by neufer » Wed May 01, 2013 1:41 pm
Chris Peterson wrote:casus wrote:
i just can't fathom that 10 million stars in a 150 light year space haven't collapsed together after 12 billion years due to gravity. It's a weak force, for sure, but it aint that weak, especially with no significant spin or "cetrifugal" force from rotation. Wouldnt the earth accelerate to the sun if it had no orbital velocity? of course, indeed technically we're falling to the sun constantly, just happens to be at the same rate we're also flying out tangentially into space. But clusters don't seem to have an orbital axis.
Clusters don't have an overall orbital axis. But each star in a cluster is in orbit around the cluster's center of gravity. That's why clusters don't collapse. In fact, it's just the opposite: clusters eventually fall apart, losing their stars to intergalactic space. That happens because the complex, multiple body orbits inside a cluster are fundamentally chaotic, and as stars perturb each other in their orbits, they transfer orbital angular momentum. This results in stars occasionally being knocked into hyperbolic orbits, meaning their velocities exceed the cluster escape velocity. Over billions of years,
globular clusters evaporate.
Conservation of Energy
http://en.wikipedia.org/wiki/Virial_theorem wrote:
<<In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy,
![Image](http://upload.wikimedia.org/math/3/e/2/3e2c02e5c3a34e2f438f0d70903b632a.png)
, of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy,
![Image](http://upload.wikimedia.org/math/c/3/8/c38888f07a86192dae9ad0829de2a0b8.png)
, where angle brackets represent the average over time of the enclosed quantity. If the force between any two particles of the system results from a potential energy V(r) = αr
n that is proportional to some power n of the inter-particle distance r, the virial theorem takes the simple form:
![Image](http://upload.wikimedia.org/math/b/5/7/b5770a447559f46f3b0c7d8e98adff94.png)
. Thus, twice the average total kinetic energy
![Image](http://upload.wikimedia.org/math/3/e/2/3e2c02e5c3a34e2f438f0d70903b632a.png)
equals n times the average total potential energy
![Image](http://upload.wikimedia.org/math/c/3/8/c38888f07a86192dae9ad0829de2a0b8.png)
. Whereas V(r) represents the potential energy between two particles, VTOT represents the total potential energy of the system, i.e., the sum of the potential energy V(r) over all pairs of particles in the system. A common example of such a system is globular star cluster, where n equals −1 (i.e.,
the total kinetic energy of a globular star cluster amounts to only half the negative total potential energy.>>
http://en.wikipedia.org/wiki/Globular_cluster#Mass_segregation.2C_luminosity_and_core_collapse wrote:
<<In measuring the luminosity curve of a given globular cluster as a function of distance from the core, most clusters in the Milky Way increase steadily in luminosity as this distance decreases, up to a certain distance from the core, then the luminosity levels off. Typically this distance is about 1–2 parsecs from the core. However about 20% of the globular clusters have [already] undergone a process termed "core collapse". In this type of cluster, the luminosity continues to increase steadily all the way to the core region. An example of a core-collapsed globular is M15.
Core-collapse is thought to occur when the more massive stars in a globular cluster encounter their less massive companions. Over time, dynamic processes cause individual stars to migrate from the center of the cluster to the outside. This results in a net loss of kinetic energy from the core region, leading the remaining stars grouped in the core region to occupy a more compact volume. When this gravothermal instability occurs, the central region of the cluster becomes densely crowded with stars and the surface brightness of the cluster forms a power-law cusp. (Note that a core collapse is not the only mechanism that can cause such a luminosity distribution; a massive black hole at the core can also result in a luminosity cusp.) Over a lengthy period of time this leads to a concentration of massive stars near the core, a phenomenon called mass segregation.
The dynamical heating effect of binary star systems works to prevent an initial core collapse of the cluster. When a star passes near a binary system, the orbit of the latter pair tends to contract, releasing energy. Only after the primordial supply of binaries are exhausted due to interactions can a deeper core collapse proceed. In contrast, the effect of tidal shocks as a globular cluster repeatedly passes through the plane of a spiral galaxy tends to significantly accelerate core collapse.
