We’ve often speculated here about how many stars exist in the Milky Way. Earlier estimates have ranged from one hundred billion up to four hundred billion, with a few wildcard guesses in the range of one trillion. The number is still, of course, inexact, but recent work has led to a serious misunderstanding of the subject. As reported in this earlier post, Harvard’s Mark Reid and colleagues have discovered that the Milky Way is likely to be as massive as the Andromeda galaxy, which means that it could have the mass of three trillion stars like our own Sun.
Does that mean that the Milky Way contains three trillion stars? Absolutely not. I’m seeing the three trillion star number popping up all over the Internet, and almost reported it that way here when I first encountered the work. The misunderstanding comes from making mistaken assumptions about galactic mass. Reid used the Very Long Baseline Array to examine regions of intense star formation across the galaxy, a study the scientist reported at the American Astronomical Society’s winter meeting this past January. The Milky Way does indeed turn out to have much more mass than earlier studies had indicated.
Mass on the Galactic Scale
Science News ran a story on Reid’s work with this headline: “This Just In: Milky Way as Massive as Three Trillion Suns.” The headline is catchy, but read it carefully. It does not say the Milky Way contains three trillion stars. What it does say is that the galaxy has been found to be as massive as three trillion suns. In other words, it has the mass, at the upper limit, of three trillion G-class stars like the Sun.
Now factor in our understanding of galactic mass. Current thinking says that dark matter accounts for nine-tenths of a galaxy’s mass, and perhaps more. What Reid’s work shows us is that the galaxy is massive indeed, about fifty percent heavier than previously thought. But bumping up the mass estimate also bumps up the estimate of dark matter, and does not imply that the galaxy contains three trillion stars, or anywhere near it. Again, most of the mass in a galaxy is in the form of dark matter, which is what most of that additional mass would be made of.
The Dominance of Dark Matter
Because I wanted to be sure I had this right, I wrote to Dr. Reid asking whether the idea that the galaxy contained three trillion stars wasn’t a serious error, one that did not follow from his work. He agreed:
What we’ve found is that the Milky Way is rotating about 15% faster (254 km/s) than previously assumed (220 km/s). The faster rotation speed matches that of the nearby Andromeda galaxy (M31). The simplest interpretation is then that the Milky Way and Andromeda have a similar overall mass and size (that is dominated by dark matter halos). Estimates of the total mass of Andromeda are typically between 1 and 3 trillion solar masses. However, only a small fraction of that is in normal matter (eg stars), probably only about 0.1 trillion [italics mine].
A tenth of a trillion — a hundred billion — solar masses is what we have to work with in terms of normal matter. That figure would then need to be adjusted to reflect the relative abundance of stellar types, from the tiniest brown dwarf to the largest blue giant, to get a star count. There is still room for a range of estimates, but we’ve learned that while the Milky Way is crammed with stars, it’s a long way from having three trillion of them.
I think I understood that the number of stars in a galaxy is not primarily, or at least not only, determined by its mass, but by its total luminosity.
If indeed the normal matter content of our MW is some 100 billion solar masses, then this amount divided by average star mass gives the number of stars.
What mass is an ‘average’ star? Red dwarfs are by far the most abundant, a typical red dwarf being 0.2-0.25 solar mass ?
That would still make a (very) rough estimate of some 400 billion stars in the MW.
From luminosity measurements and reasonable assumptions about the Galaxy’s Initial Mass Function, and stellar mass-luminosity relation, the total is about 100 billion stars. About half the baryonic mass of the Galaxy is floating around as unconsolidated gas and dust, so maybe 50 billion solar masses is in stars. The high end mass distribution would skew the average away from the red dwarfs potentially. I think we’ve all got some reading to do before we can make a sensible guess.
70-percent plus of the stars are thought to be M-class dwarfs, but I have no information on how to work the overall mass distribution. A classic case for readers to chime in; I suspect some of our resident astronomers will be able to help us out. Ronald’s question is on the money: What mass is an ‘average’ star? I’m still flummoxed — it took me all this time to realize I was thinking about Reid’s work the wrong way…
Hi Paul;
I am no expert on the Milky Way Galaxy, but I have heard of estimates of the number of stars within the Milky Way at about 400 billion.
