I did a little more simulation–this time, I picked a random direction on the celestial sphere, and tracked which stars were the brightest as you moved radially outward. The results (10k tries):
82.25%: Sol (0), Sirius (32263), Canopus (30365)
9.15%: Sol (0), Sirius (32263), Rigil Kentaurus (71456)
4.81%: Sol (0), Sirius (32263), Capella (24549)
2.92%: Sol (0), Sirius (32263), Procyon (37173)
0.46%: Sol (0), Sirius (32263), 8087
0.20%: Sol (0), Sirius (32263), 19799
0.19%: Sol (0), Sirius (32263), 16496
0.02%: Sol (0), Sirius (32263), Lalande 21185 (53879)
Well, Sol is obviously first. I did not find any direction where Sirius was not second. The third finally showed some variety. The top two hits are not too surprising; Canopus dominates, but sometimes you hit Alpha Centauri. It’s mildly surprising that you can get lucky with Capella and Procyon, but I guess they aren’t all that far away. As for the rest–Lalande is a tiny, nearby red dwarf, which I managed to hit a couple of times. I’d suppose the same is true of the unnamed ones as well.
I get way too much noise if I let it go to 4 stars, but there are some expected amusements, such as that Sirius often makes two appearances, at spots 2 and 4. Spot 3 is just a quick pit stop at various nearby dim stars.
Unsurprisingly, the distribution gets smoothed out as you get to larger volumes. Canopus puts in a good showing at the 40 and 400-ly levels, but can’t compete in the 4000s.
I find it kinda interesting that the 400-ly cube has the highest fraction of named stars. I guess it’s appropriate; 40-ly isn’t that large a volume and there are a bunch of wimpy stars in there; at the 400-ly level there’s a good smattering of giants, and many will be part of constellations. Then at the 4000-ly mark there’s just too many to name.
Oh, and a 4-ly cube for good measure:
Sirius (hd48915): 55.88%
Sol (hd0): 41.63%
Rigil Kentaurus (hd128620): 2.49%
I did notice some odd things in the HYG dataset–it lists some absurdly bright (-16 abs mag) stars that dominate if you get even further away. I don’t think these stars exist… maybe they’re supposed to be something else, like a cluster.
I think you’re referring to stars like Mu Cephei (Herschel’s Garnet Star):
[QUOTE=Wikipedia]
A very luminous red supergiant, Mu Cephei is likely to be the largest star visible to the naked eye, and one of the largest known…
This is a runaway star with a peculiar velocity of 80.7 ± 17.7 km/s. The distance to Mu Cephei is not very well known. The Hipparcos satellite was used to measure a parallax of 0.55 ± 0.20 milliarcseconds, which corresponds to an estimated distance of 1,333–2,857 parsecs. However, this value is close to the margin of error. A determination of the distance based upon a size comparison with Betelgeuse gives an estimate of 390 ± 140 parsecs, so it is clear that Mu Cephei is either a much larger star than Betelgeuse or much closer (and smaller and less luminous) than expected.
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In the HYG data I downloaded, Mu Cephei is shown with a distance of “100000.0000” parsecs. Over 10200 stars are shown with this “100000.0000” distance (as a marker that the distance is not known) with a correspondingly huge absolute magnitude. These 10000+ stars include Mu Cephei and Beta Phoenicis:
[QUOTE=Wikipedia]
Beta Phoenicis is a relatively wide visual binary consisting of two G-type giant stars, both with spectral types of G8III. The two orbit each other every 170.7 years and have a relatively eccentric orbit. The stars are separated by almost one arcsecond… The distance to Beta Phoenicis is poorly known. The original reduction of the Hipparcos satellite’s data yielded a parallax value of 16 miliarcseconds, yet its standard error was larger than the parallax value itself. The new reduction of the Hipparcos data gave 0.12 ± 14.62 milliarcseconds, still unusable
[/QUOTE]
BTW, some of the bright stars are highly variable. Careful study of the questions looked at by Dr. Strangelove and myself would need to consider this. (I just worked with each star’s “default” magnitude.)
Ahh, that must be it. I didn’t look at the distances at all, just the XYZ positions. I probably would have realized what was going on had I seen a nice round number like 100000.
All of this analysis should be taken with a grin of salt, as you imply. The numbers are sensitive to distance and the absolute magnitude, and we just don’t have good figures for these in a lot of cases. Nearby stars are better known, of course, but the ridiculously bright ones are far away, and the stellar physics less well known, so there’s a bit more guesswork involved.
