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kzb
2006-Jul-18, 06:00 PM
In my how many stars in the galaxy thread, some comments there lead me off on a slightly different angle. I've been seeing references, whilst I was searching for the number of stars in the MW, which strongly imply the estimate of 80-100,000 LY as the diameter of the MW stellar disc is too low.

For example below I've pasted in something from

http://www.skynightly.com/reports/Deriving_The_Shape_Of_The_Galactic_Stellar_Disc.ht ml

QUOTE
....Over the past years, there has been changing evidence of a difference in the warp amplitude between stars and gas. These studies have led to the idea that the Milky Way stellar disc is truncated beyond 14,000 pc from the Galactic centre. ....The new analysis by Momany and his team provides the first clear and complete view of the outer stellar disc warp. ....This means that a global and large-scale Milky Way feature has been identified to about 25,000 pc from the Galactic centre: the team thus clearly demonstrates that there is no truncation of the stellar disc beyond 14,000 pc.

Now a radius of 25,000 parsec translates to a diameter of over 160,000 light year. That puts the MW comfortably wider than M31 (Andromeda), which is 130,000LY across.

Then there's the mass. I've seen abstracts which imply the mass of the MW is probably larger than that of M31.

Anyone got more to add?

Kaptain K
2006-Jul-18, 06:54 PM
From what I've read, the current concensus is:
Diameter - M31
Number of stars - M31
Mass - MW

ToSeek
2006-Jul-18, 08:23 PM
"We are almost exactly twice as massive as Andromeda," Gilmore said.

- http://www.space.com/scienceastronomy/060221_stues_dark_matter.html

kzb
2006-Jul-19, 05:39 PM
If the mass of the MW is double that of M31, how reasonable is it, that it's diameter is lower and it contains less stars?

The diameter question is pertinent, as the reference I pasted in above implies a 160,000LY diameter.

Now I know the bulk of galactic mass is thought to be non-baryonic matter. But wouldn't larger amounts of DM automatically attract larger amounts of ordinary matter? In other words, wouldn't you expect the amount of ordinary mattter to be proportional to the amount of DM?

antoniseb
2006-Jul-19, 07:08 PM
The relationship between the masses has plenty of room for doubt, but answering the question of how it is possible, imagine (if you will):
that there are several large blobs of equal proportions (to each other) reactive matter and dark matter floating around in what will eventually be a galaxy cluster. Imagine that two of them go through each other in opposite directions right next to a third one. The reactive matter from each has a large fraction collect and stay behind, and the dark matter just sails through carrying a depleted supply of normal matter. A reactive matter-rich galaxy forms at the site of the interaction. A dark-matter rich galaxy will probably form in each of the other two blobs.

I'm not saying this is how it happened, but it is *a* way to separate the two types of matter.

kzb
2006-Jul-20, 12:16 PM
I suppose so Antoniseb. I'd have to agree, if the relationship (mass reactive matter) is proportional to (mass non-baryonic dark matter) holds at all, it will only be in a statistical sense. For the reason you stated, you probably can't pick out two galaxies and say one will definitely have more ordinary matter than the other, because it has more dark matter. It can only be a balance of probabilities.

Still, there now seem to be a number of papers that would extend the MW stellar disc diameter from 90,000 LY to 130,000LY or even further.

Also, on my "number of stars in galaxy?" thread, this is from a Tim Thompson reply:

<<So, the old standard 100,000 LY for the diameter of the Milky Way is just too small. Certainly it is no less than 130,000 LY across, but is not likely larger than ~200,000 LY. The literature seems to justify the standard conclusion that M31 & the Milky Way are about the same size.>>

Now when he says "about the same size" I think he is using that in the astrophysics sense of "about", which seems to be, "within an order of magnitude". Other branches of science would interpret "about" as being perhaps +/-10% or so.

He also goes on to say the often-seen estimate of a "trillion" stars in M31 should be interpreted as "between 100 billion and 10 trillion".

I started this thread as a separate thread to the number of stars thread, as I thought more people would notice it, and contribute arguments to what I think could be a very important conclusion. Before this, I didn't know there was such huge uncertainty on the number of stars in the MW. I'm beginning to wonder if perhaps the often seen numbers like 200 or 400 billion are way too low, perhaps by a factor of 3. (That's the important conclusion BTW)

Anyway:
There's two references on the relative masses below, although probably a bit old now, from 2000 and 2002.