I try to put my mind on the number 400 billion, in consideration of the mass of a star and the size of the average seperation of such stars or of the unit volumetric space cell occupied by such stars. One way I like to think about the number 1 billion is to think of one liter packed tightly with the finest flower grains that exist within a bag of fine grained flower such as Gold Medal Brand fine grained flower. Assumming each flower grain is about 100 microns accross, a one liter bottle packed stuffed with the smallest flower grains would contain a billion flower grains. About 2 average sized bath tubs packed solid with such flower grains would yield 400 billion. Although the math is simple and obvious, when one takes a mere pinch of fine grained flower in tosses it into the air, there are so many airborne flower grains that it would be impossible for one to count the number of such grains even by those with photographic memory. The human sensory perceptual distinguishing ability with respect to ordinal quantities of distinct visual elements is too poor by several orders of magnitude to even properly percieve but a pinch or air borne flower interms of knowingly visualizing the number of grains from perceptual inspection.
The point it that the Milky Way itself, not to mention the visible universe, let along the whole universe, has so many stars in it, and apparently roughly the same order of magnitude number of planets that it boggles the intuitive aspects of our minds. Imagine the huge variety of plants, animals, and perhaps ETI, and ETI cultures that might exist in just the Milky Way. Every time I view the Milky Way at night in a dark location, I can never ger enough of it. There is just plain something spiritual to looking out at the night sky at the Milky Way in all of its granduer. It is going to be a lot of fun for future generations to explore.
Thanks;
Jim
Hi Paul
The IMF is currently being actively researched and from the bit I’ve read the average stellar-substellar mass is somewhere between 0.2-0.4 solar masses, which means 125-250 billion stars and brown dwarfs. Or there abouts. In some clusters the lower mass range seems depleted and the higher mass range is skewed by mass-loss as the heavier stars evolve very rapidly. Between about 1-8 solar masses the end state of the stars is a white dwarf of roughly 0.5-0.7 solar masses, obscuring the initial mass of the stars So a definite answer isn’t yet available. I think we can safely say there aren’t more brown-dwarfs than stars, but there may yet be as many brown-dwarfs as stars. Maybe.
It was surprising to me how poorly known is the number of stars in the milky way.
As I understand things, the speed of rotation of a galaxy is primarily governed by baryonic mass. The non-baryonic mass is much more diffuse and fills a huge spherical volume, chiefly outside the visible disk. It was hypothesised into existence to explain the flat rotation curve with distance from the galactic centre, not primarily the speed per se.
Anyway if M31 is said to be a fast rotator because of its trillion star content, if the milky way rotates at the same speed, I can’t see why that cannot have a trillion stars also.
Here’s a source on the ‘trillion stars in Andromeda’ issue:
http://www.newscientist.com/article/dn9282-andromeda-galaxy-hosts-a-trillion-stars.html
I’m also finding this puzzling in relation to the star count in the Milky Way. Anyone else want to jump in?
This is from a Harvard-Smithsonian Center for Astrophysics news release from 2006 related to the same work:
Friends,
I did some modest research myself on our stellar neighborhood population, assuming that it is reasonably representative for the MW or at least the disc. I used data from RECONS and Nstars database, which I already had in my possession and analyzed, for resp. 10 parsec (32.6 ly), 50 ly and 70 ly.;
Not surprisingly, the % of red dwarfs seems to go down and vice versa the % of F, G, K stars seems to go up a bit, as distance increases. This is most likely, as sources also mention, because of the reduced (harder) detectability of the smallest stars, i.e. observational bias. This is also reflected in the fact that the average density of stars seems to decline, going from 32.6 via 50 to 70 ly, namely from 0.0023 via 0.0018 to 0.0014 stars per cubic ly.
Taking this into account, and assuming that the nearest neighborhood is most representative with regard to the red dwarfs, the % distribution of the local galactic stellar population is as follows, taking all main sequence (V), subgiants (IV) and subdwarfs (VI) together (by far most of these are V anyway), but giants (III) separate:
O and B: 0
A: 1 %
F: 3 %
G: 6 %
K: 14 %
M: 70 %
White dwarfs: 5 %
Giants (III): 1 %
(The % of M may actually be 72% and of F and K 1 % lower each).
