# Thread: How did we find how many stars there are in the Milky way galaxy?

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## How did we find how many stars there are in the Milky way galaxy?

How did we find how many stars there are in the Milky way galaxy?
Why do we estimate that there are about 400 Billions stars in the Milky Way galaxy?

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Please look at the following article:

http://www.atlasoftheuniverse.com/50lys.html

In a radius of 50 LY: "There are roughly 1400 star systems within this volume of space containing 2000 stars, so this map only shows the brightest 10% of all the star systems, but most of the fainter stars are red dwarfs.
Let's assume that the are 2000 stars in that volume.

In a 50 LY radius sphere there are:

4 * 3.14 * 50 ^3 /3 = 523,333 LY ^3.

So, in each 523,333 Ly ^ 3 Volume, there are 2,000 stars

In 1000 Ly cube there is

1000 ^ 3 = 1,000,000,000 LY ^3

1,000,000,000 / 523,333 = 1,911

Hence, in each 1000 LY ^3 cube there are:

1911 * 2,000 = 3,822,000 stars.

There are 5 arms in the Milky Way. Let's assume that the length of each one is 50,000 light year.

So there are 50 cubes of 1000 LY^3 in each arm.

Therefore, the total stars in all the arms are:

5 * 50 * 3,822,000 = 955,500,000 stars.

So, there are only one Billion stars in the arms.
Is it realistic
Last edited by Dave Lee; 2018-Apr-28 at 02:05 PM.

3. Originally Posted by Dave Lee
How did we find how many stars there are in the Milky way galaxy?
Why do we estimate that there are about 400 Billions stars in the Milky Way galaxy?
https://www.space.com/25959-how-many...milky-way.html
http://www.astronomycafe.net/FAQs/q76x.html
https://www.huffingtonpost.com/dr-st...b_4976030.html

4. Just a few comments before the discussion starts:

1. There is a lot of variation in estimates of the mass of our galaxy, because it's an extremely difficult thing to measure. A useful rule of thumb estimate is one trillion solar masses, but I have seen values quoted between 750 billion and 4 trillion.
2. Roughly 80% of this mass is dark matter, so 200 billion solar masses are baryonic matter.
3. Not all of this mass is stars - there is a significant mass in gas clouds, etc.
4. Using the density of stars in the neighbourhood of the sun as being indicative of the density throughout the Galaxy is not valid. Density around here is lower than more centrally in the central part of the disc.
5. You have ignored the halo.
6. You incorrectly assume that there are no stars between the spiral arms. You have been corrected on this in previous threads. There are.
7. The sun is heavier than the median. By far the most common stars are red dwarves, much lower mass than our sun. Hence, a collection of typical stars massing (say) 100 billion solar masses will actually comprise many more than 100 billion stars.
8. You calculation has a width of each spiral arm of 1000 light years. That's understated.
Last edited by AGN Fuel; 2018-Apr-28 at 02:17 PM.

5. kzb
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I too have a lot of difficulty with this question.

Mass models of the Milky Way estimate relatively small stellar masses, e.g the paper below finds 60.8 billion solar masses of stars in the disk+bulge (and 1 billion in the halo, although this is smaller than the uncertainty on the disk+bulge estimate).

To obtain the number of stars you divide this by the average star mass. To end up with 400 billion stars you need an average star mass of 0.15 solar.

This doesn't seem right because most references give the average as 0.3 solar masses.

61.8 billion divided by 0.3 is 206 billion (I've added the halo stellar mass to get the total here but it makes little difference whether you do or not).

So I am a bit puzzled how this 400 billion number came about.

https://arxiv.org/abs/1407.1078

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It is stated:
"Using radial velocities and the recently determined proper motions for the Magellanic Clouds and the dwarf spheroidal galaxies in Sculptor and Ursa Minor, we have modeled the satellite galaxies' orbits around the Milky Way. Assuming the orbits of the dwarf spheroidals are bound, have apogalacticon less than 300 kpc, and are of low eccentricity, then the minimum mass of our galaxy contained within a radius of 100 kpc is 590 billion solar masses, and the most likely mass is 700 billion. These mass estimates and the orbit models were used to place limits on the possible maximum tangential velocities and proper motions of the other known dwarf spheroidal galaxies and to assess the likelihood of membership of the dwarf galaxies in various streams"

How do they extract the total mass out of radial velocities of dwarf galaxies?
Any Idea for real calculation?
Last edited by Dave Lee; 2018-May-01 at 06:37 PM.