The mass of the Milky Way: Limits from a newly assembled set of halo objects
T. Sakamoto1, M. Chiba2 and T. C. Beers3 (2002)

The mass of the milky way is 1.4 to 2.5 trillion (10^12) sun-masses

Whereas according to this:

Dynamical Mass Estimates for the Halo of M31 from Keck Spectroscopy
Author(s) N. Wyn Evans, Mark I. Wilkinson, Puragra Guhathakurta, Eva K. Grebel, and Steven S. Vogt
Identifiers The Astrophysical Journal, volume 540, part 2 (2000),

Abstract The best-fit values for the total mass of M31 are (710)&#215;1011 M, depending on the details of the modeling. The mass estimate is accompanied by considerable uncertainty caused by the small size of the data set; for example, the upper bound on the total mass is 24&#215;1011 M, while the lower bound is 3&#215;1011 M. These values are less than the most recent estimates of the most likely mass of the Milky Way halo. Bearing in mind all the uncertainties, a fair conclusion is that the M31 halo is roughly as massive as that of the Milky Way halo. There is no dynamical evidence for the widely held belief that M31 is more massive it may even be less massive.

NOTE -I think the copying and pasting did not work properly on this, I think in "The best-fit values for the total mass of M31 are (710)&#215;1011 M", the figure is actually 7.10 x 10^11 M. "M" is 1 solar mass.

antoniseb
2006-Jul-20, 12:30 PM
One point that Tim made that I'm not sure you picked up on is this: we can say that the galaxy has a certain radius, but it is a question of what we are measuring and calling the galaxy. The bulk of the stars are within the 50,000 light year radius. What is outside that is more sparse, and less formed. As a parallel, what is the radius of our Solar System? Beyond the orbit of Neptune there isn't anything very big, but the Oort cloud goes out a thousand times that far. You can't just take someone's statement as to the radius of the galaxy and assume the whole thing is just like it is here.

kzb
2006-Jul-20, 05:24 PM
That's true, but what I'm trying to get at is the similarity, or otherwise, of the MW and M31. I agree the star density of both galaxies probably peters out gradually towards the outer regions, rather than there being a sudden cut off. So you do have a definition problem straight away. As a starting point, I'd say define the edge of both galaxies' main disc as "the star density at 65,000LY radius from the centre of M31".

That's because there seems to be a consensus the "stellar disc" of M31 is around 130-133,000 LY in diameter. This ought to be fairly reliable by now, as the distance to M31 is now alleged to be accurate to 3 significant figures, at 2.52 million LY. I would also guess that we know the M31 star density distribution out from the centre pretty well by now, because we can see the thing from outside.

Now, these latest references suggest the star-containing regions in the MW are ALSO of 130,000LY diameter. But now we come across the problem, we can't tell if the star density is similar to M31, because we can't see our own galaxy well.

One way of addressing this is to check how well the regions of our galaxy we CAN see well, ties up with star densities in corresponding regions of M31. Another way is to count the M-giant stars in the outskirts of M31 and the MW, and find the density in each galaxy in the outlying regions. I've chosen M-giants because those are the objects detected towards the outskirts of our own galaxy.

I would contend that, if the density of stars in our local region of the MW is similar to that in M31 at a similar distance from its centre, AND the M-giant density in the outskirts is similar to the MW, then M31 is a reasonable model for the MW. If the central estimate of M31 star numbers is "one trillion", then that would go for the MW also.

dgruss23
2006-Jul-20, 06:50 PM
When comparing diameters of galaxies it is important to make sure that they are compared at the same isophotal level. One standard that is typically used is the diameter at which the mean surface brightness drops to 25 mag arcsec^-2. So if you want to compare the diameters of the MW and M-31 that is one criteria that could be used. This was attempted by Goodwin et al (1998 - PDF) (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1998Obs...118..201G&amp;data_type=PDF_H IGH&amp;type=PRINTER&amp;filetype=.pdf). They find a D25 diameter of 26.8 kiloparsecs (kpc) for the MW - which is 87,400 light years. M-31 has a D25 diameter of 170' (from HyperLeda) which gives a diameter of 39.1 kpc or 127,500 LY.