Mass distribution is indicated here: http://www.chara.gsu.edu/~thenry/RECONS/mf.2009.0.html
The relationship between number and stellar mass is C*M^-1.20, where C = 4.6
With regard to the average star mass, I found a few interesting publications, notable this one: “ON THE MASS DISTRIBUTION OF STARS IN THE SOLAR NEIGHBOURHOOD”, by S. Ninkovi_c and V. Trajkovska, Serb. Astron. J. } 172 (2006), 17 – 20
It literally mentions “mean star mass should be about 0.6 solar masses”.
Another source also mentioned 0.6 solar mass, while another one guesstimated about 0.5 solar mass as average.
I find that average rather high: using the RECOS and Nstars data, I myself come to an average of not more than (and probably even a bit less than) 0.25 Msol for red dwarfs and about 0.4 Msol for all stars in a sample (of 354 stars).
What I found hard to find with any reliability and accuracy is the total stellar mass of our MW galaxy: various sources’ estimates (guesstimates) vary from 50 to 200 billion solar masses, most however mention 50 to 100 billion. Still quite a range.
“The mass to light ratio and the initial mass function in galactic discs”, by Portinari et al., 2006 mentions 50 billion solar masses in stars.
My impression is, that Adam is on the mark about this and that indeed most authors mean to say that the total ‘normal’ matter content of the MW galaxy is about 100 billion Msol, of which about half is in stars and about half in gas/dust.
If this is indeed the case, it implies, given the average stellar mass of 0.5 – 0.6 Msol, that the total number of stars in our MW galaxy would be ‘only’ about 100 – 120 billion, even the maximum estimate being no more than 200 billion.
Ronald, this is outstanding work. Thanks for digging so deeply into this thorny issue; you’ve provided lots of material here for further digging! The 120 billion star figure you specify as an upper limit makes sense given what we have to work with. I do note that the brown dwarf exclusion will be controversial.
On further addition to my previous post, I should have added, with regard to total number of stars estimate: including white dwarfs, but excluding brown dwarfs. The abundance of the latter category is still obscure and they are not considered ‘true’ stars anyway.
Paul and others: I noted one flaw in my own (elaborate) post, towards the end: 50 billion divided by 0.6 is of course not 120 billion, but about 83 billion. Which makes the estimate even more modest, based on 50 billion Msol in stellar mass: roughly 80 – 100 billion stars.
As a very upper limit: if the total stellar mass in the MW is 100 billion Msol, and my own estimate of 0.4 Msol for the average star is indeed closer to the truth, than the total number of stars in the MW would be a maximum of 250 billion.
Reading quickly, I went right past that. Thanks for the correction, Ronald.
Nice work, Ronald! I’ve dug up similar papers in the past myself, but wanted to see what the latest work was saying. According to what I’ve read studies of clusters indicate a “knee” in the number/mass distribution, with the power-law index changing as the mass decreases, somewhere around 0.5 solar masses. If we used the classic power-law index of -2.35 then there would be about 10 times the number of brown dwarfs in the mass range 0.013-0.08 solar masses than regular stars between 0.08-150 solar masses. Since that’s not observed then the power law must change quite sharply.
So based on the figures Ron has dug up that means stars are about 1/60th of the new mass of the Milky Way. We seem to be but a ripple on a deep, Dark sea of ‘stuff’…
Question: if the number of stars in our own galaxy is probably some 100-200 billion and 400 billion is really pushing it, how do they justify a trillion for Andromeda? I read that they based this on comprehensive light measuments, but how does this compare with our MW, considering that the total masses are comparable?
Or in other words: what essential differences in structure and mass distribution might there be between these two, otherwise quite comparable galaxies, as an explanation for this huge discrepancy?
Some possible hints: total luminosity of Andromeda seems to be about twice that of our MW, so does that indicate also about twice the number of stars (and not 5 times)?
Also, star formation rate and supernova rate in Andromeda is much lower. And the (inner) disc seems to be raher old and stable (according to the mentioned New Scientist article). Does this together indicate anything, such as somewhat higher age and relatively much mass in stars and less in gas/dust?