7. Originally Posted by Dave Lee
How do they extract the total mass out of radial velocities of dwarf galaxies?
Any Idea for real calculation?
From the equation for orbital speed, I assume. They have the velocity, the distance and hence can calculate the mass of the galaxy inside the orbit.
https://en.wikipedia.org/wiki/Orbital_speed

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https://arxiv.org/abs/astro-ph/0102243

"Finally, we discuss the possibility that Phoenix may be a bound Milky Way satellite. The minimum required mass of the Milky Way for Phoenix to be bound is MMW(<450kpc)≥1.2×1012 M⊙ which comfortably fits within most current estimates."

I really can't understand how they extract the estimated Milky way mass by: "may be a bound"
If it is just "may be", than "may be" it is not bound???

9. Originally Posted by Dave Lee
Thanks

https://arxiv.org/abs/astro-ph/0102243

"Finally, we discuss the possibility that Phoenix may be a bound Milky Way satellite. The minimum required mass of the Milky Way for Phoenix to be bound is MMW(<450kpc)≥1.2×1012 M⊙ which comfortably fits within most current estimates."

I really can't understand how they extract the estimated Milky way mass by: "may be a bound"
If it is just "may be", than "may be" it is not bound???
The main problem is time. The paper describes a radial velocity but we haven't been able to observe the system long enough to get a grasp on the eccentricity of its orbit. You can image that one orbit of the galaxy will take many, many millions of years but we have only been observing it for the tiniest fraction of one orbit! So we don't really know if the orbit is nearly circular, quite elliptical (and if so, it it nearer periapsis or apoapsis?) or completely unbound.

So what is done here is to model what minimum mass the Milky Way must be for the dwarf galaxy to be bound. Less mass based on the currently understood orbital parameters means that the Milky Way wouldn't be able to hold onto the dwarf and it would escape the system.

10. kzb
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MW virial mass using combined GAIA and Hubble data = 1.67 trillion solar masses. Including the claimed uncertainties gives a range of 1.17 to 2.46 trillion solar masses.

So the 700 billion figure is looking too small, and the 3 trillion figure too large, going by this latest estimate.

Evidence for an Intermediate-Mass Milky Way from Gaia DR2 Halo Globular Cluster Motions

https://arxiv.org/abs/1804.11348

11. Following is a general response to questions asked by the OP and others. In principle it would be simple to estimate the mass of a galaxy if we knew the vector velocities and orbit types of the orbiting clusters with any certainty. That is simply a matter of using Newton's formula for gravitational acceleration and the formula for the centripetal acceleration associated with a path of any given curvature. In the real universe things are not as neat and clean as in thought exercises in a physics classroom, and until recently we had only radial velocity information. The recent achievement of measuring proper motion of these remote objects is a major advance in determining their true velocities. We still cannot tell whether a given cluster is near periapsis in a large elliptical orbit, apoapsis in a small one, or somewhere in between. By observing numerous such objects we can use statistical methods to derive reasonable upper and lower bounds on the possible mass of the galaxy. The aforementioned possibilities tend to average out.

12. kzb
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Then again, the majority of the stars are in the bulge and disk.

The mass of these galaxy components is found from the rotational velocity, rather than satellite galaxy orbits and all the difficulties associated with those measurements.

13. Originally Posted by kzb
Then again, the majority of the stars are in the bulge and disk.

The mass of these galaxy components is found from the rotational velocity, rather than satellite galaxy orbits and all the difficulties associated with those measurements.
Are we sure they are not outnumbered by far-flung and faint K and M stars in the halo? That is one detail I have not seen so far in my browsing. Much of the outlying halo mass as estimated from satellite galaxy motions appears to be dark matter, but there could be lots of stars out there, and they would be inconspicuous.

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Originally Posted by Hornblower
Are we sure they are not outnumbered by far-flung and faint K and M stars in the halo? That is one detail I have not seen so far in my browsing. Much of the outlying halo mass as estimated from satellite galaxy motions appears to be dark matter, but there could be lots of stars out there, and they would be inconspicuous.
If you look at that reference in my Post #5 in this thread, they estimate about 1 billion solar masses of stars in the halo. That's fairly minor compared to the 60.8 billion in the disc + bulge in the same reference.