D25 diameters do not measure the full extent of the galaxy, but if you want to compare diameters in a consistent way this is what you have to do. A D25 diameter is a pretty good estimate for the size of the optical disk. Then most spiral galaxies will have extended neutral hydrogen disks that sometimes are twice the diameter of the optical disk. For example see Table for on page 12 of this paper (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1994A%26AS..107..129B&amp;db_key=AST &amp;data_type=HTML&amp;format=&amp;high=3e5c03c80a08919). Click PDF at the top to download the paper.

As for the masses, M-31 has a larger rotational velocity than the MW by most estimates. Using the virial theorem the mass inside the D25 isophote would be ~ 3.0 x10^11 solar masses for M-31.

For the MW I've seen rotational velocity estimates from 220 km s-1 to 270 km s-1. Using the diameter given by Goodwin et al you get a mass in the range of 1.5 x 10^11 to 2.3 x 10^11 solar masses.

So it would appear that M-31 has the more massive and larger diameter optical disk.

kzb
2006-Jul-25, 11:54 AM
Thanks dgruss23, this is the kind of thing I am after. I hadn't found that first paper before, probably because I don't know which key words to search for. I hadn't come across the term "isophotal" before.

I've only had time to to have a quick first read so far, but one weakness seems to be how do you measure the isophote distributions or contours for the galaxy you are inside?

dgruss23
2006-Jul-25, 03:39 PM
Thanks dgruss23, this is the kind of thing I am after. I hadn't found that first paper before, probably because I don't know which key words to search for. I hadn't come across the term "isophotal" before.

I've only had time to to have a quick first read so far, but one weakness seems to be how do you measure the isophote distributions or contours for the galaxy you are inside?

That is definitely a great source of uncertainty. You have to look at the distribution of stars - essentially the density of stars at different distances. As stellar density decreases, surface brightness should too. But I'm not familiar with the details of how that is done.

An alternative route to estimating which galaxy is bigger - and probably the most reliable route - is simply to measure the rotational velocity of the galaxy. M-31 is a faster rotator than the MW and therefore should be the more massive galaxy - unless the MW had a significantly larger diameter (using the traditional M = V^2xR/G).

Of course MOND works extremely well for modeling galaxy rotational dynamics. With MOND the radius is not even part of the equation for calculating mass: V^4 = M x a0 x G where a0 is the MOND acceleration constant.

Just based upon rotational velocity, the mass of M-31 should be larger than the MW.

kzb
2006-Jul-25, 06:12 PM
Hi dgruss23

<<You have to look at the distribution of stars - essentially the density of stars at different distances.>>

Well all I can say to this is, in the discussion on my 'number of stars in the galaxy' thread, I was surprised how much uncertainty there is in the total number of stars in the MW. As I kept saying there, estimates range from 100 to 500 billion. If the total number is THAT uncertain, then I'd guess the distribution is even more uncertain.

<<Just based upon rotational velocity, the mass of M-31 should be larger than the MW>>

There's some references from above:

<<"We are almost exactly twice as massive as Andromeda," Gilmore said.
- http://www.space.com/scienceastronom...rk_matter.html>>

and see also my post on 20 July 06 12:16

That imply the reverse, i.e. the MW is the more massive. However, perhaps they are not talking about quite the same thing? Those references include the total mass including halo, whereas you are talking about the stellar disc (D25 diameter)?

yuzuha
2006-Jul-26, 12:50 AM
Interesting. Read somewhere that galaxy mass is proportional to the mass of the sm black hole in the center. M31's is 30 million solar masses while ours is closer to 3. So, where will the debate end?

Kaptain K
2006-Jul-26, 07:02 AM
Interesting. Read somewhere that galaxy mass is proportional to the mass of the sm black hole in the center. M31's is 30 million solar masses while ours is closer to 3. So, where will the debate end?
IIRC, the SMBH at the center of the MW is 3 billion solar masses!

sol_g2v
2006-Jul-26, 08:07 AM
IIRC, the SMBH at the center of the MW is 3 billion solar masses!

