Chris Peterson wrote: ↑Thu Jun 03, 2021 3:11 pm
neufer wrote: ↑Thu Jun 03, 2021 2:45 pm
Chris Peterson wrote: ↑Thu Jun 03, 2021 1:36 pm
The stars all orbit around the center
point. Not some center
axis (which seems to be what your drawing suggests). They have random semimajor axes (but with more stars having small values than large) and random inclinations. Picture the obsolete drawings of atoms with their electrons orbiting at different angles.
They don't often collide because the stars are tiny compared with the distances between them. I worked out a problem many years ago involving this GC. If you started projecting lines through it randomly (like shooting bullets or arrows), you'd have to do so thousands of times before your line intersected a single star. A GC is, by a large factor, mostly empty space.
Omega Centauri is roughly the same apparent size as the Sun
but it is
~30 apparent magnitudes dimmer than the Sun.
Thus the chance of our visual line intersecting an actual
Omega Centauri star is on the order of 100-{30/5} or 10-12.
The simulation I conducted utilized a "line" that was the diameter of a star. That makes a collision somewhat more likely.
I'll have to think a bit more about your approach here. Maybe we need to consider the strong density gradient?
I don't know how/if each of you estimated any stellar density gradient, or if you assumed a uniform density within a 150ly diameter sphere. For either uniform or increasing centralized gradients, the maximum, integrated line-of-sight density is within a column of stars passing directly through the center of the spherical cluster.
→ For 10-million stars uniformly distributed within a 150-ly sphere, the max central line-of-sight density ≈ 5 stars/arcsec
2
→ For 9 million stars with a varying density that yields ω-Cen surface brightness, the peak density could be ≈ 40 to 50 stars/arcsec
2.
Clearly this projected density is extremely sparse, and assuming constant-sized stars, their angular diameters ≈ 1.1
microarcsec (uas). The total blocked area from 45 stars is only 43 uas
2
→ The probability of the Sun colliding with a star while passing through the center ≈ 3x10-12
So, though the projected density increases by ~10X over the uniform density case, the resultant collision probability is still infinitesimal.
In case you're curious, I've questioned this Omega Centauri APOD over the years, and looked at this GC in detail to verify the "10 million" star count claim. I couldn't find a paper that explicitly concluded that so I conducted my own analysis mostly using
New Limits on IMBH Mas in Omega Centauri_Paper II and
Gemini and Hubble Space Telescope Evidence for an Intermediate Mass Black Hole in omega Centauri
I decided to use the largest published mass estimate for Omega Cen: ~5.1 million M☉ (
Meylan, 1995), and considering the first APOD posting the 10-million stars was in 1996, this legacy quote is likely based on Meylan's mass estimate. Following the published analysis technique, and assuming a constant Mass/Luminosity for all the stars such that the GC surface brightness profile replicated:
→ The result is ~9 million stars, and
→ A peak projected line-of-sight density = 44 stars/arcsec2 yielding a central stellar volume density ~1200 stars per cubic light year.
Lastly, the high central volume density requires an upward slope in the projected column density starting at ~100 arcseconds radius. In the paper(s), this "subtle" upward slope is driven by an intermediate black hole postulated to exist in Omega Cen. With the upward slope removed, the maximum projected line-of-sight, centrally-flat, column density ~40 stars/arcsec
2, which drops the maximum central volume density down to ~235 stars/ly
3
LoS GC Star Density.jpg
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