GREAT GALAXY: The Milky Way maintains a fleet of some two dozen satellite galaxies whose motions help reveal its mass.
Image: NASA/ESA/Hubble Heritage Team
-
The Best Science Writing Online 2012
Showcasing more than fifty of the most provocative, original, and significant online essays from 2011, The Best Science Writing Online 2012 will change the way...
Read More »
Although scientists know the masses of the sun and Earth, it's a different story for the galaxy. Mass estimates range widely: At the low end, some studies find that the galaxy is several hundred billion times as massive as the sun whereas the largest values exceed two trillion solar masses. Astronomers would have an easier task if the galaxy consisted solely of stars. But a huge halo of dark matter engulfs its starry disk and vastly outweighs it. Now remarkable observations of a small galaxy orbiting our own have led to a new number.
In studies of the Milky Way's mass one little galaxy plays an outsize role: Leo I. "The value of Leo I is twofold," says Michael Boylan-Kolchin of the University of California, Irvine. "It's both very distant and moving quite quickly." Discovered in 1950 and located 850,000 light-years from the Milky Way's center, Leo I is a dwarf spheroidal galaxy and the farthest of the many galaxies that are thought to orbit our own. Most of the Milky Way's dark matter halo should fit inside Leo I's orbit—that is, if the dwarf galaxy is actually in orbit and not just passing by.
Astronomers know from Leo I's Doppler shift that it is racing away from us. If the Milky Way has enough mass, its gravity will hold it in orbit. Moreover, astronomers would be able to observe the motion of Leo I and use it to deduce the Milky Way's total mass—including its dark matter halo—out to the dwarf galaxy's great distance. But if the Milky Way does not have enough mass, Leo I will fly away, its high speed revealing little of consequence.
To deduce Leo I's path through space, astronomers have to determine the small galaxy's precise motion. The Doppler shift reveals Leo I's velocity along our line of sight, but no one knew how fast the little galaxy was moving across it. Determining that requires measuring its proper motion—the change in the galaxy's position from one year to the next. Proper motion is easy to gauge for a nearby star but difficult to measure for another galaxy, because far-off objects have tiny proper motions.
Sangmo Tony Sohn of the Space Telescope Science Institute and his colleagues therefore used the Hubble Space Telescope to compare Leo I's position in 2006 and 2011 with more than a hundred background galaxies. In work submitted to The Astrophysical Journal, Sohn's team reports success: the first proper motion measurement of Leo I.
"It's a powerful piece of work," says Timothy Beers, the director of Kitt Peak National Observatory, who was not affiliated with the research. "It strikes me as utterly amazing that we have instruments that can measure proper motions that far away." Scott Tremaine, an astronomer at the Institute for Advanced Study, agrees: "The measurement of the proper motion really is a tour de force."
Combined with the Doppler shift, the proper motion reveals that Leo I orbits the Milky Way at 200 kilometers per second. By comparison, that's nearly as fast as the sun orbits the Milky Way's center, even though the dwarf galaxy is much farther away. Says Boylan-Kolchin, "To sustain a similar velocity at that far a distance requires a lot of extra mass."
How much mass? In a companion study Boylan-Kolchin and his colleagues simulate how giant galaxies such as the Milky Way grow by swallowing lesser galaxies, finding that dwarf galaxies moving as fast as Leo I are almost always bound to the giants, which means Leo I is a true satellite. His team then derives a mass for the Milky Way of 1.6 trillion suns. "That's on the high side," Beers comments. "But it's not outrageous."
Rights & Permissions
See what we're tweeting about
39 Comments
Add CommentExcellent article discussing in quite analytical manner issue estimating the mass of MW galaxy. However, article does not specifies the elements of MW apart from stars which constitute the mass of MW. Apart from stars, there are also Black Holes, MACHOs etc in MY galaxy. There is no census of BHs ( both micro and supermassive) in MW galaxy.
