APOD: The Milky Way's Black Hole (2022 May 13)

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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Chris Peterson » Wed May 18, 2022 1:54 pm

Ann wrote: Wed May 18, 2022 1:51 pm
Chris Peterson wrote: Wed May 18, 2022 1:19 pm
Ann wrote: Wed May 18, 2022 5:32 am I know that this discussion should be over now, but there is a question that you haven't answered.

Why is it that so many galaxies are so bright in their cores?
Because the stellar density in the cores is very high. Much higher than in the bulge in many cases.
So why shouldn't we assume that the stellar density is also very high in the core of the Milky Way, so that there may be many stars just a few - say, 1-7 light-years - from the black hole?

Ann
I'm sure there are many stars within a few light years of the black hole! I haven't suggested otherwise.
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Fred the Cat » Wed May 18, 2022 2:56 pm

Chris Peterson wrote: Wed May 18, 2022 1:54 pm
Ann wrote: Wed May 18, 2022 1:51 pm
Chris Peterson wrote: Wed May 18, 2022 1:19 pm

Because the stellar density in the cores is very high. Much higher than in the bulge in many cases.
So why shouldn't we assume that the stellar density is also very high in the core of the Milky Way, so that there may be many stars just a few - say, 1-7 light-years - from the black hole?

Ann



I'm sure there are many stars within a few light years of the black hole! I haven't suggested otherwise.
Just how many seems not to be easily digested but one could try to assimilate this thesis.

In it, one image does illuminate his studies.
Galactic Center (2).png
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by johnnydeep » Wed May 18, 2022 3:22 pm

Fred the Cat wrote: Wed May 18, 2022 2:56 pm
Chris Peterson wrote: Wed May 18, 2022 1:54 pm
Ann wrote: Wed May 18, 2022 1:51 pm

So why shouldn't we assume that the stellar density is also very high in the core of the Milky Way, so that there may be many stars just a few - say, 1-7 light-years - from the black hole?

Ann



I'm sure there are many stars within a few light years of the black hole! I haven't suggested otherwise.
Just how many seems not to be easily digested but one could try to assimilate this thesis.

In it, one image does illuminate his studies.
Galactic Center (2).png
How DO you manage to find these interesting papers? This one begins with a very nice well-written summary and description of the Milky Way. Thanks for the link! So, the upshot of this picture (figure 1.5 in the thesis) is that there are many stars - perhaps over 100? - within 5 arcsecs of the central BH, putting them within 0.2 pc (5 * 0.04), or 0.65 ly. Pretty crowded down there!
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Fred the Cat » Wed May 18, 2022 4:12 pm

johnnydeep wrote: Wed May 18, 2022 3:22 pm
Fred the Cat wrote: Wed May 18, 2022 2:56 pm
Chris Peterson wrote: Wed May 18, 2022 1:54 pm


I'm sure there are many stars within a few light years of the black hole! I haven't suggested otherwise.
Just how many seems not to be easily digested but one could try to assimilate this thesis.

In it, one image does illuminate his studies.
Galactic Center (2).png
How DO you manage to find these interesting papers? This one begins with a very nice well-written summary and description of the Milky Way. Thanks for the link! So, the upshot of this picture (figure 1.5 in the thesis) is that there are many stars - perhaps over 100? - within 5 arcsecs of the central BH, putting them within 0.2 pc (5 * 0.04), or 0.65 ly. Pretty crowded down there!
Give the credit to Ann. She asks interesting questions that I get a gut reaction to look for answers. :thumb_up:
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Ann » Wed May 18, 2022 5:51 pm

Fred the Cat wrote: Wed May 18, 2022 4:12 pm
johnnydeep wrote: Wed May 18, 2022 3:22 pm
Fred the Cat wrote: Wed May 18, 2022 2:56 pm
Just how many seems not to be easily digested but one could try to assimilate this thesis.

In it, one image does illuminate his studies.
Galactic Center (2).png
How DO you manage to find these interesting papers? This one begins with a very nice well-written summary and description of the Milky Way. Thanks for the link! So, the upshot of this picture (figure 1.5 in the thesis) is that there are many stars - perhaps over 100? - within 5 arcsecs of the central BH, putting them within 0.2 pc (5 * 0.04), or 0.65 ly. Pretty crowded down there!
Give the credit to Ann. She asks interesting questions that I get a gut reaction to look for answers. :thumb_up:
Thanks a bunch! :oops:

Galactic center stellar cluster from Near and mid infrared observations of the galactic center.png
NADEEN BASSAM IZZAT SABHA wrote:
Figure 1.5: L-band (3.8 µm) mosaic of the Galactic Center stellar cluster obtained with VLT NaCo in
2012. Most sources are identified based on Viehmann et al. (2005). One arcsec translates to ∼0.04 pc
for an 8 kpc distance to the GC. The position of the supermassive black hole Sagittarius A* (Sgr A*) is
marked by a cross. North is up and east is to the left.
´
The galactic center is a crowded place! Indeed.