3 Billion solar masses! I think you are off by about a factor of 1000. I've never seen an estimate higher than 4 million solar masses, it keeps going up, but I've never seen an estimate that high. M31 SMBH is around 30 million solar masses, the usual rule of thumb is central SMBH is 1.5% the mass of the galaxy as a whole. Since the latest research implies the MW is more massive than M31, probably MW has retained an extensive halo while M31 has not. The Milky Way's rotational velocity curve does not fall off w/increasing distance from the center like some galaxies like M81. I can't remember where I read this, but a paper I read used "violent relaxation" as the explanation for M31 having a substantially larger disk than MW even though our galaxy has greater mass. It seems M31 has a more violent history of galactic interaction. It even has a double nucleus!

ArgoNavis
2006-Jul-26, 10:09 AM
3 Billion solar masses! I think you are off by about a factor of 1000. I've never seen an estimate higher than 4 million solar masses, it keeps going up, but I've never seen an estimate that high.

A study of the motions of objects around Sgr A* has indicated 4 million solar masses within 100 AU and 400,000 solar masses within 1 AU of the centre of the MW

kzb
2006-Jul-26, 11:44 AM
<<...rule of thumb is central SMBH is 1.5% the mass of the galaxy as a whole...>>

I think it's strange that galaxy mass is held to be proportional to central black hole mass, but NOT to cold dark matter mass.

Look at antoniseb's reply in this thread #5 (19-July-06 07.08pm), wouldn't much the same arguments apply to a central black hole ? OK they can't pass through each other, but they can still steal matter when they sail past each other.

antoniseb
2006-Jul-26, 11:53 AM
the usual rule of thumb is central SMBH is 1.5% the mass of the galaxy as a whole.

This is not true. The general rule of thumb is that the SMBH has a mass of about a tenth of a percent of the mass of the central bulge of a galaxy. Your rule of thumb overstates the mass by a huge amount. Note for example that the mass of the Milky Way may be as much as 500 billion Suns, but the SMBH has a mass of 3 million Suns. That should be a tip-off that your rule of thumb is wrong.

kzb
2006-Jul-26, 11:54 AM
yuzuha wrote:
<<Interesting. Read somewhere that galaxy mass is proportional to the mass of the sm black hole in the center. M31's is 30 million solar masses while ours is closer to 3. So, where will the debate end?>>

I think you're right on that last comment. At this point we are saying

M31 SMBH is 10X mass of MW SMBH
M31 has 1/2 total mass of MW
Isophotal diameters: MW c. 90,000LY, M31 c.130,000LY.
Number of stars: MW 200-400 billion, M31 1000 billion.

Doesn't seem to hang together that well ?

antoniseb
2006-Jul-26, 11:56 AM
IIRC, the SMBH at the center of the MW is 3 billion solar masses!

You do not remember correctly. The most masive SMBHs we think we've measured seem to be about 10 billion, but they are the exceptions, in the giant ellipticals in the centers of giant clusters. Ours seems to be about 3 million as others have noted below.

dgruss23
2006-Jul-26, 12:24 PM
Hi dgruss23

<<You have to look at the distribution of stars - essentially the density of stars at different distances.>>

Well all I can say to this is, in the discussion on my 'number of stars in the galaxy' thread, I was surprised how much uncertainty there is in the total number of stars in the MW. As I kept saying there, estimates range from 100 to 500 billion. If the total number is THAT uncertain, then I'd guess the distribution is even more uncertain.

The uncertainty in the number of stars is greatly affected by the faint end of the stellar population. Even a modest G2 star like the Sun is in the top 10% of the stellar population - mass-wise. In other words ~90% of the stars in the MW are smaller than the Sun.

Dynamically, using the Virial theorem we just need the rotational velocity at a certain radius. Using MOND, the radius is irrelevant - only the rotational velocity is needed.

So the dynamical mass is much easier and far more relevant than a star count.


<<Just based upon rotational velocity, the mass of M-31 should be larger than the MW>>

There's some references from above:

<<"We are almost exactly twice as massive as Andromeda," Gilmore said.
- http://www.space.com/scienceastronom...rk_matter.html>>

and see also my post on 20 July 06 12:16

That imply the reverse, i.e. the MW is the more massive. However, perhaps they are not talking about quite the same thing? Those references include the total mass including halo, whereas you are talking about the stellar disc (D25 diameter)?

Yes, we are talking about two different things. Notice the article says this:


Andromeda is still believed to be bigger and have many more stars than the Milky Way—possibly because it swallowed up (http://www.space.com/scienceastronomy/060123_andromeda_plane.html) a bunch of smaller galaxies—but it has slightly less dark matter.