Reply | Report Abuse | Link to thisFurther article states that orbit of Leo I cuts across dark matter halo enveloping and that Leo I is about 8,50,000 light years away from us i.e. from Sun. There are no correct estimates for the size of dark matter halo enveloping MW. May be dark matter halo of MW might be extending much further than 8,50,000 light years away from Leo I and this dwarf galaxy might also be having its own dark matter halo. Apart from MW galaxy, Leo I could also be under gravitational influence of other dwarf galaxies in its neighborhood. Due to close proximity of Leo I with other dwarf galaxies in local group, its motion may be influenced more by these local galaxies rather than MW galaxy. Further, all those dwarf galaxies in local group may also have their dark matter halo
In view of above, estimation of mass of MW galaxy solely from the motion of Leo I appears to follow a quite simplistic model
Its going to be the same size as our national debt
Reply | Report Abuse | Link to thisInteresting paper on a better approximation to our galaxy's info.
Reply | Report Abuse | Link to thisOf course it still depends on IF Leo I actually orbits the MW or not. Authors have considered this, so it seems all is in its right perspective - a slightly better guess at how big the MW is.
Nice, interesting one, SA.
My enthusiasm about this topic outweighs my ignorance, so please excuse my ignorance. Would someone be able to answer this question:
Reply | Report Abuse | Link to thisWhy can't it be that there's something with more mass pulling the dwarf galaxy away from us, black hole maybe? Undetected galaxy?
Recall our method of determining distance is derived from
Reply | Report Abuse | Link to thisvariables such as brightness of distant objects. So any
estimates are just that. Though learning about space is important, if we don't pay more attention to conditions here on Earth, the possibility exists we may never find out.
i do not know what area leo 1 is in , but , is andromeada only 150,000 ly away from it , as it is 1,000,000 ly from us , and it has aproximate mass/size maybe it is influential ?
Reply | Report Abuse | Link to this0.06 Mly = radius of Milky Way
Reply | Report Abuse | Link to this0.35 Mly = radius of MW dark matter halo
0.85 Mly = distance from MW to Leo I
2.54 Mly = distance from MW to Andromeda
3.20 Mly = distance from Andromeda to Leo I
Thanks for putting it into perspective.
Reply | Report Abuse | Link to thisInteresting indeed! While the proper motions of Leo I and M31 have been precisely determined of the past several years, Leo I's full orbit has been implied by very complex evaluations of models (including large numbers of assumed conditions) representing potential orbits extrapolated from the very small sample of measured proper motions.
Reply | Report Abuse | Link to thisSeveral commentators have raised interesting points about relative locations. Cramer supplies some relative distances to relevant objects from some source. A very interesting chart is included in
http://en.wikipedia.org/wiki/Local_group#Component_galaxies
That chart is based on current positions of objects relative to the Milky Way, not considering any past or future relative locations. It is difficult to see, but the reference planar chart axis includes both the MW and Andromeda (M31); other objects are not found on that plane (the position of each is indicated by a small white dot).
Th collective center of mass for the Local Group currently lies somewhere in between the MW and Andromeda. It must be considered that Leo I may not be orbiting the MW but, like most Local Group members, may be moving generally about its center of mass, severely perturbed by its larger members. At these distances, Local Group members cannot be confined to orderly Keplerian orbits. Reading the referenced research report, I did not find any determinant evaluation of this possibility, despite Acoyauh2's confidence that they have done so.
While Cramer points out the current relative distance from the MW to Leo I and to Andromeda, the research identifies potential orbital paths of Leo I around the MW. If I interpret Figures 10-12 in the research report correctly, the projected orbits of Leo I should take it to locations nearer the Andromeda galaxy than the MW! Based on the article's quote of an estimate of the Andromeda galaxy's mass as being twice the MW's it's difficult to understand how a stable orbit around the MW could possibly be maintained by Leo I!
The very difficult analysis seems highly unorthodox to me, as I understand it. First, the orbit of Leo I is derived based on a low mass model of the MW. Then the MW mass was evaluated for mid and maximum mass values. It was eventually determined by the researchers "that the observed kinematics of Leo I are more consistent
with high-mass than with low-mass MW models." That is to say, they find that the larger of three parametric evaluations of MW mass seems to best fit the orbit they derived for Leo I.
(continued)
Reply | Report Abuse | Link to thisA most interesting example of extraordinary assumptions made in their analyses is that, as the presumed mass of the MW was incremented, the mass of M31 was commensurately decremented!