As David Bowman said in the movie 2001: A Space Odyssey:

My God, it's full of stars!

Ann
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by johnnydeep » Wed May 18, 2022 8:04 pm

Ann wrote: Wed May 18, 2022 5:51 pm
Fred the Cat wrote: Wed May 18, 2022 4:12 pm
johnnydeep wrote: Wed May 18, 2022 3:22 pm

How DO you manage to find these interesting papers? This one begins with a very nice well-written summary and description of the Milky Way. Thanks for the link! So, the upshot of this picture (figure 1.5 in the thesis) is that there are many stars - perhaps over 100? - within 5 arcsecs of the central BH, putting them within 0.2 pc (5 * 0.04), or 0.65 ly. Pretty crowded down there!
Give the credit to Ann. She asks interesting questions that I get a gut reaction to look for answers. :thumb_up:
Thanks a bunch! :oops:

Galactic center stellar cluster from Near and mid infrared observations of the galactic center.png
NADEEN BASSAM IZZAT SABHA wrote:
Figure 1.5: L-band (3.8 µm) mosaic of the Galactic Center stellar cluster obtained with VLT NaCo in
2012. Most sources are identified based on Viehmann et al. (2005). One arcsec translates to ∼0.04 pc
for an 8 kpc distance to the GC. The position of the supermassive black hole Sagittarius A* (Sgr A*) is
marked by a cross. North is up and east is to the left.
´
The galactic center is a crowded place! Indeed.

As David Bowman said in the movie 2001: A Space Odyssey:

My God, it's full of stars!

Ann
So now let's compare the density of stars in this pic with that of a globular cluster. In this pic, I'd guesstimate there are at least 10*10*10 stars in the 5x5x5 arcsec volume around the BH at the center plus mark. That would be a density of 1000 / 0.23 stars/pc3, or 1 star per 0.000008 pc3

Per Wikipedia,
https://en.wikipedia.org/wiki/Stellar_density wrote:The locations within the Milky Way that have the highest stellar density are the central core and the interior of globular clusters. A typical mass density for a globular cluster is 70 MSun pc−3, which is 500 times the mass density near the Sun.[2] In the solar neighborhood, the stellar density of a star cluster must be greater than 0.08 MSun pc−3 in order to avoid tidal disruption.[3]
That would mean the stellar density in the vicinity of the BH (excluding the BH itself!) is much higher than that at the center of GCs, namely, a density of 125000 stars per pc3 around the BH! No? Unless I got my math screwed up...(which I admit to not being entirely confident in).
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Ann » Thu May 19, 2022 5:59 am

johnnydeep wrote: Wed May 18, 2022 8:04 pm
Ann wrote: Wed May 18, 2022 5:51 pm
Fred the Cat wrote: Wed May 18, 2022 4:12 pm
Give the credit to Ann. She asks interesting questions that I get a gut reaction to look for answers. :thumb_up:
Thanks a bunch! :oops:

Galactic center stellar cluster from Near and mid infrared observations of the galactic center.png
NADEEN BASSAM IZZAT SABHA wrote:
Figure 1.5: L-band (3.8 µm) mosaic of the Galactic Center stellar cluster obtained with VLT NaCo in
2012. Most sources are identified based on Viehmann et al. (2005). One arcsec translates to ∼0.04 pc
for an 8 kpc distance to the GC. The position of the supermassive black hole Sagittarius A* (Sgr A*) is
marked by a cross. North is up and east is to the left.
´
The galactic center is a crowded place! Indeed.

As David Bowman said in the movie 2001: A Space Odyssey:

My God, it's full of stars!

Ann
So now let's compare the density of stars in this pic with that of a globular cluster. In this pic, I'd guesstimate there are at least 10*10*10 stars in the 5x5x5 arcsec volume around the BH at the center plus mark. That would be a density of 1000 / 0.23 stars/pc3, or 1 star per 0.000008 pc3

Per Wikipedia,
https://en.wikipedia.org/wiki/Stellar_density wrote:The locations within the Milky Way that have the highest stellar density are the central core and the interior of globular clusters. A typical mass density for a globular cluster is 70 MSun pc−3, which is 500 times the mass density near the Sun.[2] In the solar neighborhood, the stellar density of a star cluster must be greater than 0.08 MSun pc−3 in order to avoid tidal disruption[3]
That would mean the stellar density in the vicinity of the BH (excluding the BH itself!) is much higher than that at the center of GCs, namely, a density of 125000 stars per pc3 around the BH! No? Unless I got my math screwed up...(which I admit to not being entirely confident in).
Johnny, if your math can sometimes screw up, mine is non-existent.

