How far away are stars in a typical star cluster from each other?

[swampwiz]

I'm trying to grok what this would look like to an observer on an Earth-like planet around a star in the center of such a cluster.

 

[Drakkith]

Open clusters tend to disperse very quickly, so the chances of finding a planet with life inside an open cluster is very low.

However, globular clusters last for very long time and have hundreds of thousands to a million stars within a radius of 100 light years or less. The density of stars is about 1,000 to 10,000 times denser near the core of the cluster compared to our local neighborhood. I'd guess the view from the center of the cluster would be spectacular, with a sky full of very bright stars and a background much brighter than our night sky.

 

[snorkack]

Open clusters tend to disperse very quickly, so the chances of finding a planet with life inside an open cluster is very low.

On a member star.
But there is a large number of Ursa Major Moving Group stars all around Sun - yet Sun is not a member of Ursa Major Moving Group.
Does the Big Dipper cluster itself contain nonmembers? That is, stars that (unlike Dubhe and Alkaid) share the radial distance of the members but that (like Dubhe and Alkaid) do not share the peculiar motion and age? A Sun-like star in Big Dipper would be around magnitude +7, like HD115043 (this one is a member).

 

[Drakkith]

I believe you're referring to the Ursa Major Moving Group. My understanding is that this really isn't a cluster anymore, its stars having spread out into a loosely bound formation that are moving in roughly the same direction. But it is certainly possible that an older star system could stumble through the middle of a newly formed open cluster.

What the view would be would depend on the number of stars in the cluster, their sizes, and how closely packed they are. It could be similar to a globular cluster, where the sky is full of brilliant stars, or it might look fairly similar to ours if there aren't too many stars or they aren't very massive.

 

[berkeman]

globular clusters last for very long time and have hundreds of thousands to a million stars within a radius of 100 light years or less. The density of stars is about 1,000 to 10,000 times denser near the core of the cluster compared to our local neighborhood. I'd guess the view from the center of the cluster would be spectacular, with a sky full of very bright stars and a background much brighter than our night sky.

https://www.sciencephoto.com/media/814339/view/globular-cluster-from-planet-surface

 

[snorkack]

And that´s supposed to be ω Centauri?
The total brightness of ω Centauri is quoted as +3,9, with 36 arc minute diametre.
At 100 times smaller distance, ω Centauri would still be just -6,1, across 60 arc degrees.
Compare Pleiades. Alcyone and Atlas each outshine ω Centauri, and the quoted diametre of ω Centauri would fit both. Alternatively you might use a wide angle eyepiece (100 and even 110 degrees eyepiece FOV have been quoted, but are these really usable?) at full exit pupil (are these offered with wide angle eyepieces?) - what would Pleiades look like in a 100x700 telescope with a wide field of view?

 

[Drakkith]

@berkeman Interesting depiction. I'm imagining dozens or hundreds of stars within, say, 1-10 light years of the planet if it is near the core of the globular cluster. Compare this with Earth, where we only have about 12 stellar objects within that distance, including one white dwarf and three brown dwarfs. Most stars in globular clusters are about 2 solar masses or less since higher mass stars have already burned out and the majority of star formation ceased long ago. For comparison, Sirius, the brightest star in the night sky, is just about 2 solar masses and only about 8.6 ly away.

So I'm thinking there would be several dozen stars at roughly the same brightness of Sirius or perhaps a bit brighter, many hundreds of stars a magnitude or two dimmer, and thousands upon thousands of dimmer stars that gradually merge into a grey background that's the result of the combined light of so many stars that can't be resolved individually.

Perhaps you have a star or two that are within a light year or less of the planet. A star like Sirius at 1 light year has an apparent magnitude of about -6.35. That's MUCH brighter than Jupiter gets at opposition, which is -2.94. It would be brighter than even Venus, at -4.92. It would be absolutely brilliant in the night sky.

 

[snorkack]

@berkeman Interesting depiction. I'm imagining dozens or hundreds of stars within, say, 1-10 light years of the planet if it is near the core of the globular cluster. Compare this with Earth, where we only have about 12 stellar objects within that distance, including one white dwarf and three brown dwarfs. Most stars in globular clusters are about 2 solar masses or less since higher mass stars have already burned out and the majority of star formation ceased long ago. For comparison, Sirius, the brightest star in the night sky, is just about 2 solar masses and only about 8.6 ly away.

Nope. The main sequence turnoff in Milky Way globular clusters is around 1 solar mass.
But my problem is with the phrase "typical star cluster".
Look at the nearest. Big Dipper. Nicely around 20 degrees across, good to grasp by eye. (25 degrees counting Alkaid, but it actually is a background star). Contains a rough quadrangle, longest side 10,3 degrees (again counting a background star Dubhe).
https://owlcation.com/stem/Angular-distances
Brightest stars at about +1,8 easy night sky objects.
And now look at another cluster. Orion Trapezium.
https://skyandtelescope.org/observing/star-trapping-in-orions-trapezium/
Also contains a rough quadrangle.
Except... the long side is 14,9´´.
If you want to see it in a comparable scale with Big Dipper, you will need 2500x magnification.
And remember proper light gathering area, too. You would need maybe 18 m aperture.
In such a 2500x18000 telescope, the objects are brightened by 17 magnitudes... which means that θ¹ Ori C, magnitude +5,1 in sky, will be -11,9 in your telescope. Or for an observer living about 0,6 ly from Trapezium. Almost as bright as full Moon. It is almost 14 magnitudes brighter than the brightest star in Big Dipper.
Two very different clusters. Which of them are you calling "typical"?

