Q. average size of Globular Clusters?

[mental4astro]

Hi all,

The rise of Sagittarius in the early evening has brought a few questions to mind:

*what is the average size of Globular Clusters?

*what is their upper and lower range?

*number of member stars?

I have been enthralled by the variety of G.C.s visible at this time of year. Some small and intense, others large but obscured by interstellar dust, others resembling exploding firecrackers. Just beautiful, :jump2:.

Mental.

[Robh]

Alexander,

This is a difficult question to answer as we don't even know all the details of the 158 known globular clusters in our own galaxy. The Andromeda Galaxy may have up to 500 globular clusters and M87 in Virgo as many as 10000.
Of the Messier globulars, M71 in Sagitta has a diameter of 26 ly (light years) while M3 has a diameter of 180 ly. A rough average diameter appears to be around 100 light years. 47 Tuc has a diameter of 120 ly and the great Omega Centauri 172 ly.
The small globular M71 has perhaps some 10000 stars while Omega Centauri has several million stars. 47 Tuc and NGC 2808 in Carina have around one million stars. M2 in Aquarius contains around 150000 stars. The average is perhaps in the range 100000 to 500000 stars.
Visually, the brightest globulars (Vmag<10) vary in size from about 5 arcminutes e.g. NGC 6316 in Oph to 36 arcminutes for Omega Centauri at Vmag 3.7.

Regards, Rob

[ngcles]

Hi Alexander, Rob & All,

The "average" is not really easy to answer because there are probably 10-20 still undiscovered and all of those will be of the light-weight, low luminosity variety. It is very unlikely that there will be any more "big-boys" discovered to balance that.

Take a look at this table which orders the Milky Way GC's by intrinsic luminosity ie by their total absolute magnitude (M Vt) (at visual wavelengths) -- which will give a good guide to their masses and therefore likely sizes (disregarding core collapse for the moment).

http://venus.mporzio.astro.it/~marco/gc/table2a.php?sel=M_Vt

There are a total of 147 clusters with assigned M Vt values in the table. The highest M Vt is Omega Centauri (NGC 5139) with a value of -10.29. The smallest is AM-4 with a tiny M Vt of -1.6. We can comfortably assume the other 7 in the table without values are all small, low-mass low luminosity clusters, so that makes the total 154 with known values (or at least we can assume the ones without values are at the bottom, not the top). 154divided by 2 is 77 ...

Quick and dirty, the mid-point in the table (77) is therefore NGC 6496 with a M Vt of -7.23. This is, quick & dirty, Mr Average. Better still add all the M Vt values together and divide by the 154 -- but will probably give you a pretty similar number.

I see M4 (the second closest GC is No 78 on the list and is for all intents and purposes Mr Average too (well, close enough).

So my answer is look at M4 and you are pretty much looking at Mr Average.

http://www.seds.org/messier/m/m004.html

Roughly speaking, it contains 100,000 stars:

http://www.seds.org/hst/M4WD.html

and the tidal radius is about 70 light-years.

Interestingly, M4's M Vt (the total luminosity of the sum of its stars) is only a little more than the M Vt of Alpha Orionis (Rigel). Yep, one supergiant 30-40 odd solar-mass star almost equals it in brilliance. Because of their age, GCs are massive but inherently "wimpy" in light output.

Others may give a different answer -- that's my one! Hope it helps.


Best,

Les D

[Paddy]

How amazing! Many thanks for the question and the answers.

[mental4astro]

Rob & Les,

I must say I am astounded at what you have provided. I second Paddy's vote of thanks for your answers. I didn't expect this level of thourghness.

The little I know about GCs is that they tend to be concentrated in a volume of space inside us around the Milky Way's core. This would explain the level of dust obstruction we observe. Imagine the brilliant show that would behold our eyes if the dust were not there!

It so happens that Mr Average, M4, is one of my favourite targets. Not being as dense a Omega Centuri, it affords finer patterns to be traced. I had also noticed a slight 'yellowing' of its stars, Les, compared to Omega. Now I know why, and it is not a peculiarity of GCs.

Fabulous stuff, gentlemen.

Alex.

[Robh]

Some more interesting stuff ...