I get, more or less, the expression 1 star per 0.000008 pc3. If nothing else, I certainly know how to ask Google to explain exactly what it means. So, for example, how many stars would that be per cubic light-year? Google should be able to tell me.

But I don't get this: A typical mass density for a globular cluster is 70 MSun pc−3, which is 500 times the mass density near the Sun. Yeah? This just talks about stellar mass, not about the number of stars.

Is there a way to figure out how many stars per cubic parsec, on average, it would take to create a 70 MSun pc−3 situation in a globular cluster?

(Or, alternatively, does anyone know how many stars there is in the cubic parsec centered on the Sun?)

We should keep a few things in mind here. First of all, stars in globular clusters are typically low in mass. With the exception of a handful of blue stragglers, my guess is that the most massive members of globular clusters are about as massive as the Sun. On the other hand, there may be a bit of a shortage of very low-mass red dwarfs, because the lowest-mass stars are the ones that are most likely to be kicked out of the globular cluster due to tidal interactions. So what is the average mass of a stellar member of a globular cluster? How about, say, 0.4 MSun?

So... if every star in a globular cluster contains a mass of 0.4 MSun, then there would be 175 stars in every cubic parsec of a globular cluster. But the stars inside a globular vary in mass, of course. And even if there is a (relative) scarcity of the most light-weight stars inside globulars, the light-weight red dwarfs are still very likely to be the most common denizens.


Go to this page to see a 13 MB Hubble closeup of globular cluster M4. Try to make an assessment of how many tiny little red dots you can spot among the brighter stars. There aren't that many, in my opinion, but there certainly are a number of them. Could there even be quite a few little red dwarfs that are too faint to show up even in this Hubble closeup?

There are also a few tiny blue dots in the globular cluster, which are white dwarfs.

The mass of the faintest red dwarfs in the Hubble image might be, I guess, around 0.3 or 0.2 solar masses. The mass of a typical white dwarf might be, say, 0.6-0.7 solar masses or so. The mass of the multitude of white-looking stars would be, I guess, a bit less than the mass of the Sun, because these stars are metal-poor, and therefore they shine whiter and brighter than a metal-rich star of the same mass. Let's say that the mass of the white-looking stars are some 0.9 solar masses, or in some cases a little more. Most of the evolved, bright-looking stars are probably also less massive than the Sun, because they have lost mass during their evolution. Let's say that their mass is perhaps 0.6-1.1 solar masses.

So, what do you think? How many stars will there be in a cubic parsec of a globular cluster, if the stellar mass inside it is 70 MSun? Okay, let's define "stars" as objects that sustain themselves through some kind of fusion, but let's also count white dwarfs as stars. But let's forget about the brown dwarfs, even if they can, at least in theory, contribute a non-negligent amount of mass to the globular.

Ann
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by VictorBorun » Thu May 19, 2022 5:27 pm

This 4 millions suns BH may be an impostor after the original 1 billion suns BH fired a gravitational thunder with linear momentum and moved out of the Milky Way.

All it took was a merger with another small galaxy, a migration of two BHs down to the new center of gravity and a merger of the two BHs at such collision course that the main BH had a large spin in the plane of the in-spriral.

Ethan Siegel gave this story a headline almost ready for a libretto:

Did the Milky Way lose its black hole?
Lose its black hole, my fair Lady

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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by johnnydeep » Thu May 19, 2022 8:41 pm

Ann wrote: Thu May 19, 2022 5:59 am
johnnydeep wrote: Wed May 18, 2022 8:04 pm
Ann wrote: Wed May 18, 2022 5:51 pm

Thanks a bunch! :oops:

Galactic center stellar cluster from Near and mid infrared observations of the galactic center.png

´
The galactic center is a crowded place! Indeed.

As David Bowman said in the movie 2001: A Space Odyssey:

My God, it's full of stars!