The research this article discusses estimated the mass of the MW from the radial velocities of satellite galaxies. The end result would be the Milky Way has the more massive DM component while M-31 has the more massive stellar component. Of course with MOND individual galaxies do not have dynamically significant DM so one wonders where that leaves this study based upon dwarfs. But that's another story.

Kaptain K
2006-Jul-26, 02:20 PM
3 Billion solar masses! I think you are off by about a factor of 1000. I've never seen an estimate higher than 4 million solar masses, it keeps going up, but I've never seen an estimate that high. M31 SMBH is around 30 million solar masses, the usual rule of thumb is central SMBH is 1.5% the mass of the galaxy as a whole. Since the latest research implies the MW is more massive than M31, probably MW has retained an extensive halo while M31 has not. The Milky Way's rotational velocity curve does not fall off w/increasing distance from the center like some galaxies like M81. I can't remember where I read this, but a paper I read used "violent relaxation" as the explanation for M31 having a substantially larger disk than MW even though our galaxy has greater mass. It seems M31 has a more violent history of galactic interaction. It even has a double nucleus!
Oops! That's what I get for posting while sleepy! :o

antoniseb
2006-Jul-26, 04:41 PM
Oops! That's what I get for posting while sleepy!
I write some of my stupidest posts when writing sleepy. Fortunately the crowd here understands when you have to correct yourself or acknowledge that you were wrong.

kzb
2006-Jul-28, 11:44 AM
<<M-31 is a faster rotator than the MW and therefore should be the more massive galaxy >>

Thus far, I've been unable to find any recent references about rotation speed of M31, that give actual figures, in units of velocity. Undoubtedly that's due to my inability to think up the correct keywords to search.

However, do you know of any recent measurements of this, and what's the uncertainty?

dgruss23
2006-Jul-28, 12:11 PM
<<M-31 is a faster rotator than the MW and therefore should be the more massive galaxy >>

Thus far, I've been unable to find any recent references about rotation speed of M31, that give actual figures, in units of velocity. Undoubtedly that's due to my inability to think up the correct keywords to search.

However, do you know of any recent measurements of this, and what's the uncertainty?

Tully&Pierce (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2000ApJ...533..744T&amp;db_key=AST&amp;d ata_type=HTML&amp;format=&amp;high=3e5c03c80a15034) presented data on hundreds of galaxies. The paper is long - but if you want to see it click the pdf link at the top if the page. I've also summarized below. M-31 (NGC 224) is the first entry in their Table 1.

These rotational velocities are determined from hydrogen linewidth profiles. In column 16 of table 1 (pg 747) the rotational velocity is given as the logarithm of twice the rotational velocity. That number is 2.712 which tranlates to a 2Vrot of 515 km s-1 or a Vrot of 257.5 km s-1. The uncertainty in Vrot is ~5 km s-1.

kzb
2006-Jul-31, 11:43 AM
Thanks dgruss23. If the rotational velocity of M31 is 257.5 km/s, and that of the Milky Way is 220 to 270 km/s, why is it said M31 is the faster rotator of the two?

OK, the mean of 220 and 270 is 245, slightly below 257.5 (+/- 5.0), but I wouldn't think that was significantly different, given the rotation velocity is not exactly flat across the galactic radius.

dgruss23
2006-Jul-31, 12:09 PM
Thanks dgruss23. If the rotational velocity of M31 is 257.5 km/s, and that of the Milky Way is 220 to 270 km/s, why is it said M31 is the faster rotator of the two?

OK, the mean of 220 and 270 is 245, slightly below 257.5 (+/- 5.0), but I wouldn't think that was significantly different, given the rotation velocity is not exactly flat across the galactic radius.

The standard rotational velocity at the Sun's distance from the center of the Milky Way is 220 km s-1 as recommended by the International Astronomical Union (IAU). That number could be wrong or perhaps we're not in the flat part of the rotation curve for our galaxy.

At any rate other research gives conflicting results. For example this study (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2004MNRAS.347..119B&amp;db_key=AST&amp;d ata_type=HTML&amp;format=) found 220 km s-1. However, this study (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2000AJ....119..813M&amp;db_key=AST&amp;d ata_type=HTML&amp;format=) found 270 km s-1.