Anyone?
I’m with you Ronald on your latest post. There seems to be inconsistency between fields in astronomy.
Also, about the “average mass” of a star. In this context, we need the median mass, not the average?
Stars have been detected out to 25kpc galactic radius, which implies a diameter of circa 150,000 light years. The disk is not 150pc thick as mentioned elsewhere on this site. That is the thin disc only. There is a stellar population detectable 3-4000 light years “above” the sun, and since the sun is thought to be close to mid-plane, the disc thickness is 6-8000 light years at the sun’s radius. (Recently there was a report the thickness is 12,000 light years, but that was gas and dust I believe.)
The star-containing volume of the bulge plus disk must be of the order of 10^13 to 10^14 cubic light years.
I’m in agreement with both of you, and hope we can get some further feedback on how the stellar population in Andromeda is arrived at vs. the Milky Way. Lots of issues here.
@Keith: no, I think we really need the average for this, not the median, because the various classes are so different in abundance.
“The star-containing volume of the bulge plus disk must be of the order of 10^13 to 10^14 cubic light years.”
This mean, with an average stellar density of 0.002 per cubic light year, a total of between 20 and 200 billion stars. Again, same order of magnitude.
Ronald:
Now I think about it, yes we need the arithmetic mean star mass. Like you say above though, based on RECONS, this could be significantly lower than assumed elsewhere.
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Ah but there’s the rub. The MW stellar population is very sensitive to the average stellar separation distance, because of the cubic relation. The value you have here (0.002 st/ly^3) is close to the RECONS data within 10pc of the sun. From RECONS, I calculate the average separation is 7.28 light years. (The average between stellar SYSTEMS is higher, because many of the stars are in binaries or multiples).
If we think of the central bulge as a globe 12,000LY in diameter, that’s 9E+11 cubic LY. Now think of some average stellar separations for the central bulge:
If 2.0 LY, that’s 8 cubic LY/star, hence 90bn stars in the bulge
If 1.5LY, that’s 3.37 cubic LY/star, hence 268bn stars in the bulge.
If 1.25LY, that’s 1.95 cubic LY/star, hence 461bn stars in the bulge
You can see the number is extremely sensitive to the average separation distance. I think I read somewhere the separation in the bulge is less than 2LY, but that memory is vague and I can’t reference it. (You would think that this number could be tied down better since we can apparently find out exactly what is going on within a few AU of Cygnus A*.)
Also, I wonder how complete is the RECONS sample? Proper motions close to perpendicular to us will not be detected, similarly there must be blind spots towards the poles where the telescopes can’t see?
Question: does the Milky Way favour G0, G5, G8 and K0 ?
Friends,
now that we are doing some population dynamics for the MW: I did some more detailed follow-up sampling of solar type stars in the nearby MW, using RECONS and particularly the Nstars database.
I made an inventory of all F7 through K2 stars within 70 ly, all main sequence (V) or just moving into IV, i.e. no real giants (‘full’ IV several times solar luminosity, or III).
I came up with a total of 326 stars (of which 21 ‘early’ IV).
Now, the distribution was as follows:
F7–>17
F8–>18
F9–>7
G0–>30
G1–>9
G2–>16
G3–>14
G4–>4
G5–>33
G6–>8
G7–>4
G8–>27
G9–>4
K0–>58
K1–>34
K2–>43
As we all know and can also be seen from my post of 15 March, stars get more abundant with decreasing mass and temperature, i.e. spectral class moving from early (O, B) to late (M). Therefore it is no surprise that in the above sample G is more abundant than F and K more so than G.
However, what is surprising, is the fact that *within* a spectral class, this abundancy/temperature relationship cannot be seen, i.e. the sybtypes (0 to 9) do not get increasingly more abundant, on the contrary, they are not even approaching this relationship.
Within class G, subtypes G0 and G5 are over-represented, G8 is also rather common (which is to be expected), and within class K, K0 is very abundant.
On the other hand, G4, G7, G9 are almost absent.
What can be the reason for this skewed distribution?
I would expect the subtypes to represent more or less equal temperature and/or color ranges, or am I wrong about this? Or is the classification biassed?
Or is there a real physical phenomenon here?