Ann
So now let's compare the density of stars in this pic with that of a globular cluster. In this pic, I'd guesstimate there are at least 10*10*10 stars in the 5x5x5 arcsec volume around the BH at the center plus mark. That would be a density of 1000 / 0.23 stars/pc3, or 1 star per 0.000008 pc3

Per Wikipedia,
https://en.wikipedia.org/wiki/Stellar_density wrote:The locations within the Milky Way that have the highest stellar density are the central core and the interior of globular clusters. A typical mass density for a globular cluster is 70 MSun pc−3, which is 500 times the mass density near the Sun.[2] In the solar neighborhood, the stellar density of a star cluster must be greater than 0.08 MSun pc−3 in order to avoid tidal disruption[3]
That would mean the stellar density in the vicinity of the BH (excluding the BH itself!) is much higher than that at the center of GCs, namely, a density of 125000 stars per pc3 around the BH! No? Unless I got my math screwed up...(which I admit to not being entirely confident in).
Johnny, if your math can sometimes screw up, mine is non-existent.

I get, more or less, the expression 1 star per 0.000008 pc3. If nothing else, I certainly know how to ask Google to explain exactly what it means. So, for example, how many stars would that be per cubic light-year? Google should be able to tell me.

But I don't get this: A typical mass density for a globular cluster is 70 MSun pc−3, which is 500 times the mass density near the Sun. Yeah? This just talks about stellar mass, not about the number of stars.

Is there a way to figure out how many stars per cubic parsec, on average, it would take to create a 70 MSun pc−3 situation in a globular cluster?

(Or, alternatively, does anyone know how many stars there is in the cubic parsec centered on the Sun?)

We should keep a few things in mind here. First of all, stars in globular clusters are typically low in mass. With the exception of a handful of blue stragglers, my guess is that the most massive members of globular clusters are about as massive as the Sun. On the other hand, there may be a bit of a shortage of very low-mass red dwarfs, because the lowest-mass stars are the ones that are most likely to be kicked out of the globular cluster due to tidal interactions. So what is the average mass of a stellar member of a globular cluster? How about, say, 0.4 MSun?

So... if every star in a globular cluster contains a mass of 0.4 MSun, then there would be 175 stars in every cubic parsec of a globular cluster. But the stars inside a globular vary in mass, of course. And even if there is a (relative) scarcity of the most light-weight stars inside globulars, the light-weight red dwarfs are still very likely to be the most common denizens.


Go to this page to see a 13 MB Hubble closeup of globular cluster M4. Try to make an assessment of how many tiny little red dots you can spot among the brighter stars. There aren't that many, in my opinion, but there certainly are a number of them. Could there even be quite a few little red dwarfs that are too faint to show up even in this Hubble closeup?

There are also a few tiny blue dots in the globular cluster, which are white dwarfs.

The mass of the faintest red dwarfs in the Hubble image might be, I guess, around 0.3 or 0.2 solar masses. The mass of a typical white dwarf might be, say, 0.6-0.7 solar masses or so. The mass of the multitude of white-looking stars would be, I guess, a bit less than the mass of the Sun, because these stars are metal-poor, and therefore they shine whiter and brighter than a metal-rich star of the same mass. Let's say that the mass of the white-looking stars are some 0.9 solar masses, or in some cases a little more. Most of the evolved, bright-looking stars are probably also less massive than the Sun, because they have lost mass during their evolution. Let's say that their mass is perhaps 0.6-1.1 solar masses.

So, what do you think? How many stars will there be in a cubic parsec of a globular cluster, if the stellar mass inside it is 70 MSun? Okay, let's define "stars" as objects that sustain themselves through some kind of fusion, but let's also count white dwarfs as stars. But let's forget about the brown dwarfs, even if they can, at least in theory, contribute a non-negligent amount of mass to the globular.

Ann
Well, I was content to accept the approximation that 70 solar masses meant 70 stars. :) If various dwarf stars are also included, the number of stars would go up. The Milky Way is said to have between 100 and 400 billion stars depending on the average star mass used. So maybe the best we could do is use a similar range for the estimate near the MW's central BH.

BTW, I think I'm going to decrease my calculation by a factor of 10 since I might have been too optimistic that there are 1000 stars in the 0.2 pc cube centered on the BH. But 12500 stars per cubic pc is still much higher than the average density of 70 in a globular cluster. Not sure about the center of the GC though. Could that be a lot higher than 12500?
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Ann » Fri May 20, 2022 3:51 am

Well, stupid me!!!!

I wrote:
(Or, alternatively, does anyone know how many stars there is in the cubic parsec centered on the Sun?)
The answer is, of course, one. Because a parsec is less than four light-years, and the distance to the nearest star after the Sun is more than four light-years. So there is exactly one star in the cubic parsec centered on the Sun, namely, the Sun itself.