The uncertainty here is much larger than the rotational velocities derived for external galaxies. The older value will be kept until the higher values are verified with enough evidence.

kzb
2006-Jul-31, 06:06 PM
<<At any rate other research gives conflicting results. For example this study found 220 km s-1. However, this study found 270 km s-1.>>

The point I was making was, how is it that the rotation velocity of M31 is deemed faster?

We are comparing a range of 220-270 for the MW against 257.5 +/-5 for M31. From that, I personally would not conclude "M31 rotation velocity is greater than that of the MW".

No, the conclusions I would state would be along the lines of, "there is no evidence the rotation velocities are significantly different". Or, "the magnitude of the uncertainty does not allow any conclusion as to which has the greatest rotation velocity".

Delving a little deeper, the 2004 study, quote, "Vc= 220 ± 40 km s1 in the radial range 35 ≤RGC≤ 100 kpc".

In other words, that is what they found for the rotation velocity at galactic radius 114,000 LY to 326,000LY. That is way out beyond the most extreme estimates of the radius of the stellar disc of either galaxy?

We have to compare like with like, the rotation curve for both galaxies have to be compared on the same footing.

dgruss23
2006-Jul-31, 07:03 PM
<<At any rate other research gives conflicting results. For example this study found 220 km s-1. However, this study found 270 km s-1.>>

The point I was making was, how is it that the rotation velocity of M31 is deemed faster?

It is deemed faster because the value of 220 km s-1 formally accepted by the IAU is almost 40 km s-1 smaller than the well established rotational velocity of M-31. All I was pointing out is that there are more recent estimates for the MW that might indicate a faster rotational velocity ... but to my knowledge there is no formal acceptance of those results as superior to the older value.


We are comparing a range of 220-270 for the MW against 257.5 +/-5 for M31. From that, I personally would not conclude "M31 rotation velocity is greater than that of the MW".

Keep in mind that the higher values are recent and not necessarily correct - probably still under investigation. It can take a while for new results to get noticed and then be tested. According to the best information available M-31 is the faster rotator.


No, the conclusions I would state would be along the lines of, "there is no evidence the rotation velocities are significantly different". Or, "the magnitude of the uncertainty does not allow any conclusion as to which has the greatest rotation velocity".

Whether or not the difference is significant depends upon the use of the rotational velocity. If you're comparing the global properties of spiral galaxies, then the difference is relatively small. In other words, the difference between M-31 and the MW is small compared to the difference between the MW and the Large Magellanic cloud. If you were using those rotational velocities to calculate distances via the TFR a difference of 40 km s-1 is very large.


Delving a little deeper, the 2004 study, quote, "Vc= 220 ± 40 km s1 in the radial range 35 ≤RGC≤ 100 kpc".

In other words, that is what they found for the rotation velocity at galactic radius 114,000 LY to 326,000LY. That is way out beyond the most extreme estimates of the radius of the stellar disc of either galaxy?

We have to compare like with like, the rotation curve for both galaxies have to be compared on the same footing.

But it is important to note that the value is consistent with that the IAU accepts for the Sun's radius - indicating the rotation curve has flattened by the Sun's distance. So to have the same value at much greater distances is not unusual.

kzb
2006-Aug-01, 12:14 PM
On one web site I found a plot of rotation velocity against radius for the MW. I haven't time to find it again just now, I'll find it later. Anyway, the plot is not a straight horizontal line, it rises quickly to a peak of about 260km/s then falls off to about 220 at the sun's radius, and tails off very gradually after that.

So we need something similar for M31

In the equations you gave:

M = V^2xR/G
and
V^4 = M x a0 x G

the mass is going to be very sensitive to V since it's squared in the first equation, and raised to the 4th power in the second. BTW, what's "G", the gravitational constant?

dgruss23
2006-Aug-03, 04:37 AM
On one web site I found a plot of rotation velocity against radius for the MW. I haven't time to find it again just now, I'll find it later. Anyway, the plot is not a straight horizontal line, it rises quickly to a peak of about 260km/s then falls off to about 220 at the sun's radius, and tails off very gradually after that.

So we need something similar for M31

In the equations you gave:

M = V^2xR/G
and
V^4 = M x a0 x G

the mass is going to be very sensitive to V since it's squared in the first equation, and raised to the 4th power in the second. BTW, what's "G", the gravitational constant?