Of course, the principal assumption made is that the MW (and presumedly all other galaxies) are enveloped by a dark matter halo that (in the case of the low mass MW scenario) contains more than 90% of total galactic mass.
Interestingly, the researchers also evaluated a Keplerian model, correctly explaining:
"The assumption of a Keplerian potential for the MW is not as unreasonable as it may seem at first. The large Galactocentric distance of Leo I, ... 260.6 kpc, combined with its significant tangential velocity, implies that much of the MW's mass is inside the Leo I orbit at all times." It must be added, however, that another prerequisite condition for Keplerian compliance is that the orbital's motion not be perturbed by external masses.
The Keplerian model of the galaxy and found it to be inadequate, as "a Keplerian model is too concentrated, and therefore overestimates the acceleration as Leo I approaches the MW." Of course, these researcher's evaluations presumed an enormously massive dark matter halo, which would produce overestimates of acceleration if the dark matter halo did not actually exist...
Other researchers have noted that, when evaluated without presuming any dark matter halo, hundreds of nearer halo objects comply with Keplerian rotation curves, for the reasons given above. However, if a dark matter halo does exist for the MW, there is no explanation for why those nearer halo objects would comply with Keplerian rotation curves while galactic disk objects do not. For references, please see: "Inappropriate Application of Kepler's Empirical Laws of Planetary Motion to Spiral Galaxies Created the Perceived Galaxy Rotation Problem - Thereby Establishing a Galactic Presence for the Elusive, Inferred Dark Matter",
http://fqxi.org/data/essay-contest-files/Dwyer_FQXi_2012__Questionin_1.pdf
- especially the "Supplemental Information" section.
While these researchers precise determination of the proper motions of Leo I and M31 are very important, I find nothing has been definitively determined about the orbital motions of galaxies in the Local Group, whether Leo I is in stable orbit around the Milky Way or the actual mass of the Milky Way.
Maybe, but not growing as rapidly!
Reply | Report Abuse | Link to thisI recalculated the distances based on the coordinates given in Table 3 on page 10 of the Sohn et al paper:
Reply | Report Abuse | Link to thisrLeoI = (-125.0, -120.8, +194.1) kpc
rM31 = (-378.9, +612.7, -283.1) kpc
1 kpc = 3262 ly
gives
0.85 Mly = distance from MW to Leo I
2.52 Mly = distance from MW to Andromeda
2.97 Mly = distance from Andromeda to Leo I
Sohn et al gives a virial radius of 299 kpc (0.98 Mly) for the dark matter halo assuming a virial mass of 1.5x10^12 solar masses.
jtdwyer,
I am not sure how you are interpreting Figures 10-12 to show that Leo I will move closer to M31 than MW. The three figures show the orbital history of Leo I for three different MW masses. They show nothing of the future orbit. Leo I is still in its first orbit around MW. Leo I has been closer to MW for the past 6 billion years (according to the figures). Even if you extrapolate the future path of Leo I (which would not make sense -- it needs to be modeled), Leo I would be closer to MW for the next 4 billion years. M31 and MW are expected to collide in 4.5 billion years.
I also do not see MW and M31 being in the same "planar chart axis" in the wikipedia image you provided. That plane is the same plane of the MW disk. M31 is below that plane by 283.1 kpc. Leo is above the plane by 194.1 kpc. rM31 = (-378.9, +612.7, -283.1) kpc. Maybe I misunderstood what you meant.
Looking again at Figures 10-12, it looks as if a discussion on influence of M31 on Leo I is pointless (or any other galaxy in the Local Group for that matter). MW and M31 will have collided long before Leo I completes its first orbit. And will it even orbit the combined MW/M31 galaxy??? Can't tell what other group it is heading toward in the Virgo Supercluster. Any ideas?
Reply | Report Abuse | Link to thisTo start, I'd stated:
Reply | Report Abuse | Link to this"If I interpret Figures 10-12 in the research report correctly, the projected orbits of Leo I should take it to locations nearer the Andromeda galaxy than the MW!"
You are correct that these figures present not the projections of the future orbits of the MW, M31 and Leo I, but projections of their PAST orbits. On that one point I stand corrected.
My corrected statement should read:
"... the projected orbits of Leo I should have taken it to locations nearer the Andromeda galaxy than the MW!"