Well, groan. So, if there are 500 times more stars per cubic parsec in globular clusters than in the cubic parsec centered on the Solar system, then there must be 500 x 1 stars = 500 stars per cubic parsec in globular clusters, right?

Except that - no. I'm still thinking of "stars" as if they all had the same mass as the Sun. (Double-dummy, Ann.) Because the Sun isn't an average star at all - it really isn't! - because some 90-95% of the stars in the Solar neighborhood are less massive than the Sun. And globular clusters are going to lack stars more massive than the Sun altogether, apart from a few blue stragglers with, at best, up to a little more than twice the mass of the Sun.

Let's go to Wikipedia and see what it wrote about Omega Centauri!
Wikipedia wrote:

Located at a distance of 17,090 light-years (5,240 parsecs), it is the largest-known globular cluster in the Milky Way at a diameter of roughly 150 light-years. It is estimated to contain approximately 10 million stars, and a total mass equivalent to 4 million solar masses, making it the most massive-known globular cluster in the Milky Way.
So, I asked Google. How many parsecs are 150 light-years? Google said about 45.9. I simplified it to 45, because my brain can't take complicated numbers. So how many cubic parsecs do you get from 45 parsecs? I daringly asked Google to multiply 45 x 45 x 45, and Google gave me 91,125. I'm going to simplify that to 90,000 and say that there are 10 million stars in 90,000 cubic parsecs.

So, groan. I asked Google to divide 10,000,000 by 90,000. Google wasn't too interested. So I asked Google to divide 1000 by 9. Google said 111.1111111....

Does that mean that there are about 100 stars or a little more per cubic parsec in Omega Centauri?

It doesn't seem right though, does it? Because Wikipedia said that there are 10 million stars in Omega Centauri, but their total mass is about 4 million solar masses. So the mass of a hundred average Omega Centauri stars per cubic parsec should be only 40 solar masses per cubic parsec. That's a far cry from 500 solar masses per cubic parsec.

Does that mean that I should multiply 40 by 12.5 to get 500? And does it mean I should also multiply 100 by 12.5 to get 1250 stars per cubic parsec in Omega Centauri?

Please help the math idiot!!!

Ann
Last edited by Ann on Fri May 20, 2022 4:32 am, edited 1 time in total.
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Chris Peterson » Fri May 20, 2022 4:00 am

Ann wrote: Fri May 20, 2022 3:51 am Well, stupid me!!!!

I wrote:
(Or, alternatively, does anyone know how many stars there is in the cubic parsec centered on the Sun?)
The answer is, of course, one. Because a parsec is less than four light-years, and the distance to the nearest star after the Sun is more than four light-years. So there is exactly one star in the cubic parsec centered on the Sun, namely, the Sun itself.

Well, groan. So, if there are 500 times more stars per cubic parsec in globular clusters than in the cubic parsec centered on the Solar system, then there must be 500 x 1 stars = 500 stars per cubic parsec in globular clusters, right?

Ann
I'd go with something on the order of 1000 stars/pc2 for globulars, and on the order of 100,000 stars/pc2 at the center of the galaxy (but this only in the few central parsecs where the gravity of the BH dominates. By 100 pc out the density is down to about 100 stars/pc2, and the density gradient is low.)
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by johnnydeep » Fri May 20, 2022 4:19 pm

Ann wrote: Fri May 20, 2022 3:51 am Well, stupid me!!!!

I wrote:
(Or, alternatively, does anyone know how many stars there is in the cubic parsec centered on the Sun?)
The answer is, of course, one. Because a parsec is less than four light-years, and the distance to the nearest star after the Sun is more than four light-years. So there is exactly one star in the cubic parsec centered on the Sun, namely, the Sun itself.

Well, groan. So, if there are 500 times more stars per cubic parsec in globular clusters than in the cubic parsec centered on the Solar system, then there must be 500 x 1 stars = 500 stars per cubic parsec in globular clusters, right?

Except that - no. I'm still thinking of "stars" as if they all had the same mass as the Sun. (Double-dummy, Ann.) Because the Sun isn't an average star at all - it really isn't! - because some 90-95% of the stars in the Solar neighborhood are less massive than the Sun. And globular clusters are going to lack stars more massive than the Sun altogether, apart from a few blue stragglers with, at best, up to a little more than twice the mass of the Sun.

