Night Sky in an open cluster (APOD 2009 April 12)

[Jyrki]

I have always wondered what the night time sky would look like, if we were in orbit about a member of a cluster as opposed to good ole Sol. Today's APOD finally gives me some raw data to do the math. Let's see. An angle slightly larger than that of the Moon at 800 lys. The Moon's diameter is about 3400 km at a distance of about 380000 km, so it's a ratio of 1 to 100 (close enough!). So the diameter of this cluster would be in the ball park of 8-10 light years (give or take some).

There are apparently a few dozen stars in this cluster. May be more, but that's what it looks like to my untrained eye! I am prepared to be very wrong about this. A cubical box with a side of length 9 light years can be viewed as consisting of 27 smaller cubes wih a side of 3 light years. If there were 27 stars evenly distributed, we would have one star in each smaller box. The centers of the neighboring smaller cubes are at distances of 3, 4.2 and 5.2 light years from each other.

Hmm. That's not much denser than what we see in these parts! 4.3 lights to Alpha Centauri, 8.7 to Sirius (and some other neighbors that I don't recall). Do we live in an open cluster? I think not? Something's wrong with my premises. Anyone?

To return to my title: I cannot begin to guess the absolute brightness of the members of this cluster. If we were living in a cluster like this would we have a few dozen stars about as bright as Sirius. May be they would be an order of magnitude brighter, as it sounded like they would be more massive than Sol or Sirius?

As always, all the comments are welcome and appreciated - irrespective of whether they are backed up by more accurate knowledge/data or not!

http://apod.nasa.gov/apod/ap090412.html

[Case]

So the diameter of this cluster would be in the ball park of 8-10 light years (give or take some).

When calculating, do not use the rounded numbers, but try to get the numbers as precise as you can. Distance: 825 ly, stars contained in a volume of about 7 light years diameter. (SEDS Messier Catalog). Pretty close, but a little denser.

There are apparently a few dozen stars in this cluster. May be more, but that's what it looks like to my untrained eye! I am prepared to be very wrong about this.

That would be just the brighter ones. According to SEDS, about 30 are confirmed members, but the cluster may have close to 50 members, perhaps 50-100, depending on who you ask.

A cubical box with a side of length 9 light years can be viewed as consisting of 27 smaller cubes wih a side of 3 light years. If there were 27 stars evenly distributed, we would have one star in each smaller box.

A sphere would be more precise, and have only 52% of that volume, thus 190% of the density (with the same amount of evenly distributed stars)!

To return to my title: I cannot begin to guess the absolute brightness of the members of this cluster.

Young, very bright stars. The brightest star in the cluster has a visual magnitude of 6.83. That corresponds to an absolute magnitude of about -0.19, or about 100 times brighter than the Sun. Consider Sirius is about 25 times more luminous than the Sun.

[Chris Peterson]

Hmm. That's not much denser than what we see in these parts! 4.3 lights to Alpha Centauri, 8.7 to Sirius (and some other neighbors that I don't recall). Do we live in an open cluster? I think not? Something's wrong with my premises.

I think your conclusion is correct- the sky wouldn't look much different from here. We're not in an open cluster, because our system is too old to still be close to any other stars formed at the same time. But we might be considered to be in a loose, coincidental cluster (although not a very impressive one).

We'd have to be in a much richer area, like a globular cluster, to see a really significant change in the structure of the night sky. And even that would have less visual impact than you might expect.

[Jyrki]

To Case: Thanks for the remarks and for the data on the luminosity of these stars. Yes, for more accurate figures I should use a spherical region, *but* I should also use the densest 3D packing (that you get when you pile up identical size balls in hexagonally packed layers appropriately interlaced - imagine a pile of oranges or ball bearings if you like) as opposed to the cubical packing that I tried to use, when estimating the distance to the nearest neighbor. The changes would not likely be very dramatic given that the distance scales as the cubic root of the volume, so 190% density gives an expected distance of a factor less than cube root of 2 smaller. Significant, yes, but not for my purposes of trying to decide, whether the expected distance to the nearest neighbor would be 10 lys, 1 ly or 0.1 lys. Sorry about not making that clear right away.

To Chris: Thanks for the insight. Indeed, you correctly guessed what I was aiming at. I had been under the impression that we reside in a relatively sparsely populated region of the Milky Way, and was half expecting the difference to a cluster to be more significant in this respect. Of course, a relatively small change in the density will be enough to make a region of space stand out from its surroundings upon visual inspection.

To all:
Possibly an even bigger source of error in my calculation was the assumption of uniform distribution. Mutual gravity probably tends to make the center of the cluster denser than the perimeter. Anyway, before starting on anything more precise I would need to define exactly what I am aiming to compute. The average distance to the nearest neighbor from a *given* member star of the cluster (in which case I would take the average over all the stars belonging to a cluster), the average distance between two closest neighbors within a cluster (in which case I would take the average over several clusters of approximately the same type and size) et cetera. Undoubtedly such arithmetic has been done many times over,so let's not get into that here, and stick to the point of view of a star gazer moved onto a planet in orbit about a member star of an open cluster

On with the fantasy: would the dwellers of a compact cluster be more likely to work on interstellar travel? If the nearest neighbor is `only' a fraction of a light year away, it might not appear to be too formidable? Ok, given that at the moment a manned mission to Mars is about the limit of feasibility, we are still several orders of magnitude away from travelling even 0.1 light years . Hmm, I'm forgetting something here. The presence of a nearby neighbor might spell trouble for the stability of any putative planetary system.