APOD: Millions of Stars in Omega Centauri (2021 Jun 03)

[VictorBorun]

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.

Funny thing is that russian wiki states:
К другим отличительным особенностям Омеги Центавра относится некоторая сплюснутость, вызванная вращением со скоростью до 8 км/с. Она не распространена у шаровых скоплений и присуща в основном галактикам. Отношение малой оси к большой для данного скопления составляет 0,88

"ω Cen also features flattenedness implying rotation at 8 km/s. This thing is rare for a GC and is mostly found in galaxies. Short to long axes ratio is 0.88 for this GC"
I looked at the references and failed to see if they base such claims.

[JohnD]

Of course, stellar systems are mainly empty space, too! An alien spacecraft visiting the Sun would have to conduct a very careful survey to determine that we had any planets, and finding the terrestrial ones wouldn't be easy.
(The paper estimates 50 interstellar objects inside a 50 AU radius sphere, not inside Earth's orbit.)

Ooooooooooops! A tiny error there! 50 AU takes us out to the Oort Cloud, and encloses a much greater volume!

Fifty AU is not even double the 30 AU orbit of Neptune, and only a little beyond the 49 AU aphelion of Pluto. The Oort cloud starts much farther out. From https://en.wikipedia.org/wiki/Oort_cloud :

The Oort cloud (/ɔːrt, ʊərt/),[1] sometimes called the Öpik–Oort cloud,[2] first described in 1950 by Dutch astronomer Jan Oort,[3] is a theoretical[4] concept of a cloud of predominantly icy planetesimals proposed to surround the Sun at distances ranging from 2,000 to 200,000 au (0.03 to 3.2 light-years).[note 1][5] It is divided into two regions: a disc-shaped inner Oort cloud (or Hills cloud) and a spherical outer Oort cloud. Both regions lie beyond the heliosphere and in interstellar space.[5][6] The Kuiper belt and the scattered disc, the other two reservoirs of trans-Neptunian objects, are less than one thousandth as far from the Sun as the Oort cloud.

But 50 AU does seem to be at the farther edge of the Kuiper belt. From https://en.wikipedia.org/wiki/Kuiper_belt :

The Kuiper belt (/ˈkaɪpər, ˈkʊɪ-/)[1] is a circumstellar disc in the outer Solar System, extending from the orbit of Neptune at 30 astronomical units (AU) to approximately 50 AU from the Sun.

Once again, thnaks for the education! I misinterpreted a diagram of solar orbits that gave the range in AU, when I thought it was miles! Still an enormous volunme, but not quote so enormous, to have so many etsrasolar objects in, if they are there.

[alter-ego]

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/arcsec²
→ For 9 million stars with a varying density that yields ω-Cen surface brightness, the peak density could be ≈ 40 to 50 stars/arcsec².
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 uas²
→ 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.

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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/arcsec², which drops the maximum central volume density down to ~235 stars/ly³
 

[Ann]

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/arcsec²
→ For 9 million stars with a varying density that yields ω-Cen surface brightness, the peak density could be ≈ 40 to 50 stars/arcsec².
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 uas²
→ 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/arcsec², which drops the maximum central volume density down to ~235 stars/ly³
 

Click to view full size image

Fantastic, alter-ego. I, the math idiot, am speechless.

As for the existence of a central intermediate black hole in Omega Centauri, let me quote Wikipedia:

A 2008 study presented evidence for an intermediate-mass black hole at the center of Omega Centauri, based on observations made by the Hubble Space Telescope and Gemini Observatory on Cerro Pachon in Chile.[24][25] Hubble's Advanced Camera for Surveys showed that stars are bunching up near the center of Omega Centauri, as evidenced by the gradual increase in starlight near the center. Using instruments at the Gemini Observatory to measure the speed of stars swirling in the cluster's core, E. Noyola and colleagues found that stars closer to the core are moving faster than stars farther away. This measurement was interpreted to mean that unseen matter at the core is interacting gravitationally with nearby stars. By comparing these results with standard models, the astronomers concluded that the most likely cause was the gravitational pull of a dense, massive object such as a black hole. They calculated the object's mass at 40,000 solar masses.[24]

However, more recent work has challenged these conclusions, in particular disputing the proposed location of the cluster center.[26] [27] Calculations using a revised location for the center found that the velocity of core stars does not vary with distance, as would be expected if an intermediate-mass black hole were present. The same studies also found that starlight does not increase toward the center but instead remains relatively constant. The authors noted that their results do not entirely rule out the black hole proposed by Noyola and colleagues, but they do not confirm it, and they limit its maximum mass to 12,000 solar masses.

So the inner part of Omega Centauri is so "fluffy" and "loose" that it is not obvious where the actual cluster center is located.

Ann

[Chris Peterson]

So the inner part of Omega Centauri is so "fluffy" and "loose" that it is not obvious where the actual cluster center is located.

In fact, there is no geometric center. There is a center of mass, but its location is always changing with respect to every star in the cluster. Throw a bunch of marbles on the ground. Where is the center of that grouping? Especially, where is the center while they're still moving around?