Characteristics of globular clusters

[DaveC426913]

Quick question(s):

If a cluster is not "open", it's what?

M62 is a what cluster? (No, not peanuty nougat).

What would be the average distance between stars in a cluster like this?

What would be the average orbital period?

And ultimately, what would the motion patterns of stars in an observer's sky be like? Just looking for a magnitude of time, really. Would they see motion over months, years?

 

[DaveC426913]

I just realized - I wonder if this post got no attention because it looks like homework. Oops.

I can assure you it's not (perhaps note my # of posts. I'm no student!). I'm really merely interested in the last question - I'm trying to help someone on another board (ADP) with a story they're writing that's set in a glob cluster. I'm trying to describe what the motions of their sky would look like.

I've Googled M62, but I get only info about the asterism (object-as-imaged, not the structure of the object), and I've Googled for globular clusters, but I don't get anything about the "typical" structure of a glob cluster.

I suppose I could determine the number of stars in the cluster and find its diameter - that would give me a star2-per-cubic-ly number, which would give me an average distance between them.

Hm. No, that won't tell me about the period of their orbits, which will be based on the mass of the cluster. That's way over my head.

Really, all I'm interested in is a ballpark figure of how much proper motion might be seen on average. Would you see motion over weeks? years?

Wait, Kepler has some laws that derive the period from the orbital radius...

 

[SpaceTiger]

Hi Dave, sorry, I meant to respond to this, but have been juggling a lot of things at once.

If a cluster is not "open", it's what?

Globular clusters and open clusters are different things. Open clusters are very small (~100-1000 stars) and young, usually residing in the galactic disk. Globular clusters, on the other hand, are very old, large (as large 10⁶ stars), and live in the galactic halo.

M62 is a what cluster? (No, not peanuty nougat).

A globular cluster.

What would be the average distance between stars in a cluster like this?

It would vary a great deal from the core to the edge, but it can be as small as 0.01 pc.

What would be the average orbital period?

Globular cluster stars have typical velocities around 5 km/s, leading to proper motions of about 0.2 mas/yr at the typical distance of 5 kpc. This is very difficult to observe, even with a large time baseline. The orbital period is OOM the typical size (~10 pc) divided by the typical velocity, which leads to ~1 million years.

And ultimately, what would the motion patterns of stars in an observer's sky be like? Just looking for a magnitude of time, really. Would they see motion over months, years?

We try to use baselines of a hundred years or more. The proper motion distribution would look something like this (actually an open cluster):

http://www.astro.lu.se/~dainis/Images/hyades.gif"

The apparent convergence of the proper motion vectors is due to overall motion of the cluster relative to the sun.

 

[DaveC426913]

Thanks! Great info.

When you talk about the proper motions, are you talking about "as visible from Earth"? I'm interested in "as visible from (a planet) within the cluster".

I expect that would change things dramatically. Clearly, the best I can hope for is a ballpark idea order of magnitude in time units (since it is dependent on many factors) of the fastest reasonable movement seen.

In the story this guy is resesarching, I'm trying to demonstrate what kind of astronomy they'd have - timelines such as a single lifetime vs. recorded history.

 

[tony873004]

If I did my math right, I get 105 arcseconds / year using 5km/s and 0.01 pc distance from ST's posts. Of course this is a best case scenerio, as I'm using the closest star, and assuming that its velocity is tangental to you. That's still a pretty good proper motion. It would take this star about 16 years to travel the diameter of a full moon. I imagine people living in this cluster would identify stars that moved a bit over the course of their lifetimes, but for the most part, their constellations would remain virtually unchanged over the course of a human lifetime.

$$\begin{array}{l} \theta = \frac{{{\rm{5\rlap{--} k\rlap{--} m/\rlap{--} s (3}}{\rm{.15581 x 10}}^{\rm{7}} \rlap{--} s/yr)}}{{0.01\rlap{--} p\rlap{--} c\,x\,3.0857x\,10^{13} \rlap{--} k\rlap{--} m/\rlap{--} p\rlap{--} c}}\rlap{--} r\rlap{--} a\rlap{--} d\,57.296\rlap{--} d\rlap{--} e\rlap{--} g/\rlap{--} r\rlap{--} a\rlap{--} d(3600arc/\rlap{--} d\rlap{--} e\rlap{--} g) = 105.''475/yr \\ \end{array}$$

 

[DaveC426913]

Zow. OK thanks!

That would actually be enough for a civilization to notice. They would be well aware that their sky is in motion and they'd track it carefully - they'd just need detailed notes to do so.