Also, the numbers are constrained by the MACHO searches. The general conclusion was that only a tiny fraction of the halo mass could be in the form of stars.

I suspect looking at it from the halo mass point of view is not going to be very productive, because the stellar mass is probably lost in the uncertainty on the total mass.

15. Originally Posted by kzb
If you look at that reference in my Post #5 in this thread, they estimate about 1 billion solar masses of stars in the halo. That's fairly minor compared to the 60.8 billion in the disc + bulge in the same reference.

Also, the numbers are constrained by the MACHO searches. The general conclusion was that only a tiny fraction of the halo mass could be in the form of stars.

I suspect looking at it from the halo mass point of view is not going to be very productive, because the stellar mass is probably lost in the uncertainty on the total mass.
Sorry I missed that. My eyes must have zigged when they should have zagged.

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Originally Posted by AGN Fuel
The main problem is time. The paper describes a radial velocity but we haven't been able to observe the system long enough to get a grasp on the eccentricity of its orbit. You can image that one orbit of the galaxy will take many, many millions of years but we have only been observing it for the tiniest fraction of one orbit! So we don't really know if the orbit is nearly circular, quite elliptical (and if so, it it nearer periapsis or apoapsis?) or completely unbound.
Thanks

Yes, time is a problem.
Please be aware that in order to estimate the SMBH mass, our scientists had to trace S2 orbit cycle for almost 17 Year.
I would assume that at least several billion years are needed for just one orbit cycle of that dwarf galaxy.
So, Time is a problem.
Never the less, don't you think that it is just a mistake to evaluate the Milky Way galaxy mass based on a tiniest fraction of one orbit, without knowing if it is nearly circular or just elliptical?

With regards to your following explanation:

Originally Posted by AGN Fuel
So what is done here is to model what minimum mass the Milky Way must be for the dwarf galaxy to be bound. Less mass based on the currently understood orbital parameters means that the Milky Way wouldn't be able to hold onto the dwarf and it would escape the system.
Yes, I fully understand the target, however:
What is the chance that there are several Dwarf galaxies (or even globular clusters) near that dwarf galaxy?
We already know that in globular clusters, stars orbits around the center of mass of all the other stars in the cluster.
So, what is the chance that this Dwarf galaxy orbits around the center of mass which is a direct outcome from all the other nearby dwarf galaxies and globular clusters?
Do you agree that in this case, it is also a mistake to isolate one dwarf galaxy and try to extract any relevant data from its orbital path?

With regards to the Sun:
Based on the current hypothesis, Spiral arms don't hold it in the disc.
If it is correct, than why can't we evaluate the total mass inside the sun orbital cycle?
We know the distance, we know the velocity - so we should easily extract the requested mass.
In the same token, we could monitor the most outwards star in the disc and extract from its orbital data the requested mass of all the Milky way disc.
Last edited by Dave Lee; 2018-May-05 at 06:50 PM.

17. Originally Posted by Dave Lee
Never the less, don't you think that it is just a mistake to evaluate the Milky Way galaxy mass based on a tiniest fraction of one orbit, without knowing if it is nearly circular or just elliptical?
It may turn out to be a mistake. That is an assumption underlying all science. But, at the moment, it is the best we can do. The alternative would seem to be to just say, "we have no idea". But would definitely be a mistake, because we can make estimates based on the best data we have at the moment - even if it turns out to be inaccurate when we get more data.

If it is correct, than why can't we evaluate the total mass inside the sun orbital cycle?
We know the distance, we know the velocity - so we should easily extract the requested mass.
That is exactly the approach that is used, which you just said "is just a mistake"

18. Originally Posted by Dave Lee
Never the less, don't you think that it is just a mistake to evaluate the Milky Way galaxy mass based on a tiniest fraction of one orbit, without knowing if it is nearly circular or just elliptical?
Hang on a minute - the purpose of the paper was to discuss the HI clouds in the region of the dwarf galaxy and to discuss mechanisms for their stripping. Determining a possible mass of the Milky Way was almost a !throw in. You are talking as though the sole purpose of the paper was to calculate the mass - it wasn't. But what it does provide, is one more small data point toward finding a solution to the mass question. It's like a police investigation - every scrap of information goes toward seeing the full picture.