I was just reading about M54 in Sagittarius. It is now believed that the globular cluster lies in the recently discovered Sagittarius Dwarf Elliptical Galaxy (SagDEG). A recent estimate of its distance at 87400 light years implies its diameter could be as large as 300 light years!
This also makes Charles Messier the discoverer of the first extra-galactic globular (M54) in 1778.
For more info ...
http://www.seds.org/messier/m/m054.html

Regards, Rob

[Enchilada]

Diameters are given either as the visually observed size or some theoretical one. Telescopic diameters are often expressed in arc minutes, whose outliers make any true estimation difficult. Perhaps a better definition of the outer edges would be based on the gravitational attraction of all the stars just being sufficient enough to hold individuals from escaping.
In true diameter, a globular could extend as far as roughly 500pc., though the larger ones like Omega Centauri visually appears to extends up to 300pc. On the other end of the scale, some GSC's maybe as little as 5pc.

The average, as far as I know, is about 50 parsecs or so.

I'll post a better answer when I find some old references I have!!

[Enchilada]

The following of the Top 10 globulars of most notoriety, gives the true size of the globular from their apparent dimensions in a telescope expressed in arcmin and the known distances measured in parsecs. All basic information is taken from data in tables of Harris (2007), and I have calculated the Visual True Diameter.
Globulars are certainly much bigger than the outliers we do see the telescope, with the likelihood that stars still can be attached are roughly three or four times this diameter. Asking where the end of any globular cluster gravitationally is like asking how long is a piece of string, as the gravitational influence of the majority of the core stars extends theoretically for literally 1000's of parsecs! (actually infinitely if you wanted to be absolutely pedantic, even though it is impracticable in usefulness!)

Calculated Diameters

NGC 5139 (ω Cen) 55 arcmin 5200 pc
Visual True Diameter=83 pc

NGC 104 (Tuc) 50 arcmin 4600 pc
Visual True Diameter=67 pc

M22 / NGC 6656 (Sgr) 32 arcmin 3100 pc
Visual True Diameter=29 pc

NGC 6397 (Ara) 31' 2200 pc
Visual True Diameter= 20 pc

NGC 6752 (Pav) 29' 4200 pc
Visual True Diameter= 35 pc

M4 / NGC 6121 (Sco) 36' 2100 pc
Visual True Diameter= 22 pc

M5 / NGC 5904 (Ser) 23' 7600 pc
Visual True Diameter= 51 pc

M13 / NGC 6205 (Her) 20' 7200pc
Visual True Diameter= 42 pc

M12 / NGC 6218 (Oph) 16' 5500 pc
Visual True Diameter= 26 pc

NGC 2808 (Car) 14' 9200 pc
Visual True Diameter= 37 pc

M55 / NGC 6809 (Sgr) 19' 5200 pc
Visual True Diameter= 29 pc

NGC 6451 (CrA) 15' 6900 pc
Visual True Diameter=38 pc

The mean diameter of these globulars here is about 40 pc or 145 ly. across.

Note: Diameters for globulars can be measured in either the; Core , Half-mass or Tidal radius (expressed in arcmin). These are useful astrophysically, but express little in terms of usefulness to the novice.

Note 2: The further away the globular is the larger error in the visual size of the globular becomes. I.e. The outliers are harder to see. The smaller values given here are likely larger than stated!

[Enchilada]

Few globular clusters have any information of number of stars or the total masses. Most are frankly guesstimates, but some of the largest or closest can be roughly estimated. From the 13 billion ages of these beasties, the initial stars forming globulars have long since gone, leaving the largest stars at about 0.8 solar masses or less. This mass can be estimated from the so-called turn-off point - the place on the globular's H-R diagram. It also tells something the the cluster's age. From this a distribution can be calculated. The following list gives a rough range in mass and number of stars.

NGC 6388 in Scorpius is by far the heaviest by far, while Omega Centauri and 47 Tuc are close behind.

Top 3 by Mass and Number

NGC 6388 (Sco)
M⊙= 2 510 000 No. Stars= 3 500 000

NGC 5139 / ω Cen
M⊙ = 1 440 000 No. Stars= 2 000 000

NGC 104 / 47 Tuc
M⊙ = 150 000 No. Stars= 1 600 000

Smallest Clusters

Pal 5 (Ser)
M⊙ = 23 700 No. Stars= c.70 000

NGC 6366 (Oph)
M⊙ = 15 500 No. Stars= c.40 000

Pal 13 (Peg)
M⊙ = 1 230 No. Stars= c.25 000

On any true scale they roughly average up to about 50 parsecs or 150 light years across producing about one star per light year or 0.25+/-0.10pc.