(It’s a pity I can’t show a bar chart here, would demonstrate it so clearly).
Ronald: IIRC not all of the possible subtypes are actually used in the more common spectral classification schemes. I think you’re looking at an artifact of the classification scheme rather than a physical phenomenon.
(There are however various gaps in the main sequence thanks to various physics of stellar interiors, however again IIRC these wouldn’t be large enough to knock out an entire subtype)
Andy, thanks, I indeed suspected there was (at least partle or largely) an artifact at work here.
Your remark about possible gaps in the main sequence, however, also intrigues me.
I know, for instance, from several publications, one very interesting recent one among them (“Improved Age Estimation for Solar-Type Dwarfs Using
Activity-Rotation Diagnostics”, by Mamajek and Hillenbrand, 2008) that there is a gap in the age distribution of solar type stars in the MW, the so-called “Vaughan-Preston gap”. Although the authors state that in their improved method “the minimum at ?2-3 Gyr is
not as obvious”, in a histogram there can still be seen a minimum around 2 – 4 gy, and maximums around 0 – 1.5 (or 2) gy and 4 – 6.5 (or 7) gy.
If real, this is very fascinating with regard to solar star formation. As the MW (and the universe) ages, one would expect a gradual decline in larger-mass, brighter stars (in relative increase in small dwarfs), but for solar stars this is not yet obvious in the youngest age classes (fortunately). We won’t run out of them yet ;-)
A bit more with regard to the artifact nature of peaks and valleys in solar subtype abundance:
I found, that, even when I take 2 or 3 subtypes together (moving averages), also taking into account that part of G8 becomes K0 then, there still remain real scarcities around G3/G4 (maybe even G1-G4) and around G6/G7. On the other hand, the earliest solar types (F7 – G0, surprisingly) and the latest (G8 – K2, not so surprising) are relatively abundant, with a pleasant peak also around G5.
Again, just artefacts or interesting natural history of our MW galaxy?
Keith, I understand from you that the central bulge is very crucial with regard to total number of stars in the MW and even small deviations in average distance can result in great differences in density and number.
I wonder whether this has been and can be taken into proper account with the studies based on total luminosity (i.e. simply put: wouldn’t stars in the central bulge block out the light from others at high densities?).
Ronald, in addition to what andy says, what you have here is basically a Poisson distribution. It’s a lottery. When you have small numbers such as this, the randomness can take over and obscure any underlying pattern.
On another topic, has anyone got any comments on the completeness or otherwise of the RECONS star count within 10pc?
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I don’t know. When looking at external galaxies, presumably they sum the energies at all wavelengths to arrive at the energy output?
When you get to our OWN galaxy, this external measurement cannot be made. The total luminosity is in itself a calculated or estimated value. This value depends on the number of stars and their mass distribution. So you have this circular argument in effect.
In trying to find information in this topic, I seem to be coming up against this circular reasoning in several areas. When I get chance I will try and re-find the web sites as I found out a few interesting things. Unfortunately I am very busy at present :(
Why does the MW love G0, G5 and K0, part two.
@Keith, Andy, and others; Keith said: “When you have small numbers such as this, the randomness can take over and obscure any underlying pattern”
Well, I have done the same sampling with the Hipparcos catalogue up to 150 ly, taking all F7 through K2, main sequence (V) and early IV, i.e. excluding the real (sub)giants. Total sample size: 2780.
The results are rather spectacular: contrary to what one would expect with randomness due to small numbers, the pattern described by me before just becomes clearer and, in fact, quite outrageous:
– There is an increasing abundance from F7 through G0 (as expected, with a conspicuous dip at F9, but this may be an artefact as mentioned by Andy);
– Then there is a conspicuous ‘valley’ from G1 through G4;
– Then a spectacular peak at G5;
– Then another valley from G6 through G9 (with a minor peak or lesser dip at G8);
– Then peak from K0 through K2 (as expected, but K0 being most abundant of the three).
G5 in particular is very abundant comprising almost 20% of all sunlike stars!
The mentioned dip from G1 through G4 is very clear and comprises 4 spectral subtypes.
If these are all just artefacts and the result of (very) subjective classification, spectral subclassification (0-9) would almost lose its meaning.