To support my conclusion, please carefully read the caption to Figure 10. It begins:
"The mean orbital history of Leo I for the low mass MW model..."
It goes on:
"... Panel (a) shows the separation between Leo I and the LMC, MW and M31 as a function of time."
Panel (a) of course occupies the top left quadrant of Fig. 10. As you indicated, this chart clearly shows that about 6 billion years ago, the distance between Leo I and both the MW and M31 was the same, at just about 750 kpc. This is where the blue and green lines cross. The chart also shows that prior to about 6 billion years ago, Leo I was closer to M31 than it was to the MW.
The research concludes that Leo I's velocity is solely due to its gravitational interaction with the MW, allowing estimation of the MW's mass from Leo I's proper motion. As I stated previously, the evidence presented in this study seems to best describe a condition in which Leo I is moving about the center of the Local Group, with motions significantly perturbed by the cluster's largest members. IMO, unless Leo I has not gravitationally interacted with any other members of the Local Group in the past (even though it is approaching the MW from the direction of M31), the mass of the entire Local Group should have contributed to Leo I's velocity on approach to the MW.
Of course, you're correct that the very complex future gravitational interactions among all the galaxies within the Local Group (and its even more massive intracluster medium) render most intracluster motions unpredictable, even if the MW was not on a collision course with M31!
Regarding the Wikipedia chart, to my eyes M31 is located on the illustrated chart axis plane. I could not find any statement indicating that the chart grid is aligned with the MW galactic plane - where did you find that? The original source of the chart is
http://www.atlasoftheuniverse.com/localgr.html
Thanks for your corrections!
Keplerian rotation curve is based on our assumption of solar planets rotation curve theory of Newton. But Durgadas Datta published theories of rotation beyond solar system which he proposed to visualize as swirl and whirl of gravitoetherton soup which we refer as halo of dark matter. Therefore a non uniform field density fluid on mono magnetic coupling effect is very much new concept and its varying field density is changing astronomy like weather forecast .
Reply | Report Abuse | Link to thisThe paper uses two assumptions: the dark-matter hallow and the gravitational effect of Milky Way on Leo I, both of which can be misleading. Firstly, there is no clear cut view regarding what constitutes dark matter. The galaxy-rotation problem may actually be a questionable concept – especially with the discovery of the “axis of evil” which shows that the cosmic microwave background (CMB), the so-called afterglow of the big bang, is not perfectly smooth and hot and cold spots speckle the sky. These spots are not quite as randomly distributed as they first appeared - they align in a pattern that point out a special direction in space.
Reply | Report Abuse | Link to thisThe so-called “huge hallow of dark matter” could be something else like the “magnetic highway” that is expected to lead Voyager-1 out of the heliosphere.
The gravitational effect of Milky Way on Leo I may be as misleading as the others. The planets in the solar system are also gravitationally affecting each other and sometimes appear to move away and at other times coming closer to each other while orbiting the Sun. We have repeatedly asserted that this explains both dark matter and dark energy: the rotation problem and the expanding universe problem.
contd....from 16
Reply | Report Abuse | Link to thisThe galaxies are orbiting the galactic center and appear to move away from each other at the present juncture. We must not forget that this 83 year old observation is insignificant in cosmic time scales and there is a possibility that both in the past and in future, an apparently reverse motion may be observed. Further, the expansion is restricted to large galactic clusters only and not at all perceptible in local scales. This puts a question mark on the assumption that the universe is expanding – especially when we do not know the contours of the universe. Thus, there is no need to sensationalize it. Scientists should be down to Earth and objective.
Keplerian rotation curves, where rotational velocity diminishes as a function of radial distance from a common rotational axis, occur in any gravitational system dominated by an effective point mass representing most of the system's mass, and where planetary bodies each, in effect, independently orbit the dominant mass. The effect diminishes as a function of the system's mass distribution.
Reply | Report Abuse | Link to thisThere is no specific rotation curve theory. Newton had nothing to do with the development of Kepler's equations, since he hadn't been born yet, but he did later prove that Kepler's laws of planetary motion provided useful approximations only because the Solar system's planets represent less than 0.2% of total system mass and therefore do not usually significantly perturb each other's orbits. He also used his own gravitation and dynamical theories to improve on the predictions of Kepler's equations for planetary systems.