Let's go to Wikipedia and see what it wrote about Omega Centauri!
Wikipedia wrote:

Located at a distance of 17,090 light-years (5,240 parsecs), it is the largest-known globular cluster in the Milky Way at a diameter of roughly 150 light-years. It is estimated to contain approximately 10 million stars, and a total mass equivalent to 4 million solar masses, making it the most massive-known globular cluster in the Milky Way.
So, I asked Google. How many parsecs are 150 light-years? Google said about 45.9. I simplified it to 45, because my brain can't take complicated numbers. So how many cubic parsecs do you get from 45 parsecs? I daringly asked Google to multiply 45 x 45 x 45, and Google gave me 91,125. I'm going to simplify that to 90,000 and say that there are 10 million stars in 90,000 cubic parsecs.

So, groan. I asked Google to divide 10,000,000 by 90,000. Google wasn't too interested. So I asked Google to divide 1000 by 9. Google said 111.1111111....

Does that mean that there are about 100 stars or a little more per cubic parsec in Omega Centauri?

It doesn't seem right though, does it? Because Wikipedia said that there are 10 million stars in Omega Centauri, but their total mass is about 4 million solar masses. So the mass of a hundred average Omega Centauri stars per cubic parsec should be only 40 solar masses per cubic parsec. That's a far cry from 500 solar masses per cubic parsec.

Does that mean that I should multiply 40 by 12.5 to get 500? And does it mean I should also multiply 100 by 12.5 to get 1250 stars per cubic parsec in Omega Centauri?

Please help the math idiot!!!

Ann
Just going back to the Wikipedia quote: "Located at a distance of 17,090 light-years (5,240 parsecs), it is the largest-known globular cluster in the Milky Way at a diameter of roughly 150 light-years. It is estimated to contain approximately 10 million stars, and a total mass equivalent to 4 million solar masses, making it the most massive-known globular cluster in the Milky Way."

The simplest way to look at that is to realize it means there are 1e7 stars totaling 4e6 solar masses in the volume of a 150 ly diameter sphere. To calculate the average stellar density throughout the entire volume of that sphere, it's simply 1e7 / 4/3 pi 150*150*150 stars/ly3, or 0.7 stars/ly3. And since there are 3.26 ly/pc, that's 0.7 * 3.263 = 24 stars/pc3. And again, that's just the average. The density would be much higher toward the center and much lower toward the periphery.

And since those 1e7 stars total 4e6 solar masses, the average star would be 4e6 / 1e7 = 0.4 solar masses. So, there are more small stars than large, which comports well with dwarf stars being the most common. Of course, this also ignores any dust, gas or dark matter which might also be contributing to the total mass of the cluster. But perhaps clusters have a paucity of all three?
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by Ann » Fri May 20, 2022 6:15 pm

johnnydeep wrote: Fri May 20, 2022 4:19 pm
Ann wrote: Fri May 20, 2022 3:51 am Well, stupid me!!!!

I wrote:
(Or, alternatively, does anyone know how many stars there is in the cubic parsec centered on the Sun?)
The answer is, of course, one. Because a parsec is less than four light-years, and the distance to the nearest star after the Sun is more than four light-years. So there is exactly one star in the cubic parsec centered on the Sun, namely, the Sun itself.

Well, groan. So, if there are 500 times more stars per cubic parsec in globular clusters than in the cubic parsec centered on the Solar system, then there must be 500 x 1 stars = 500 stars per cubic parsec in globular clusters, right?

Except that - no. I'm still thinking of "stars" as if they all had the same mass as the Sun. (Double-dummy, Ann.) Because the Sun isn't an average star at all - it really isn't! - because some 90-95% of the stars in the Solar neighborhood are less massive than the Sun. And globular clusters are going to lack stars more massive than the Sun altogether, apart from a few blue stragglers with, at best, up to a little more than twice the mass of the Sun.

Let's go to Wikipedia and see what it wrote about Omega Centauri!
Wikipedia wrote:

Located at a distance of 17,090 light-years (5,240 parsecs), it is the largest-known globular cluster in the Milky Way at a diameter of roughly 150 light-years. It is estimated to contain approximately 10 million stars, and a total mass equivalent to 4 million solar masses, making it the most massive-known globular cluster in the Milky Way.
So, I asked Google. How many parsecs are 150 light-years? Google said about 45.9. I simplified it to 45, because my brain can't take complicated numbers. So how many cubic parsecs do you get from 45 parsecs? I daringly asked Google to multiply 45 x 45 x 45, and Google gave me 91,125. I'm going to simplify that to 90,000 and say that there are 10 million stars in 90,000 cubic parsecs.

So, groan. I asked Google to divide 10,000,000 by 90,000. Google wasn't too interested. So I asked Google to divide 1000 by 9. Google said 111.1111111....