I said: “G5 in particular is very abundant comprising almost 20% of all sunlike stars!”.
I should have added: and over 35% of all G-stars!
Ronald, I don’t know the details of the subclass definitions, but what I would be inclined to do is bypass the judgment calls of others on the stellar classifications and go straight to the observables. It may be that if you were to set up your own equal-width spectra buckets (as an indicator of surface temperature), you might very well end up with a smoother curve. I admit that I don’t know specifically what Hipparchos and other instruments record, but hopefully the raw data would prove more useful to your study.
If we turn the argument around, is there any reason to expect the spectral classes to follow a smooth relation? If it is PURELY mass, then yes you might expect this. But my understanding is the classification is based on abundance of spectral lines. So that is a confounding factor. I don’t think the relative abundances of spectral lines is a direct indicator of temperature or mass. For one thing the chemical composition will be different star to star.
Ron, Keith, thanks!
Yes, if and when I can spare the time, I indeed want to try to analyze the raw data, in particular mass and temp.
Back to rotation speed. My maths and astrophysics is not very good I’m afraid. My question: what determines the rotation speed at any given galactic orbital radius? Is it only the mass INSIDE the orbit, or does the mass outside also contribute?
This question is important, because as I understand things, the non-baryonic matter is spread over a much greater volume of space than the baryonic matter. Mass inside the orbit of the sun would primarily be baryonic, and if we have a faster rotation speed, that implies more baryonic mass.
Hi Keith
On mass external to the galaxy: a spherical distribution of mass pulls on things interior to it evenly from all directions so there’s no net force. There is a net gravitational potential and this has to be factored in when computing general relativistic effects. A ring of mass would also produce no net force on anything interior to it lying in its plane and produces a net force back towards the ring plane on anything above or below it.
If most of the Galaxy’s mass is in Dark Matter arranged as a sphere, then the Sun, for example, is largely being gravitated by the mass interior to its orbit, a mass anchored by the super-massive Black Hole in the centre. There is a spherical mass distribution of Dark Matter which reproduces the flat Galactic rotation curve that is observed – the density decreases with radius in a tricky exponential function AFAIK. Wikipedia has a good discussion of it.
Hi Adam
Thanks for the reply, you more or less confirmed what I thought. The orbital speed at the radius of the sun is controlled by the mass interior to that orbit. I’ve looked at the reference in Wikipedia.
Where am I going with this? Well it seems to me that there are some circular arguments going on. The number of stars estimate is based on the mass to light ratio, a concept that pre-dates non-baryonic dark matter. By looking at other galaxies and finding their mass from the rotation speed, and measuring the light output, you can find the mass to light ratio. So the rotation speed is used in this calculation, and it is used in the estimation of the number of stars.
It seems to me though, that as soon as you invent non-baryonic dark matter as the major component of mass, and you also say the amount of baryonic matter does not necessarily have any relationship to the amount of dark matter, this calculation method is fundamentally broken.
There must be whole swathes of literature that have been made redundant by this?
Hi Keith
Not really. Mass-to-light is pretty certain as these things go and one of the *easiest* things measured of galaxy properties. Starlight can be measured and gas and dust can be observed in different frequencies. Put together we can get a good idea of the baryonic matter present.
Dark matter isn’t invented – it’s gravitational effects are observed in the rotational curves of galaxies and the behaviour of galaxy clusters, inter-galactic gas, and gravitational lensing. The creative license is when we try to say just what it is – is it MOND? Is it WIMPs? Neutralinos? Micro Black-Holes? A mix of weird things? A manifestation of the 5th dimension? We don’t know.
Hi Adam
Please be aware it was not my intention to turn this into another discussion on the existence or otherwise of non-baryonic dark matter (NBDM).
The Tulley-Fisher relation is still thought valid, even though it predates the widespread adoption of the NBDM theory.
For spiral galaxies external to our own, luminosity is graphically related to rotation speed. This is a real observation. What is more, luminosity is proportional to the FOURTH POWER of rotation speed, so a modest increase in the rotation speed has a large effect.