Of course, if you’re lucky, sometimes you can get better distance measurements on even very distant stars. If it’s a resolvable binary, for instance, that gives you a lot of information. And if you’re lucky enough to have an eclipsing binary, then you know pretty much everything.
True. It’s also helpful if one of them goes supernova :).
I was curious about parallax-measuring missions, and found the wiki page on the TAU spacecraft. 1000 AU distance, laser communication, nuclear reactor… pretty cool.
[Note: I added the more familiar Bayer or Flamsteed designation for many of the stars.]
For beta Hydri and beta CVn, some of their volumes must be outside the box, since they’re actually brighter than the Sun and probably have larger overall volumes. 36 Oph is actually 3 K-type stars that are all somewhat dimmer than the sun, so the magnitude you used is probably the combined magnitude of the three stars.
The further stars have “enhanced” volumes because the number of known low-luminosity stars falls off fairly dramatically as you go out from the sun. Each of those dim stars takes out a little bubble where they’re the brightest, but there’s fewer bubbles the further you are from Sol.
Also (I had to look this up too): The TAU spacecraft was never launched, just an idea since the late 1980s. It would have taken 50 years to get to its parallax-measuring position…a bit less than 1/200th of the way to Alpha Centauri.
Finally, I hadn’t known about Mu Cephei until now – cool! I want to see the most badass thing you can see with the naked eye (besides, arguably, the Andromeda Galaxy, which I taught myself to recognize years ago). I see you can find it by following the right-most “line segment” in Casseopeia when it’s oriented as a “W,” about three and a half times the distance of that line segment. I’ll look for it the next time conditions are right for me!
Thanks! I figured these must have names. Not sure why they don’t appear in the HYG dataset. If I have time I’ll probably try to merge with some other source that has more comprehensive names.
I’m sure you’re right about some stars being just inside the box at the lower levels. For instance, Rigel shows up at 1.3% in the 400-ly box but is clearly a dominant star at 4000-ly; I can only assume it barely edges in on one corner or face. The boundaries I chose are arbitrary of course so this isn’t too surprising.
Good point about the lesser-known low-luminosity distant stars. Still, Deneb, etc. are bright, so that can’t be the only thing going on.
Rigil means “foot” in Arabic, so it’s the foot fo the Centaur, as opposed to the other Rigil which is Orion’s foot. If you ever run across the name Toliman, that’s also a name for Alpha C.
As for better distances, everyone’s waiting for the Gaia mission to produce better data. It’s predecessor, Hipparcos, had problems and didn’t generate distances as well as was expected.
There’s actually a lot of cool science you could do with a probe that went that far out from the Sun, or better yet, with a few such probes sent in different directions. Get longer-baseline trigonometric parallaxes, of course, but don’t stop there. Look back at the Sun and beyond, and use the Sun’s gravitational lensing to get a really good view of objects in the other direction. Use radio interferometry between the spacecraft to get super-high-resolution radio images of distant sources. If you have enough spacecraft, use those super-high-resolution radio images to do even better parallax measurements, possibly even on quasars. Use the phase lag on telemetry from (and between) the crafts to measure low-frequency gravitational waves. And of course all of the local measurements of things like particle density and magnetic fields. If you’re going to go to the trouble of sending something that far out, then do it right.
Sirius is currently about 8 ly away, so bringing it in to 1 ly would make it 64 times brighter. It’d be a very pretty light at that brightness, somewhat brighter than Venus, but still nowhere near enough to read by.
And gravity-wise, at one light year, Sirius would have around one two millionth of the gravitational attraction as the sun. (Sirius is 2 solar masses, gravity falls off with the inverse square of distance, one light year is 63241 times Earth’s distance from the sun.)
Dr Strangelove;
Thanks for those lists - I’ve been looking for this sort of data to make some rough maps of the local galaxy. There are a few stars in your list which I’ve missed.
Of course there are a few uncertainties in the data - for the most distant stars, and for binary, irregular or variable stars, the distance calculated from parallax can be quite inaccurate. That probably explains some of the anomalies like Mu Cephei.
Another source of uncertainty is extinction due to the interstellar medium - in many, but not all, directions there is a lot of interstellar dust- that means the distant stars look a lot dimmer than they should. There are several very bright stars hidden inside dust clouds in Orion and Cygnus, for example, that would be among the brightest in the sky if we could only see them clearly.
Glad to! If you have any particular requests (different volume sizes, etc.) let me know.
There’s gotta be a better algorithm than the brute force I’m using. It’s a little tricky though since the light has infinite extent. Maybe process things in sectors and figure out the minimum brightness in each one… hmmm.