Does that mean that there are about 100 stars or a little more per cubic parsec in Omega Centauri?

It doesn't seem right though, does it? Because Wikipedia said that there are 10 million stars in Omega Centauri, but their total mass is about 4 million solar masses. So the mass of a hundred average Omega Centauri stars per cubic parsec should be only 40 solar masses per cubic parsec. That's a far cry from 500 solar masses per cubic parsec.

Does that mean that I should multiply 40 by 12.5 to get 500? And does it mean I should also multiply 100 by 12.5 to get 1250 stars per cubic parsec in Omega Centauri?

Please help the math idiot!!!

Ann
Just going back to the Wikipedia quote: "Located at a distance of 17,090 light-years (5,240 parsecs), it is the largest-known globular cluster in the Milky Way at a diameter of roughly 150 light-years. It is estimated to contain approximately 10 million stars, and a total mass equivalent to 4 million solar masses, making it the most massive-known globular cluster in the Milky Way."

The simplest way to look at that is to realize it means there are 1e7 stars totaling 4e6 solar masses in the volume of a 150 ly diameter sphere. To calculate the average stellar density throughout the entire volume of that sphere, it's simply 1e7 / 4/3 pi 150*150*150 stars/ly3, or 0.7 stars/ly3. And since there are 3.26 ly/pc, that's 0.7 * 3.263 = 24 stars/pc3. And again, that's just the average. The density would be much higher toward the center and much lower toward the periphery.

And since those 1e7 stars total 4e6 solar masses, the average star would be 4e6 / 1e7 = 0.4 solar masses. So, there are more small stars than large, which comports well with dwarf stars being the most common. Of course, this also ignores any dust, gas or dark matter which might also be contributing to the total mass of the cluster. But perhaps clusters have a paucity of all three?
Thanks, Johnny, I admire your math.

I really think that almost all Milky Way globulars are practically gas- and dust-free. That is because they are so old, and they were so unbelievably energetic when they were young, that the monstrous O-type and Wolf Rayet stars that these globulars once contained blew all the gas and dust clear out of the globulars.


Let's compare two massive clusters, Westerlund 1 whose estimated age is 4 - 5 million years, and Westerlund 2, whose age is 1 - 2 million years.


Westerlund 1 and Westerlund 2 are two very young and very massive clusters. Westerlund 1 appears to be the most massive of them, or as Wikipedia wrote:
Westerlund 1 (abbreviated Wd1, sometimes called Ara Cluster) is a compact young super star cluster about 2.6 kpc (8480 ly) away from Earth. It is one of the most massive young star clusters in the Milky Way and was discovered by Bengt Westerlund in 1961 but remained largely unstudied for many years due to high interstellar absorption in its direction. In the future, it will probably evolve into a globular cluster.
When it comes to Westerlund 2, Wikipedia doesn't stress its total cluster mass but rather the high mass and temperatures of some of its member stars:
Westerlund 2 is an obscured compact young star cluster (perhaps even a super star cluster) in the Milky Way, with an estimated age of about one or two million years. It contains some of the hottest, brightest, and most massive stars known.
Do note that there is no apparent nebulosity in or near Westerlund 1. The massive cluster has undoubtedly blown the gas and dust away.

The situation is quite different for the very young cluster Westerlund 2. Much gas remains all around the cluster:


But as you can see, even though there is a lot of gas and dust surrounding Westerlund 2, the cluster has cleared a cavity around itself, where there is a lot less gas and dust than in its surroundings.

My point is that there is no appreciable amount of gas or dust in the age-old globular clusters, and whatever gas and dust might be present there doesn't contribute significantly to the mass of the cluster.

Ann
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Re: APOD: The Milky Way's Black Hole (2022 May 13)

Post by johnnydeep » Fri May 20, 2022 8:01 pm

Ann wrote: Fri May 20, 2022 6:15 pm
johnnydeep wrote: Fri May 20, 2022 4:19 pm
Ann wrote: Fri May 20, 2022 3:51 am Well, stupid me!!!!

I wrote:



The answer is, of course, one. Because a parsec is less than four light-years, and the distance to the nearest star after the Sun is more than four light-years. So there is exactly one star in the cubic parsec centered on the Sun, namely, the Sun itself.

Well, groan. So, if there are 500 times more stars per cubic parsec in globular clusters than in the cubic parsec centered on the Solar system, then there must be 500 x 1 stars = 500 stars per cubic parsec in globular clusters, right?