19. Originally Posted by Dave Lee
Yes, I fully understand the target, however:
What is the chance that there are several Dwarf galaxies (or even globular clusters) near that dwarf galaxy?
We already know that in globular clusters, stars orbits around the center of mass of all the other stars in the cluster.
So, what is the chance that this Dwarf galaxy orbits around the center of mass which is a direct outcome from all the other nearby dwarf galaxies and globular clusters?
If there are other dwarf galaxies nearby that we hadn't detected yet, they may cause some perturbations in the orbit, but the Milky Way remains by a huge margin the dominant gravitational body in the system.

With regards to the Sun:
Based on the current hypothesis, Spiral arms don't hold it in the disc.
If it is correct, than why can't we evaluate the total mass inside the sun orbital cycle?
We know the distance, we know the velocity - so we should easily extract the requested mass.
We do exactly that.

20. Originally Posted by Dave Lee
I would assume that at least several billion years are needed for just one orbit cycle of that dwarf galaxy.
So, Time is a problem.
Never the less, don't you think that it is just a mistake to evaluate the Milky Way galaxy mass based on a tiniest fraction of one orbit, without knowing if it is nearly circular or just elliptical?
Just a little further on this, because I find this objection a little curious. The authors of the paper are describing the first radial velocity measurement of a galaxy that is probably gravitationally bound to the Milky Way, but may not be.

Natural scientific curiosity would would mean that finding that velocity would naturally lead to the creation of models based on that observation. The orbital elements of the dwarf Galaxy are not defined, but knowing the radial velocity opens the door to defining some possible parameters, including the mass of the body being orbited. It's one piece in a very large jigsaw puzzle.

Future observations (or studies of other observations) will then allow the models to be refined further (or potentially overturned altogether). In this way, our knowledge progresses - sometimes in fits and starts, to be sure, but overall we move toward a more complete understanding as we put more and more pieces of the puzzle into place.
Last edited by AGN Fuel; 2018-May-06 at 03:59 AM.

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Originally Posted by AGN Fuel
We do exactly that.
Please look at the following article:

http://pages.uoregon.edu/jimbrau/ast...Chapter23.html

"The Mass of the Milky Way Galaxy
Weighing the galaxy
The orbital speed of a star or gas cloud around the Galaxy is determined by mass inside the orbit
Calculation of the mass inside the Sun's orbit
Kepler's Law: total mass = (orbital size)^3 / (orbital period)^2
orbital size in AU
orbital period in years (225,000,000)
orbital size = 8000 pc x 206,000 AU / pc
total mass ( within 8 kpc) = 9 x 10^10 solar masses
or 90 billion times the mass of the Sun".
Last edited by Dave Lee; 2018-May-07 at 12:14 PM.

22. Originally Posted by Dave Lee
...total mass (within 8 kpc) = 9 x 10^10 solar masses
or 90 billion times the mass of the Sun".
That's pretty reasonable. Note that this isn't an estimate of the total mass of the Milky Way, just an estimate of the mass contained within the orbit of the Sun. The same page gives an estimate of about 200 billion solar masses within the luminous region of the Milky Way (out to about 15 kpc), and a mass of about 600 billion solar masses out to a radius of about 40 kpc. Most estimates I've seen recently have been higher than that, but not inordinately so. AGN Fuel's range given above for recent estimates (usually somewhere between 750 billion and 4 trillion) is pretty reasonable.

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Originally Posted by Grey
That's pretty reasonable. Note that this isn't an estimate of the total mass of the Milky Way, just an estimate of the mass contained within the orbit of the Sun. The same page gives an estimate of about 200 billion solar masses within the luminous region of the Milky Way (out to about 15 kpc), and a mass of about 600 billion solar masses out to a radius of about 40 kpc. Most estimates I've seen recently have been higher than that, but not inordinately so. AGN Fuel's range given above for recent estimates (usually somewhere between 750 billion and 4 trillion) is pretty reasonable.
Sure.

However, that is correct only if our understanding about spiral arms and Density Waves is correct.

24. kzb
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I found this interesting. Milky way disk stars found more than 26 kpc from the centre. This argues that the disk does not end at 15kpc radius.

It probably hardly affects the number of stars estimate however, because the stars are very diffuse.

Disk stars in the Milky Way detected beyond 25 kpc from its center

https://arxiv.org/abs/1804.03064

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