The more I look at the papers, the more confused I become.
Reply | Report Abuse | Link to thisIn one paper they calculate the mass as 1.6 trillion suns and the other paper as 3.15 trillion suns (within a large confidence interval).
They then say (pg 17):
"It is clear that Leo I does not get closer than 400 kpc from M31 in any model over the past 8 Gyr and neither the presence of M31 nor the LMC have an impact on the infall time or pericenter properties. However, M31 may play a role at early times in the higher MW mass models; the orbits are more energetic, reaching larger distances than if the gravity of the MW were considered alone."
To me it looks to be the opposite (both by the plots and intuitively): M31 should play a role at early times in the lower MW mass models.
I believe Figures 10-12 can make it difficult to visualize the paths because I don't believe they are including the entire path of M31 for the 8 billion years. M31 is approaching MW at 140 km/sec. Leo I is moving away from MW at 200 km/sec. I don't know how these velocities have change over the past 8 billion years, but the plots only seem to be showing the last 1 to 2 billion years of M31's path (M31 will meet MW in 4.5 billion yrs).
In the low mass model it appears to me that M31 and Leo I were approaching MW in paths that were parallel with each other (i.e. approaching from the same direction). In the high mass model they seem to be approaching MW perpendicular with each other (i.e. approaching MW from different directions).
jtdwyer,
Reply | Report Abuse | Link to thisI think it is just convention to have the Milky Way galactic plane to be the x-y coordinate plane of the Local Group.
I think confusion directly results from the researcher's methods of analyses. Again, the Fig. 10 caption states:
Reply | Report Abuse | Link to this"The mass of M31 is chosen to preserve the total Local Group mass of 3 × 10^12M [Solar masses]."
This means is that, in the higher mass models, M31's mass is diminished by the amount the MW's mass is increased! This is an absurd presumption to avoid conflicts that would result from the otherwise necessary increase in total Local Group mass. However, since this analysis involves evaluation of M31 gravitational impact on Leo I, the reduction in M31 mass in the 'higher mass models' most certainly affects any acceleration that would have been imparted to Leo I by M31. IMO, this arbitrary reduction of M31 mass invalidates the entire analysis!
As you say, it seems M31, the Local Group's massive intracluster medium (located between the MW and M31 but not even mentioned in the research report) and all other Local Group mass should have imparted acceleration to Leo I prior to its 'infall' into the MW's virial radius. To presume that Leo I's present velocity is entirely the product of the MW's mass and gravitation is completely unreasonable, given the derived path of Leo I near M31 (normally thought to be twice as massive as the MW) and through some of the densest part of the intracluster medium.
Erroneously presuming that the Leo I's current velocity is solely the product of the MW's gravitational effects produces the false requirement to increase MW mass.
Sorry, but my eyes still insist that the Wikipedia Local Group chart shows M31 to be very close to the second radial axis of the planar chart 'grid', regardless of any convention...
Reply | Report Abuse | Link to thisjtdwyer,
Reply | Report Abuse | Link to thisThanks for pointing that out about the mass of M31. I missed that -- I assumed M31's mass was kept constant. I don't know why they would have to keep Local Group's mass constant. If we are not confident of the mass of the Milky Way, why should we be more confident of the mass of the Local Group?
Regarding the Wiki image: I take it that you understand that the solid vertical lines are above the plane and the dotted vertical lines are below the plane. There is a dotted line above Andromeda. Maybe you assumed that dotted line was for M32 or M110. However, M32 and M110 are satellites of M31. The dotted line is for all those galaxies.
However, there does seem to be something screwed up that I have not reconciled. When I look at the wiki image I see 0 degrees in the foreground and 180 degrees in the background (i.e. looking at the top of the plane). But when I compare it to other images, it should be reversed (i.e. looking at the bottom of the plane) -- depending on which image is correct.
See this image:
http://www.rpi.edu/dept/phys/Courses/Astronomy/LGlayout.gif
Yep, the study's gravitational analysis seems to be fatally flawed in several areas.