Except that - no. I'm still thinking of "stars" as if they all had the same mass as the Sun. (Double-dummy, Ann.) Because the Sun isn't an average star at all - it really isn't! - because some 90-95% of the stars in the Solar neighborhood are less massive than the Sun. And globular clusters are going to lack stars more massive than the Sun altogether, apart from a few blue stragglers with, at best, up to a little more than twice the mass of the Sun.

Let's go to Wikipedia and see what it wrote about Omega Centauri!



So, I asked Google. How many parsecs are 150 light-years? Google said about 45.9. I simplified it to 45, because my brain can't take complicated numbers. So how many cubic parsecs do you get from 45 parsecs? I daringly asked Google to multiply 45 x 45 x 45, and Google gave me 91,125. I'm going to simplify that to 90,000 and say that there are 10 million stars in 90,000 cubic parsecs.

So, groan. I asked Google to divide 10,000,000 by 90,000. Google wasn't too interested. So I asked Google to divide 1000 by 9. Google said 111.1111111....

Does that mean that there are about 100 stars or a little more per cubic parsec in Omega Centauri?

It doesn't seem right though, does it? Because Wikipedia said that there are 10 million stars in Omega Centauri, but their total mass is about 4 million solar masses. So the mass of a hundred average Omega Centauri stars per cubic parsec should be only 40 solar masses per cubic parsec. That's a far cry from 500 solar masses per cubic parsec.

Does that mean that I should multiply 40 by 12.5 to get 500? And does it mean I should also multiply 100 by 12.5 to get 1250 stars per cubic parsec in Omega Centauri?

Please help the math idiot!!!

Ann
Just going back to the Wikipedia quote: "Located at a distance of 17,090 light-years (5,240 parsecs), it is the largest-known globular cluster in the Milky Way at a diameter of roughly 150 light-years. It is estimated to contain approximately 10 million stars, and a total mass equivalent to 4 million solar masses, making it the most massive-known globular cluster in the Milky Way."

The simplest way to look at that is to realize it means there are 1e7 stars totaling 4e6 solar masses in the volume of a 150 ly diameter sphere. To calculate the average stellar density throughout the entire volume of that sphere, it's simply 1e7 / 4/3 pi 150*150*150 stars/ly3, or 0.7 stars/ly3. And since there are 3.26 ly/pc, that's 0.7 * 3.263 = 24 stars/pc3. And again, that's just the average. The density would be much higher toward the center and much lower toward the periphery.

And since those 1e7 stars total 4e6 solar masses, the average star would be 4e6 / 1e7 = 0.4 solar masses. So, there are more small stars than large, which comports well with dwarf stars being the most common. Of course, this also ignores any dust, gas or dark matter which might also be contributing to the total mass of the cluster. But perhaps clusters have a paucity of all three?
Thanks, Johnny, I admire your math.

I really think that almost all Milky Way globulars are practically gas- and dust-free. That is because they are so old, and they were so unbelievably energetic when they were young, that the monstrous O-type and Wolf Rayet stars that these globulars once contained blew all the gas and dust clear out of the globulars.


Let's compare two massive clusters, Westerlund 1 whose estimated age is 4 - 5 million years, and Westerlund 2, whose age is 1 - 2 million years.


Westerlund 1 and Westerlund 2 are two very young and very massive clusters. Westerlund 1 appears to be the most massive of them, or as Wikipedia wrote:
Westerlund 1 (abbreviated Wd1, sometimes called Ara Cluster) is a compact young super star cluster about 2.6 kpc (8480 ly) away from Earth. It is one of the most massive young star clusters in the Milky Way and was discovered by Bengt Westerlund in 1961 but remained largely unstudied for many years due to high interstellar absorption in its direction. In the future, it will probably evolve into a globular cluster.
When it comes to Westerlund 2, Wikipedia doesn't stress its total cluster mass but rather the high mass and temperatures of some of its member stars:
Westerlund 2 is an obscured compact young star cluster (perhaps even a super star cluster) in the Milky Way, with an estimated age of about one or two million years. It contains some of the hottest, brightest, and most massive stars known.
Do note that there is no apparent nebulosity in or near Westerlund 1. The massive cluster has undoubtedly blown the gas and dust away.

The situation is quite different for the very young cluster Westerlund 2. Much gas remains all around the cluster:


But as you can see, even though there is a lot of gas and dust surrounding Westerlund 2, the cluster has cleared a cavity around itself, where there is a lot less gas and dust than in its surroundings.

My point is that there is no appreciable amount of gas or dust in the age-old globular clusters, and whatever gas and dust might be present there doesn't contribute significantly to the mass of the cluster.

Ann
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