The different stages of core-collapse may be divided into three phases. During a globular cluster's adolescence, the process of core-collapse begins with stars near the core. However, the interactions between binary star systems prevents further collapse as the cluster approaches middle age. Finally, the central binaries are either disrupted or ejected, resulting in a tighter concentration at the core. The interaction of stars in the collapsed core region causes tight binary systems to form. As other stars interact with these tight binaries, they increase the energy at the core, which causes the cluster to re-expand. As the mean time for a core collapse is typically less than the age of the galaxy, many of a galaxy's globular clusters may have passed through a core collapse stage, then re-expanded.
The Hubble Space Telescope has been used to provide convincing observational evidence of this stellar mass-sorting process in globular clusters.
Heavier stars slow down and crowd at the cluster's core, while lighter stars pick up speed and tend to spend more time at the cluster's periphery. The globular star cluster 47 Tucanae, which is made up of about 1 million stars, is one of the densest globular clusters in the Southern Hemisphere. This cluster was subjected to an intensive photographic survey, which allowed astronomers to track the motion of its stars. Precise velocities were obtained for nearly 15,000 stars in this cluster.
A 2008 study by John
Fregeau of 13 globular clusters in the Milky Way shows that three of them have an unusually large number of X-ray sources, or X-ray binaries, suggesting the clusters are middle-aged. Previously, these globular clusters had been classified as being in old age because they had very tight concentrations of stars in their centers, another test of age used by astronomers. The implication is that most globular clusters, including the other ten studied by Fregeau, are not in middle age as previously thought, but are actually in 'adolescence'.>>
[quote="Chris Peterson"][quote="casus"]
i just can't fathom that 10 million stars in a 150 light year space haven't collapsed together after 12 billion years due to gravity. It's a weak force, for sure, but it aint that weak, especially with no significant spin or "cetrifugal" force from rotation. Wouldnt the earth accelerate to the sun if it had no orbital velocity? of course, indeed technically we're falling to the sun constantly, just happens to be at the same rate we're also flying out tangentially into space. But clusters don't seem to have an orbital axis.[/quote]
Clusters don't have an overall orbital axis. But each star in a cluster is in orbit around the cluster's center of gravity. That's why clusters don't collapse. In fact, it's just the opposite: clusters eventually fall apart, losing their stars to intergalactic space. That happens because the complex, multiple body orbits inside a cluster are fundamentally chaotic, and as stars perturb each other in their orbits, they transfer orbital angular momentum. This results in stars occasionally being knocked into hyperbolic orbits, meaning their velocities exceed the cluster escape velocity. Over billions of years, [u]globular clusters evaporate[/u].[/quote]
[c][size=150][color=#FF0000]Conservation of Energy[/color] :?: :!: [/size][/c][quote=" http://en.wikipedia.org/wiki/Virial_theorem"]
<<In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy,[img]http://upload.wikimedia.org/math/3/e/2/3e2c02e5c3a34e2f438f0d70903b632a.png[/img], of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, [img]http://upload.wikimedia.org/math/c/3/8/c38888f07a86192dae9ad0829de2a0b8.png[/img], where angle brackets represent the average over time of the enclosed quantity. If the force between any two particles of the system results from a potential energy V(r) = αr[sup]n[/sup] that is proportional to some power n of the inter-particle distance r, the virial theorem takes the simple form: [img]http://upload.wikimedia.org/math/b/5/7/b5770a447559f46f3b0c7d8e98adff94.png[/img]. Thus, twice the average total kinetic energy [img]http://upload.wikimedia.org/math/3/e/2/3e2c02e5c3a34e2f438f0d70903b632a.png[/img] equals n times the average total potential energy [img]http://upload.wikimedia.org/math/c/3/8/c38888f07a86192dae9ad0829de2a0b8.png[/img]. Whereas V(r) represents the potential energy between two particles, VTOT represents the total potential energy of the system, i.e., the sum of the potential energy V(r) over all pairs of particles in the system. A common example of such a system is globular star cluster, where n equals −1 (i.e., [color=#FF0000][b]the total kinetic energy of a globular star cluster amounts to only [size=150][u]half[/u][/size] the negative total potential energy[/b][/color].>>[/quote][quote=" http://en.wikipedia.org/wiki/Globular_cluster#Mass_segregation.2C_luminosity_and_core_collapse"]
[float=right][img3="[b][color=#0000FF][size=150]A[n evolved] core-collapsed globular: M15[/size][/color][/b]"]http://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Messier_15_HST.jpg/600px-Messier_15_HST.jpg[/img3][/float]<<In measuring the luminosity curve of a given globular cluster as a function of distance from the core, most clusters in the Milky Way increase steadily in luminosity as this distance decreases, up to a certain distance from the core, then the luminosity levels off. Typically this distance is about 1–2 parsecs from the core. However about 20% of the globular clusters have [already] undergone a process termed "core collapse". In this type of cluster, the luminosity continues to increase steadily all the way to the core region. An example of a core-collapsed globular is M15.