So what I am getting at is, if the rotation speed of our galaxy is higher than previously thought, that implies the central estimate of its luminosity must also be increased, according to the Tulley-Fisher relationship. If the rotation speed has gone up be 15% then the luminosity has gone up by 1.15^4=1.75.
Now the implication earlier in the thread was that the number of stars estimate should not be increased, despite this new rotation speed. I am contesting otherwise.
Logically, the stellar population estimate is increased by a factor of 1.75. (Unless the milky way is some exception to the Tulley-Fisher relation.)
keith wrote:
That seems like a reasonable extrapolation, and certainly takes us to an estimate of the Milky Way’s stars far below the three trillion that’s been so widely circulated because of misunderstanding of the ‘three trillion solar mass’ figure.
I’m glad we’re coming to some agreement here!
To add some further weight to my argument, in the link below it says that the Fisher-Tully correlation is remarkably tight and free of scatter.
http://www.scholarpedia.org/article/Tully-Fisher_relation
This means the relationship is NOT fundamentally broken by non-baryonic dark matter, as I feared above.
Now the new Milky Way rotation speed (254 km/s) is very close to that of the Andromeda galaxy (M31) -from memory 257km/s. I wonder if I’m going too far in saying the number of stars in both galaxies must now be nearly equal ?
Just my thought, and I hope others will continue to weigh in. The Andromeda issue remains vexing to me.
In the link below, we have a plot of K-giant star numbers “above” the sun perpendicular to the Milky Way disk plane:
http://www.astro.utu.fi/~cflynn/kzpress.f1.html
Notice there is a considerable stellar density right out to 1000 parsecs, and at least some stars out at 1300 parsecs. I am often seeing disk thickness values much smaller than this on various web sites. This plot implies a disk thickness of around 2kpc (since the sun is known to be close to the mid-plane). This is more than 6000 light-years, considerably more than the values of around 1000 light years that you often see.
Having said all that, I do wonder if I am interpreting that plot correctly. I don’t understand why the star count should start off low near the sun, then rise to a peak before tailing off. Why the initial minimum in the plot? The only explanations I have thought of are:
(1) K-giant stars are a greater proportion of “thick disk” stars,
OR
(2) The count is not corrected for the field of view area increasing with distance from the telescope.
Can anyone help with that?
In March andy, Ron S and Keith Bradshaw responded to my observation, that the MW galaxy seems tom favor certain spectral subtypes (skowing conspicuous peaks for G0, G5, G8 and K0) by stating that this is probably al just an classification artefact and bias. And that I should try to look at the raw data rather than this derived classification.
I then promised I would do some more homework, when I found the time.
Well, I have, and the results seem to settle the above matter, as follows; I checked and analyzed the NStars and Hipparcos data, however not for mass and temperature, as I originally mentioned, since both are also derived and not found in the original raw data.
Instead, I analyzed two other relevant parameters: total luminosity (from Mv) and color index B-V for all solar type stars from 0.20 to 3.00 solar Lum (Mv 6.58 – 3.64), B-V from 0.45 – 1.35, subdivided in equal (0.05) width classes. Total 291 NStars, 2370 Hip stars.
The results are rather sobering and maybe not too surprising (maybe I even risk kicking in an open door);
* Both collections show a ‘normal’ (i.e. expected) exponentially increasing abundance with decreasing luminosity class. For Hip the relationship is: N = 132e-^0,0536x, with a R2 fit of 0.93. However, this is just simple Excel statistics and other statistical analyses may give better correllations.
* Both collections show a more or less ‘normal’ parabolic B-V distribution, with a peak roughly from (0.55) 0.60 – 0.75 (0.80), and almost nothing below 0.45 and above 1.10.
(The NStars also show a second peak from 0.80 – 0.90, but this may simply be due to the much smaller sample size).
My conclusion now confirms the above-mentioned gentlemen’s suspicion, namely: that the ‘traditional’ subtype spectral classification and more particularly the observed peaks therein (G0, G5, G8 and K0) as well as a few valleys, is not supported by analysis of the raw luminosity and B-V color index data, which do not show any of these peaks, but rather show the normally expected distributions.
I will also sent my data to Paul and his colleague Kelvin Long, with whom I have been corresponding about similar data before.
Interesting stuff, BTW, stellar population biology ;-)