(IAAC) Re: Relaxation/Evaporation

----- Original Message -----

From: Yann Pothier <yann.pothier@fnac.net>

To: <netastrocatalog-announce@jovian.com>

Sent: Wednesday, December 15, 1999 6:20 PM

Subject: (IAAC) relaxation/evaporation

> Hi to all,
> Somewhat out of our main purpose (deep sky observing), but does someone
> know the difference between RELAXATION and EVAPORATION phenomena in
> clusters (open and globular, it works for both I believe)??
> Thanks in advance if you can help, yann.
> Yann Pothier
> 11 impasse Canart, 75012 PARIS, FRANCE
> yann.pothier@fnac.net
> http://www.astrosurf.org/cielextreme
> http://www.astrosurf.com/cielextreme
> http://astrosurf.org/skylink/publi/cielextreme,
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> Yann,


Your time for posing this question couldn't have been better, as I am presently writing something about this on globulars.

The relaxation and evaporation phenomena are important modern ideas about star clusters as it describes something about the dynamics of the stars within it and the cluster as a whole. To explain this, the kinematics of the inner workings of a globular might be worthwhile.

Dynamics of a Cluster.

Overall, the mental picture of any cluster is often poorly represented, mainly because the motion of all the stars is unfamiliar to normal orbital motions we see in double stars and planets. We can compare globulars to be similar to bees buzzing around a hive. However, this is not a very accurate view. The simplest picture is to imagine that the cluster is a combination of a mass collection of so-called temporary binaries. Most of the single stars travel, averaging about 5 kilometres per second, along independent orbits until they eventually and inevitably encounter the gravitational field of another star. In this view, each star is forming (and breaking) a continuous series of temporary partnerships. Gravitational effects change the star's direction, sending it along a new deviant path - a process repeated endlessly. As a consequence an individual star's motion weaves throughout the cluster. In the end, the effects are like a merry-go-round, where the motions of the whole merry-go-round act like the entire cluster, even though the individual motions of "horses" (or someone walking on the floor of the merry-go-round) are acting (nearly) independently of each other.

Clusters dynamics are internally controlled by so-called core binaries. These are close binary systems that hold most of the angular momentum and kinetic energy - and subsequently control the rate of membership loss. Two subgroups of "core binaries" exist - the soft core binaries and hard core binaries.

* Hard-core binaries make the central controlling factor on the stability of the GSC.

* Soft core binaries act as an additional but smaller "gravity potentials", which acts within a more localised area of the cluster.

Each "core binary" also holds the greatest potential, and the combination of the gravitational forces by a number of surrounding stars may cause this 'Gravitational potential' to be exceeded. In this unusual case, the kinetic energy causes the ejection of a star - unceremoniously "turfed-out" into either anagalactic, or more likely, extragalactic space. In recent years, this method of rejection may account for the number of isolated stars that have been found between galaxies within the Local Group. (One group of B-stars still are yet to be explained, and some theorists suggest they might have formed independently but at the same time as the GSC's.) Compared velocities with the Milky Way, such individual stars may exceed 300kms-1.

Over the long term, combinations of these effects make the calculation of a cluster's behaviour and stability to be both uncertain and unpredictable. Technically, we call this discontinuous behaviour. In some ways, the existence of these types binaries makes a globular similar to an open star cluster, though their numbers are very much greater.


Relaxation of a star cluster is where gravitation is slowly contracting the cluster. Explanation of this is complicated, and relates to properties of each individual cluster. The picture of a globular, according to King (1981), divides orbital behaviour of the cluster into three time durations;

* t_cr - Crossing time (Time for star motion across a globular)

* t_rix - Relaxation Time (Accounting for Stellar Encounters and gravitational distributions)

* t_evol - Evolution Times (Accounting for star escapes and changes in the appearance of the whole cluster.

The relaxation time "t_rix" describes how individual stars exchange gravitation energies and obtain the cluster's densities and velocities distributions. Many thing can happen during this time, including close encounters, formation of true binaries, destruction of true binaries, and even stellar collisions! (The latter incidentally may account for the so-called "blue-stragglers", appearing like "new" highly luminous stars, where no gas exists for their formation. Relaxation Times of the "half-mass radius" is typically about one billion years. For the core, the relaxation time is in the order of 100 million years.


The behaviour of Relaxation time is also prevalent to the tidal forces acting from globulars as they pass through the galactic plane in their long period orbits.

The Milky Way’s gravitational field is quite destructive, as this can cause the outer stars to be stripped away, and these become part of the Milky Way stars. The effects cause significant changes towards the dynamics of the cluster, that more likely make the cluster shrink in size. Some think this is how the globular ends up to pulsating in size (like a jellyfish), where the gravitational potentials are relaxed and compressed.

Relaxation time is also affecting certain structures of the cluster. For example many clusters have significant cores, so the effects of much of this usually only apply to the core. Another consequence of these dynamical effects is so-called core collapse, which has been proved to be as a direct consequence of evaporation of stars. King (and others) believes some clusters (like M15 in Pegasus) may be presently undergoing core collapse.


You are best to refer to October 1998's Sky and Telescope "The Dynamic Lives of Globular Clusters."

Another brilliant article is "The Dynamics of Globular Clusters" ; QJRAS, (1981), 22, 227-243.

You might also like to get a copy of William Harris’s "Catalogue of Parameters for Globular Clusters" (Version: June 22nd 1999)

Table III "Metallicity, Kinematics, and Structural Parameters" has the parameters relating to globular structures. Here the relaxation times are given (Column 11 and 12)

Esprez que c'est d'aide vous,
Les Meilleurs Voeux