalous cluster/pattern of radio sources.
Between the analysis we’ve done so far and revisiting Anders and Stuart’s colonization analysis, I think it’s unlikely that there are unobserved aliens who are worth looking for. Especially given that 1/1000 of a galaxy is a pretty negligible budget, I expect someone would have been willing to spend >1 galaxy on this project if it makes sense and that’s a key margin.
My current plan is to award you and Stuart each $100 prizes and declare the contest closed.
It could be a drawing, but consisting of quasars, not from individual stars. A cube with a side of 1 billion ly could have a few million galaxies in it, so the drawing’s patter could be rather complex and provide tens or hundred kilobytes of information. Or else, the drawing could be rather simple beacon like a circle.
According to this paper (which I linked to), it looked in detail at a set of S > 1.3 Jy radio sources (274 of them), in a small patch of the sky, which makes me think that there are enough bright radio sources that 1.5 Jy wouldn’t stand out that much. EDIT: Oh you can’t tell the redshift of a radio source without looking at it optically, but that requires “determine positions accurate enough to establish optical counterparts” which can’t be done with the NVSS survey data. The paper linked above did it by using another more accurate radio survey to establish optical counterparts but that survey only covered a small patch of the sky.
Don’t these numbers not add up? If mass is 1000x luminosity, and quasars are 100x galaxy, then how is the ratio 75x? Seems like a random order of magnitude missing.
I tentatively think this resolves the 1 and 1000x questions, but leaves open the 1/1000 question. Will leave this up for rebuttal for a week before concluding that. By default it probably gets 1⁄2 credit if unrebutted.
For 1/1000, you have about the same amount of power as a galaxy, and you could only make a very dim quasar, so it seems like you’d need a different line of analysis. (E.g. that we’d notice something as bright as a galaxy with a weird spectrum.)
The ratio for the sun is actually 1480 to be exact, plus the rest of the galaxy is apparently dimmer per unit mass than the sun is.
For 1/1000x, I think if you put most of the energy into the radio spectrum, perhaps a single frequency or a few frequencies that you predict others will survey for, it should be easily noticeable. I’ll look for details when I get home, unless someone beats me to it.
If you put 1/1000 the mass of a galaxy into radio signals over 10 GHz bandwidth over 10 billion years, you get 2.7e28 W/Hz power spectral density. According to this paper table 2, at redshift z=2.083 (about 10 billion light years away) a radio source of 10^25.78 W/Hz was detected on Earth at a flux density of 3.54 mJy so 2.7e28 W/Hz should translate to 1580 mJy on Earth. According to this paper, NVSS has cataloged all objects of flux density >2.5 mJy over 82% of the sky so it likely has detected and cataloged the alien beacon. Unfortunately according to section 2.1.1 of this paper, “However, the large beam size does not allow one to determine precise structure of sources or to determine positions accurate enough to establish optical counterparts.” so we may not have noticed it as an anomalous object.
Back to the visible spectrum, according to this article:
So if the alien beacon is brighter than a major galaxy (not sure what that means exactly) and within 7 billion LY, then it would have been cataloged, and SDSS captures images at 5 color bands so it would be easy to use color to stand out. (SDSS runs a bunch of algorithmic filters to try to classify each light source based on color, and if none of the filters fit, the source is classified as OTHER and a human looks at it.) 1/1000 the mass of Milky Way over 10 billion years translates to 54 times the luminosity of Milky Way so it should have been noticed by SDSS. But SDSS only covers 35% of the sky, and it doesn’t seem like there’s another survey that’s comparable, so I guess there’s still a pretty good chance it wouldn’t have been noticed after all.
1580 is much more than 2.5, and even there are only a million things in their survey, surely we would notice such a bright source and inspect it in detail? It seems like there is basically nothing in the sky that bright at that redshift.
Just realized, if you combine colonization and radio beacons, 1/1000x galaxy mass would be enough to make an artificial pattern of >2.5mJy sources over an area of the sky that’s bigger than NVSS’s beam size, and that may have been noticed by someone as an anomalous cluster/pattern of radio sources.
Between the analysis we’ve done so far and revisiting Anders and Stuart’s colonization analysis, I think it’s unlikely that there are unobserved aliens who are worth looking for. Especially given that 1/1000 of a galaxy is a pretty negligible budget, I expect someone would have been willing to spend >1 galaxy on this project if it makes sense and that’s a key margin.
My current plan is to award you and Stuart each $100 prizes and declare the contest closed.
It could be a drawing, but consisting of quasars, not from individual stars. A cube with a side of 1 billion ly could have a few million galaxies in it, so the drawing’s patter could be rather complex and provide tens or hundred kilobytes of information. Or else, the drawing could be rather simple beacon like a circle.
According to this paper (which I linked to), it looked in detail at a set of S > 1.3 Jy radio sources (274 of them), in a small patch of the sky, which makes me think that there are enough bright radio sources that 1.5 Jy wouldn’t stand out that much. EDIT: Oh you can’t tell the redshift of a radio source without looking at it optically, but that requires “determine positions accurate enough to establish optical counterparts” which can’t be done with the NVSS survey data. The paper linked above did it by using another more accurate radio survey to establish optical counterparts but that survey only covered a small patch of the sky.