Core-collapse is thought to occur when the more massive stars in a globular cluster encounter their less massive companions. Over time, dynamic processes cause individual stars to migrate from the center of the cluster to the outside. This results in a net loss of kinetic energy from the core region, leading the remaining stars grouped in the core region to occupy a more compact volume. When this gravothermal instability occurs, the central region of the cluster becomes densely crowded with stars and the surface brightness of the cluster forms a power-law cusp. (Note that a core collapse is not the only mechanism that can cause such a luminosity distribution; a massive black hole at the core can also result in a luminosity cusp.) Over a lengthy period of time this leads to a concentration of massive stars near the core, a phenomenon called mass segregation.
The dynamical heating effect of binary star systems works to prevent an initial core collapse of the cluster. When a star passes near a binary system, the orbit of the latter pair tends to contract, releasing energy. Only after the primordial supply of binaries are exhausted due to interactions can a deeper core collapse proceed. In contrast, the effect of tidal shocks as a globular cluster repeatedly passes through the plane of a spiral galaxy tends to significantly accelerate core collapse.
The different stages of core-collapse may be divided into three phases. During a globular cluster's adolescence, the process of core-collapse begins with stars near the core. However, the interactions between binary star systems prevents further collapse as the cluster approaches middle age. Finally, the central binaries are either disrupted or ejected, resulting in a tighter concentration at the core. The interaction of stars in the collapsed core region causes tight binary systems to form. As other stars interact with these tight binaries, they increase the energy at the core, which causes the cluster to re-expand. As the mean time for a core collapse is typically less than the age of the galaxy, many of a galaxy's globular clusters may have passed through a core collapse stage, then re-expanded.
The Hubble Space Telescope has been used to provide convincing observational evidence of this stellar mass-sorting process in globular clusters. [b][u][color=#FF0000]Heavier stars slow down and crowd at the cluster's core[/color][/u][/b], while lighter stars pick up speed and tend to spend more time at the cluster's periphery. The globular star cluster 47 Tucanae, which is made up of about 1 million stars, is one of the densest globular clusters in the Southern Hemisphere. This cluster was subjected to an intensive photographic survey, which allowed astronomers to track the motion of its stars. Precise velocities were obtained for nearly 15,000 stars in this cluster.
A 2008 study by John [url=http://en.wikipedia.org/wiki/Frege%27s_Puzzle]Fregeau[/url] of 13 globular clusters in the Milky Way shows that three of them have an unusually large number of X-ray sources, or X-ray binaries, suggesting the clusters are middle-aged. Previously, these globular clusters had been classified as being in old age because they had very tight concentrations of stars in their centers, another test of age used by astronomers. The implication is that most globular clusters, including the other ten studied by Fregeau, are not in middle age as previously thought, but are actually in 'adolescence'.>>[/quote]