Maximum densities could be as high as 1 000 stars per parsec! :eyepop:

According to the data derived by Cheroff and Diorgovski; AJ., 339, pg.904-918 (1989), in real terms, NGC 5854 in Hydra is the most tightly packed. Second is the core of 47 Tucanae, while ω Centauri comes in at a surprisingly low 15th. One of the least compact globulars we presently know of is Pal 15.

I can give you more technical details, if so required, especially if you have some cluster in mind. :thumbsup:

[Enchilada]

Hi all. :hi:
A more up-to-date version of the list is of 2003 at;
http://physwww.physics.mcmaster.ca/%7Eharris/mwgc.dat

or even more recent is of August 2007, at;
http://www.seds.org/~spider/spider/MWGC/mwgc.html

Both are by William (Bill) Harris... :thumbsup:

[Paddy]

More amazing stuff! Looks like I'd better have another look at m54 next dark clear night!

[erick]

Imagine living on a planet of a star inside a globular cluster!

Hypotheses:-

1) Probably pretty hot!
2) Never gets dark!
3) Thousands of "suns" always in the sky!

Better not call it "living"! :D

[Robh]

Enchilada, thanks for your knowledgeable input. And educational as usual.

However, I disagree on the above point. I'd rather a diameter based on say an estimated 99% mass (or higher) which might correspond more closely to the visual image of the globular cluster. If you start looking at outliers, the data is going to be forever changing and inescapably debatable at the radius of extremity. As you mentioned, the theoretical gravitational influence goes to infinity. The same would apply to galaxies. In the overall picture, the outliers are pretty insignificant.

Regards, Rob.

[Enchilada]

Oh, if only it was just that easy!

The problem is that the distribution of the mass is not simply 1/r² , where the stars just exponentially drop as you approach the edge of the cluster. (For globulars the value of the exponent is more likely between 1/r^2.2 to 1/r^2.4!) In fact, the actual drop of the distribution is different in the core than the distribution beyond it. An interesting simple example portraying this idea, is the measure of the so-called the half-mass radius — a value measuring very roughly towards the boundary of the inner core. If we take ω Centauri in particular, the half mass radius is 4.2 arcmin — with the rest of the mass distributed to 55 arcmin (and beyond). Hence, actually half the mass is only 1/2000th the volume! The worse thing is that no two globulars are the same in this kind of core and non-core distributions. (This does not take it account the ellipticity of the globular shape or the pulsation over time of the core itself — even more complicated.)

Sadly, there is absolutely no correlation here, so your good idea just doesn't work very well. :sadeyes: Others have thought of that path too., and had to think in different ways.

The best use is the so-called tidal radius, whose boundary is where the density of stars of the globular equal the density of stars in nearby galactic field. It sounds easy to do, but it is an absolute nightmare to calculate properly.

I don't know your expertise here, but an article you might like to read is available at the ADS; Lee, Hyunk Mak, "Tidal Densities of Globular Clusters and the Galactic Mass Distribution" JKAS, 23, p.97-105 (1990). http://adsabs.harvard.edu/abs/1990JKAS...23...97L

Determining Diameters of Globulars by Photographic Images

A neat useful trick is to get an image of a globular and blur it until the majority stars are eliminated. This produces a three toned image — for ω the size of the small globular core (10 arcmin), the visual size in a 'scope (35 arcmin), the softer outliers (55 arcmin). [See the attached image.]
(Considering the values in Harris (Aug. 2007), the values are; 55, 35, and 8.4 arcmin. Not bad for something so roughly done!)



Outliers are those seen at the edge of the cluster, the cut-off is general dramatic - though it is worth mentioning the scattering of stars just merges with the garden variety field stars. Some of the stars are indeed part of the globular, (often obviously in coloured images the more redder ones.) Looking at an image of ω Centauri, these outliers really end at about 65 to 70 arcmin. Beyond this, membership or not really matters little for imagers or visual observers, even though they are theoretically astrophysically important.

I have also attach another small graphic showing the general range of observed sizes seen with globulars. (Notice how tiny the infamous M13 (20 arcmin) is against ω Centauri or 47 Tucanae! :scared:)

[Robh]

Enchilada,

Yes, I can see your point about the 99% mass boundary calculation. Nice in principle and perhaps impossible to measure.
It seems that measurements of tidal radius for globulars is fraught with its own problems as well.
I like the "blurring" photographic method you've featured. Simple, perhaps crude, but effective. It would do me!
Maybe we are trying to be too accurate. After all, no measurement is exact.

Thanks again for your input.

Regards, Rob