The true size of the Jewel Box is difficult to decipher, as the main bright stars are further west when compared with the majority of component stars. Kappa Crucis' true centre is about 2.1OW of Kappa Crucis itself, and southwest of 6.8 mag "Star 4"/ HIP 62913 / HD 11934 (See "Individual Stars"). My own estimates place the centre at 12h 53m 33s -60° 22' 25". Some doubt still exists of the cluster's true centre, and this likely will remain for some time - at least until the distribution of the individual stellar masses are truly known.
Overall, any quoted star cluster diameter is often fairly difficult to ascertain. The problem seems to be that most of the bright stars are contained within the central region of the cluster, while the least massive stars may appear significantly further away - not only dynamically, but in deciding if a particular star is either a true member or just merely a field star.
In some ways saying where the cluster physically ends is nonsense, as it is like asking "How long is a piece of string?" Theoretically, an infinite distance of influence is possible, though from superclusters of galaxies, individual galaxies, open and globular clusters, to planetary moons within solar systems, and the boundary of influence is limited by other gravitation from bodies outside the system. Among stellar dynamicists such debates continue - even though nearly eighty years has passed since the first questions were asked about this problem. Gravitationally, the effects decrease by the simple Newtonian inverse square power law, (I.e. 1 / x2 ) meaning that the influence of gravity decreases according to the square of the distance. However, the exponent ' n ' in the '1 / x n ' doesn't necessarily have to be 2, as values like 1.8 to 2.2 are also possible - and this also applies to the sister cluster types - the globulars. These variations are not a challenge to Newtonian Laws, but are the reflections of the influences from other bodies in the system, which can accelerate or decelerate the "average" velocity of the component stars.
At some arbitrary distance, the gravitational influence of the nearby stars and Milky Way are powerful enough to strip stars from clusters. This marks the end of the open cluster and any stars beyond this limit are simply lost to the Milky Way's stellar precession, never to return.
To complicate this further, the existence of core binaries influences the size and stability of all open clusters. A core binary controls the "net potential energy" in the centre of the cluster. These act as "gravity sinks", containing more angular momentum than the cluster. These "sinks" are thought to hold the cluster together, and influence the duration for which the cluster stars are kept together. A solitary close binary can act as a so-called hard-core binary, while several of the surrounding binaries can be referred as soft-core binaries. In addition, the "compactness" of the cluster is strongly influenced by these binaries. Eclipsing variables in the Jewel Box, if they are truly cluster members, are likely to be all soft-core binaries.
Incidentally, stars that are not "core" binaries of either type orbit the cluster move in continuously varying orbits depending on the proximity to the other stars. In some ways, it is like a pinball game, with the direction of the star bouncing around the confines of the playing area of the game. Also they accelerate and decelerate depending on the relative positions. Ejection is one possible outcome for them, but other possibilities are just as interesting. For example, it is possible for two stars to become temporary binaries, whose fragile existence is influenced by nearby stars. In certain instances, these can be forced together to make soft-binaries. (Some have thought that combining these influences, makes all clusters more like collections of many binary stars.) Furthermore, and likely the issue that captures the imagination, is the likelihood of stellar collisions. The chances of two stars colliding in the general field in the Milky Way are highly improbable, and this also precludes the improbable James Jeans' 1745 "Tidal Theory" of the formation of our Solar System, which it is said, was produced by a passing star making "tongues of flames" to leap the gulf between the two stars. However, inside clusters the chance of collisions significantly increases. Those that undergo such collisions are thought to produce "blue stragglers" - apparent "new stars" seen on colour-magnitude diagrams. Blue stragglers are far more common in globulars than open clusters.
But back to the problem of the true "edge" of clusters.
Like globular star clusters, open clusters' edges can "globally" be roughly calculated using the distribution law and the laws of probability. Statistically, the distribution can be set at the "3σ- level", where 99.97% of all stars should appear within that size boundary. Not wishing to get into much mathematical "mumbo-jumbo", the "3σ - level" is very roughly three diameters, or six cluster radii, larger than the apparent telescopic diameter of the cluster. An example of this relative extension is HIP 62732. which is at the very edge of the distribution for the Jewel Box.
>p align="justify"> From the cluster data available, it seems the most practical means of determining the diameter is to multiply the factor of 2.83 (2 sqrt 2) times the proper motion, and then compare this against the central proper motion of the dominating brighter cluster stars. This methodology, for example. was applied by Gretchen. L. Hagen in "An Atlas of Open Cluster Colour-Magnitude Diagrams"; Vol.4., Pub. David Dunlap Observatory, University of Toronto (Canada) (1970), and this has remained the general size "bench mark".
Figure 5. - "
The Jewel Box's True Size "
Calculating the true size of NGC 4755, assuming the main asterism is 5' across and at an accepted distance of 2.1 ± 0.2 kpc, finds the true diameter to be about 3.3 ± 0.3pc, corresponding to a volume of 14.7 pc.3 (cubic parsecs.). For the 170-odd stars, down to 16.5 mag, that can be seen in large Dobsonians, the volume must then average about twelve stars per cubic parsec.
If we assume the rough "3σ", then the likely size where gravity has a significant effect on cluster stars, makes the apparent diameter extend to 15'arcmin.
At the distance of 2.1kpc, the cluster covers the true scale of about 10 ± 1pc in the volume of about 500 pc3. This favours about 240 stars within the 15' volume, dropping the stellar densities to an average of two stars per cubic parsec.
For the accepted observations made prior to 1970, is Hagen p.24 (1970) who assumes the size as 3'arcmin. This is used for the Jewel Box's C-M Diagram in this reference. The distance accepted in this text is an unusually close 850 pc, and this is taken from observations by Feast (MNRAS, 126, 11 (1963)) and those of Hernández (1960)), giving NGC 4755 the true diameter of c.7pc for about 130 of the cluster stars.
Southern Astronomical Delights © Andrew James (2002) Sydney, Australia