Yes, G is the gravitational constant. Since the units are different in the two equations it actually converts to a different numerical value when you convert to astrophysical scales - but it is still the same G - not variable.

And mass is sensitive to errors in Vrot.

kzb
2006-Aug-03, 12:37 PM
I've managed to find a few more references now and the picture is becoming a little clearer in my mind. In this, on the second page, there are plots of the Andromeda rotation velocity versus radius:

www.its.caltech.edu/~suyu/Paper/PaperAndromeda03.pdf

The data date from 1989 and 1991. It certainly appears the M31 velocity is 250-odd km/s at 8kpc (the sun's galactic radius in our own galaxy), and I guess this is a fairly concrete measurement. The velocity appears to be maximal at 8-10kpc, but there's a step change at around 15kpc down to about 220.

When you come to our own galaxy, the maximum occurs well inside the sun's radius at 260 km/s. The velocity at the sun's radius is 220, and tailing off only slightly after that. In comparison, the MW velocity by 8kpc is 220, whereas in M31, the velocity is 220 by 15kpc.

However, the MW 220km/s is a straight average "reference value" derived in 1986, and the data used in that derivation would presumably pre-date it by some time in many cases (although I've not looked into that yet).

Some more recent studies have indicated 243 or 268 km/s as the true figure. All the studies on MW rotation velocity depend on assumptions and models: for example, the galactic radius of the sun is assumed, but there appears to be quite an uncertainty attached, values from 7 to 8.5 kpc. Changing the velocity at the sun's radius would change the whole galactic rotation profile proportionately, since all other velocities are measured relative to the sun.

So my conclusion is: it's very much up in the air. The current official view is that M31 rotates faster than the MW from 1 to 16kpc radius. BUT it's quite possible given some recent measurements, this is not actually true.

dgruss23
2006-Aug-03, 01:24 PM
I've managed to find a few more references now and the picture is becoming a little clearer in my mind. In this, on the second page, there are plots of the Andromeda rotation velocity versus radius:

www.its.caltech.edu/~suyu/Paper/PaperAndromeda03.pdf (http://www.its.caltech.edu/~suyu/Paper/PaperAndromeda03.pdf)

The data date from 1989 and 1991. It certainly appears the M31 velocity is 250-odd km/s at 8kpc (the sun's galactic radius in our own galaxy), and I guess this is a fairly concrete measurement. The velocity appears to be maximal at 8-10kpc, but there's a step change at around 15kpc down to about 220.

Good paper kzb. Please note that in fig. 1 of that paper the drop to 220 km s-1 occurs outside the optical radius. Those last few data points are made with neutral hydrogen (21cm emission).




So my conclusion is: it's very much up in the air. The current official view is that M31 rotates faster than the MW from 1 to 16kpc radius. BUT it's quite possible given some recent measurements, this is not actually true.

Now setting all that aside, I'm curious where you're going with this. I gather from your star count thread that you see this issue as important. If M-31 is faster or if the MW is faster (pick whichever), what is the issue you think that raises?

kzb
2006-Aug-03, 05:39 PM
<<what is the issue you think that raises?>>

Let's bear in mind none of this is any practical use whatsoever. Off hand, I can't think of a branch of science that has less potential benefit per dollar spent, than deep-space astronomy or astrophysics.

The reason people like me want to keep paying for it is purely because it feeds our imaginations.

Now, I grew up with M31 being 130,000LY across and the MW being 100,000. I had taken it as read that M31 is the bigger galaxy. But when I now start delving, it seems that's far from proven beyond reasonable doubt. This thread IS an offshoot of the number of stars in the galaxy thread, as I thought this was important in itself, and more people would see it. (However it seems to have got down to just me and you now !)

Hermes
2006-Aug-04, 12:55 AM
http://www.3towers.com/Andromeda.htm

Go here

kzb
2006-Aug-04, 12:32 PM
Good site, I never found it on any of my searches ! I like how it implies, at least our galaxy has a bar.

kzb
2006-Aug-07, 11:27 AM
There's one thing still worrying me re rotation velocity. The whole point of dark matter halos is to account for flat rotation curves. Now, since the references above are pointing to the Milky Way being MORE massive than the Andromeda spiral, how come the Andromeda galaxy rotates faster ?

Gigabyte
2009-Feb-09, 08:34 PM
Topic killer!