Reply | Report Abuse | Link to thisBack to the Wiki image, yes, I'd decoded the vertical reference lines in the chart. However, I'd presumed that the white galaxy symbol indicated the actual position of M31, and hadn't noticed the vertical reference above it. Thanks to the reference chart you provided I now understand that you're correct about M31 not being located on the chart plane.
However, that second chart brings up another issue: it seems to show Leo I's location between the MW & M31, whereas the Wiki chart seems to show Leo I's location to be on the side of the MW opposite to M31. Are my tired old eyes deceiving me again, or is there some explanation for this?
Also, in the chart you provided showed a nice 500 kpc sphere, I think representing the ~250 kpc radial radius referenced by the dotted horizontal line in Fig. 10 panel (a). Then it finally occurred to me - these analyses presume that the mass of MW (and for that matter M31) has been constant for the past 8 billion years - another false critical assumption! I don't think that the past mass of any galaxy at any point in time can be definitively determined, as now large galaxies are thought to be the products of many previous mergers - in fact the Local Group may not have existed as a discretely bound object 8 billion years ago! Again, there seems to be fatal flaws with these analyses!
Thanks again for the corrections!
Both images show M31 in the 2nd quadrant and Leo I in the 3rd quadrant. Their positions do somewhat correspond to the following coordinates (as given in the paper):
Reply | Report Abuse | Link to thisrLeoI = (-125.0, -120.8, +194.1) kpc
rM31 = (-378.9, +612.7, -283.1) kpc
However, in the rpi.edu map Leo I looks too far away and the coordinates in the map look more closer to
r = (-300, -300, +300) kpc.
I neither have enough expertise in astrophysics nor gave the paper the required due diligence to be able to call it flawed. I know nothing of the models they used. I can only be certain that some of their results confused me.
That's fine - I'm no physicist but I am a highly accomplished expert information systems analyst (retired). The principal errors I think I've identified are:
Reply | Report Abuse | Link to this- Presuming that galaxy masses are constant throughout time. This is critical in evaluating the earlier path of Leo I and identifying prior gravitational influences imparting acceleration to Leo I prior to its arrival within the MW's virial radius. This seems to be indicated by the constant distance of the MW's virial radius throughout time. The past mass and even configurations of galaxies within the Local Group cannot be reasonably approximated.
- Concluding that the current velocity of Leo I is solely the product of MW gravitation; that it gained no momentum through its traversal of the Local Group - thus allowing the evaluation of MW mass derived solely from Leo I's current velocity.
- Arbitrarily reducing M31 mass as mass is added to the MW.
As I said earlier, the determination of the proper motion of Leo I and M31 over the past few years is an excellent achievement, but IMO the analyses of MW mass based on extrapolations of these data relies far too much on far too many questionable assumptions.
When I said do not have enough astrophysics expertise, I did not mean to imply I did not have expertise in physics. I am a chemical engineer with a MS in statistics and a MS in mathematics. Chemical engineers are not chemists, they are physicists that primarily study "transport phenomena." That's heat transfer, mass transfer (diffusion), and fluid dynamics. Their models of stellar dynamics that account for tidal disruption, violent relaxation, dynamical friction, phase-space mixing, etc are more-or-less chemical engineering models (relativity is less significant in these models from what I see). Fitting their models to proper motion requires statistics.
Reply | Report Abuse | Link to thisThe Milky Way and Andromeda have not grown much in mass in the last 8 billion years. The fact that you did not know that implies you are making a lot of assumptions of what these astrophysicists know/don't know or considered. If that make you feel more intelligent, I feel very bad for you.
Thanks Ken, You put forward an interesting thesis which may very well pave the way for a greater understanding of our galaxy. I have difficulty in accepting mass calculations based on estimates of distance using red shift theory which does not account for gravitational or hidden mass and also uses the result within the calculation. After fifty years we are getting closer to a unified theory ever so slowly.
Reply | Report Abuse | Link to thisI'm going by the evidence presented in the research report - that the virial mass of the MW did not vary during the past 8 billion years, regardless of how you feel.
Reply | Report Abuse | Link to thisWhile its thought that the MW is unusual in that it appears to have avoided merger with any large galaxies for perhaps 10 billion years, it has continuously and is currently absorbing many gas clouds, globular clusters and dwarf galaxies. Presuming the mass of the MW has not significantly varied over the past 8 billion years seems to be a naive assumption.