 

[phyzguy]

@berkeman 's depiction is what it would look like to be near, but still outside of a globular cluster. I think what @Drakkith is talking about is being at the center of a globular cluster, which is very different.

 

[snorkack]

@berkeman 's depiction is what it would look like to be near, but still outside of a globular cluster. I think what @Drakkith is talking about is being at the center of a globular cluster, which is very different.

Yes, but I am comparing surface brightnesses. This is not changed by distance, nor by a good telescope. Bad telescopes can decrease it (light loss, small exit pupil) but never increase.
https://esahubble.org/static/archives/releases/science_papers/omegacentauri.pdf
This (graph at page 17) suggests that a column of 1 square arcsecond through the centre of ω Cen would total about +16,6. I understand that 1 lightyear would be around 12´´ there.
Surface brightness is shown falling to +17 at maybe 60´´, then faster to +18 at 200´´.
Which means around +8 per square arc minute at the centre, right?

 

[Cerenkov]

Nope. The main sequence turnoff in Milky Way globular clusters is around 1 solar mass.
But my problem is with the phrase "typical star cluster".
Look at the nearest. Big Dipper. Nicely around 20 degrees across, good to grasp by eye. (25 degrees counting Alkaid, but it actually is a background star). Contains a rough quadrangle, longest side 10,3 degrees (again counting a background star Dubhe).
https://owlcation.com/stem/Angular-distances
Brightest stars at about +1,8 easy night sky objects.
And now look at another cluster. Orion Trapezium.
https://skyandtelescope.org/observing/star-trapping-in-orions-trapezium/
Also contains a rough quadrangle.
Except... the long side is 14,9´´.
If you want to see it in a comparable scale with Big Dipper, you will need 2500x magnification.
And remember proper light gathering area, too. You would need maybe 18 m aperture.
In such a 2500x18000 telescope, the objects are brightened by 17 magnitudes... which means that θ¹ Ori C, magnitude +5,1 in sky, will be -11,9 in your telescope. Or for an observer living about 0,6 ly from Trapezium. Almost as bright as full Moon. It is almost 14 magnitudes brighter than the brightest star in Big Dipper.
Two very different clusters. Which of them are you calling "typical"?

Perhaps you are getting confused, snorkack? The Big Dipper isn't a "typical star cluster" or any kind of star cluster.

https://en.wikipedia.org/wiki/Big_Dipper

The Big Dipper, aka Ursa Major, the Great Bear, is a constellation. A constellation is a number of stars grouped together by humans, as seen from our vantage point here on Earth. If you look at the distances of the main stars they vary from 79 to 124 light years away. So they are not necessarily physically grouped together or gravitationally bound to each other.

This is a completely different ballgame to the stars in the Trapezium, which are posited to have originated together and to be physically grouped together, being about 1.5 light years apart.

https://en.wikipedia.org/wiki/Trapezium_Cluster

I would suggest that to compare the Big Dipper to the Trapezium is to compare apples with oranges.

Thank you,

Cerenkov.

 

[snorkack]

Perhaps you are getting confused, snorkack? The Big Dipper isn't a "typical star cluster" or any kind of star cluster.

https://en.wikipedia.org/wiki/Big_Dipper

The Big Dipper, aka Ursa Major, the Great Bear, is a constellation. A constellation is a number of stars grouped together by humans, as seen from our vantage point here on Earth.

Actually, Ursa Major is a constellation, Big Dipper is an asterism. A constellation is a number of stars that are in the same direction from Sun, grouped together by people, with blank sky in between and around, in enumerated list of 88. An asterism is a grouping of stars not included in the 88.

If you look at the distances of the main stars they vary from 79 to 124 light years away. So they are not necessarily physically grouped together or gravitationally bound to each other.

Look again:

1. Dubhe	α UMa	1.8	124
   Merak	β UMa	2.4	79
   Phecda	γ UMa	2.4	84
   Megrez	δ UMa	3.3	81
   Alioth	ε UMa	1.8	81
   Mizar	ζ UMa	2.1	78
   Alkaid	η UMa	1.9	101

If you exclude Dubhe and Alkaid, the rest are between 78 (Mizar) and 84 (Phecda) - 5 stars in 6 ly. Next, Alkaid, is 23 ly behind Mizar. For comparison, the 20 degrees or so angular distance between Merak and Mizar makes nearly 30 ly projected distance at that distance.
And now have a look at the proper motions...
https://en.wikipedia.org/wiki/Big_Dipper#/media/File:Astro_4D_uma_rg_anim.gif
The 5 stars that are close together actually move together. They have always been together.
Looking around Big Dipper, you will find some dimmer stars that share the distance and proper motion. Alcor, then 2 stars at +4,9 and +5,2, one at +6,8 and three from +8,1 to +8,6. That makes a total of 12 stars, at the same distance and moving together.
It is a cluster. But...

This is a completely different ballgame to the stars in the Trapezium, which are posited to have originated together and to be physically grouped together, being about 1.5 light years apart.

https://en.wikipedia.org/wiki/Trapezium_Cluster

I would suggest that to compare the Big Dipper to the Trapezium is to compare apples with oranges.

Thank you,

Cerenkov.

No. Both Big Dipper (7 stars minus the 2 background stars but plus 7 dimmer stars) and Trapezium are stars which are physically together, move together and formed together. Both are clusters. The issue is, they are very different - which of them is typical?

 

[Cerenkov]

Ok, my bad Snockack.So perhaps swampwiz's the use of the word 'typical' is poorly chosen by being insufficiently precise?Cerenkov.