More critically, M31 is thought to have more recently significantly increased its mass through mergers with other large galaxies. However, since the history of these mergers is not practically determinable, nor the mass or positions of the now merged galaxies prior to merger, reasonably determining the gravitational influence of M31 and its progenitors of the motions of Leo I over the past 8 billion years is not possible.
In any case, I suggest that Leo's current high velocity most likely includes momentum gained during it traversal of the Local Group prior to its arrival at the MW. The researchers concluded that Leo I's current velocity is solely the product of the MW's gravitational influence, justifying their deriving MW mass directly from it.
If any of Leo I's current velocity is not the direct result the MW's gravitational acceleration, their finding that the MW's mass may be greater than expected would be erroneous. This most critical assessment is not dependent on any special knowledge of astrophysics, chemistry or even mathematics. Unfortunately, I will not be able to submit any critical assessments for publication in astrophysics journals.
P.S. I hope you get to feeling better, but please don't concern yourself with me or how I'm feeling about myself, or anything. I do appreciate your positive contribution to this discussion, although I think you were overly fixated on my irrelevant interpretation of the galactic chart. IMO, this is how technicians, and scientists, often miss the obvious forests for all the trees. There is so much minutia to be concerned with...
"reasonably determining the gravitational influence of M31 and its progenitors of the motions of Leo I over the past 8 billion years is not possible" ...
Reply | Report Abuse | Link to this"This most critical assessment is not dependent on any special knowledge of astrophysics, chemistry or even mathematics."
So I guess you were going with your gut feelings. It should be noted that you did not earlier state that Leo I path was impossible to determine. You said they were wrong and M31 had more influence than they concluded (therefore making MW less massive than 1.6 trillion suns).
Yes, I stand corrected. It is more probable that your view of your refutation of Sohn et al findings as being substantive is delusional rather than resulting from being insecure about your intellect. [especially after reading your comment about not being able to publish your critical assessments -- why not provide them here?]
P.S. regarding your minutia comment -- your entire assessment centered on Figures 10-12 of their paper. You mentioned nothing about their models.
Reply | Report Abuse | Link to thisYou made the statements about the wiki chart that you referenced; and I pointed out your errors. If it was irrelevant, why did you introduce it to the discussion?
BTW, this is and has been since 1845 a science news magazine for the lay public. I am happy to help others understand and also learn something myself. I have introduced no criticisms of this paper. My comments were only in response to other commenters (mostly yours).
"So I guess you were going with your gut feelings. It should be noted that you did not earlier state that Leo I path was impossible to determine. You said they were wrong and M31 had more influence than they concluded (therefore making MW less massive than 1.6 trillion suns)."
Reply | Report Abuse | Link to thisBut that's not what I said, is it? It would be more appropriate to quote my statements rather than misrepresent them.
Again, the researchers concluded from their path modelling that Leo I's velocity was completely attributable to the MW's gravitational influence. I do think that's untenable, based on the many undetermined assumptions employed in their models, which mean's their rational for deriving MW mass from Leo I's velocity is unfounded.
BTW, I refer primarily to Figures 10-12 because they are used to represent the results of their models. To the extent that they effectively do so, they are a simple and convenient reference to their model's results. That is why they are included in the research report...
Cramer Article at one stage states "Most of the Milky Way's dark matter halo should fit inside Leo I's orbit—that is, if the dwarf galaxy is actually in orbit and not just passing by."
Reply | Report Abuse | Link to thisAbove implies that radius of dark matter halo should be higher than radius of Leo I than only dark matter halo can fit within orbit of Leo I. But the distance estimates of dark matter halo ( .35Mly) and distance of Leo I ( .85Mly) as submitted by you in blog#7 do not match with above assertion. It seems either distance estimates as given by you are wrong or above statement in the article is wrong
Chart of Local Group of galaxies as given at wikilink and atlasofuniverse indicates that compared to MW galaxy, Leo I is more closer to other dwarf galaxies like Leo II and Canes Dwarf. In view of this, these dwarf galaxies and other dwarf galaxies in the proximity of Leo I should also be influencing the motion of Leo I. As such, is it not a simplistic model to assume that motion of Leo I is solely due to gravitational influence of MW galaxy.
Reply | Report Abuse | Link to thisFurther, estimation of mass of Sun from the motion of earth orbiting around it is based upon certain facts viz concentration of mass of Solar system in Sun ( 99.86%), very low orbital distance between earth and Sun compared to cosmological scales and absence of any large mass in the vicinity of earth. These facts may not be applicable at galactic scales. Since a galaxy does not follows a concentrated mass model system like our solar system.
In a large b-s galaxy like MW, how center of mass may be concentrated at its geometric center when there are billion of stars ( estimated 200-400 billions) scattered through out the galaxy and additionally there may be countless known and unknown black holes, quasars, planets etc scattered through out the galaxy. It is yet not known to astronomers with accuracy and certainty about location of center of mass of MW galaxy
Our Sun is estimated at a distance of about 27000 LYs from center of MW galaxy where astronomers propose a SMBH having a mass of 4 million Suns. Within this distance of 27000 LYs and on the opposite side, there may be million or even billion of stars and BHs which may be casting their influence on the motion of Sun. In view of this, it can not be stated with certainty even in case of Sun that its motion around galactic center follows centric Keplerian model. In comparison, Leo I galaxy is estimated at a distance of 850000 light years from center of MW and may be in close proximity of other dwarf galaxies having equivalent masses, therefore, how Leo I can orbit around MW in stable orbit as per Keplerian model?
Article at one stage also states that Doppler shift of Leo I indicates that it is moving away from MW. This may either be due to orbital motion of Leo I around MW. But this could also be due to gravitational influence of some other dwarf galaxy in its proximity or some other massive cosmological unknown body in its vicinity?
it appears that there is no compelling evidence to constrain the findings i) Leo I is orbiting around MW galaxy ii) Motion of Leo I is solely due to mass of MW
Vinod,
Reply | Report Abuse | Link to thisIn my comment at 05:00 PM 12/7/12 (comment #12), I provided the correct distances as provided in the Sohn et paper:
"Sohn et al gives a virial radius of 299 kpc (0.98 Mly) for the dark matter halo assuming a virial mass of 1.5x10^12 solar masses."
Sohn et al also truncates the density profile of the Milky Way at the virial radius in their models (see pg 9).
I would assume the virial radius as provided by Sohn et al is a better estimate than what I first gave (0.35 Mly). Footnote No. 8 references Sohn's estimate as coming from van der Marel (2012), Appendix A., equation A1:
http://arxiv.org/pdf/1205.6864v1.pdf
I believe I got my first estimate of the dark matter halo from wikipedia, but I can not find the exact source. I thought mine came from a midpoint of a range of 0.3 to 0.4 Mly. When reading
http://en.wikipedia.org/wiki/Milky_Way
it says the halo extends to as far as LMC and SMC. They also say DM halo is uniform to beyond 100 kpc. These numbers are closer to 0.35 Mly than to 0.98 Mly.
Vinod,
Reply | Report Abuse | Link to thisGRAVITATIONAL INFLUENCES:
Regarding gravitational influences, reading the Sohn et al paper covers a lot of your questions:
http://arxiv.org/pdf/1210.6039v1.pdf
Read Section 3 that begins on page 6.
The Local Group mass is estimated to be 3.17 x 10^12 solar masses.
The mass of M31 and MW is estmated to be 3.0 x 10^12 solar masses (i.e. 95% of the Local Group).
You mentioned Leo II and Canes Dwarf. If you simply look at the numbers you can see that they are not much influence.
The data is given in Table 3 of the Sohn paper.
Leo I = -125.0, -120.8, 194.1 kpc
Leo II = -77.3, -58.3, 215.3 kpc
d = 81.4 kpc = 0.27 Mly
You can use a simple calculator found here:
http://www.calculatorsoup.com/calculators/geometry-solids/distance-two-points.php
Leo I is 0.27 Mly from Leo II.
Leo I is 0.85 Mly from Milky Way.
Canis is 0.03 Mly from Milky Way.
MW = 1.6 x 10^12 solar masses
Leo II = 6.4 x 10^7 solar masses
Canis = 1 x 10^9 solar masses
The Milky Way is 25,000 times more massive than Leo II.
By comparison the Jupiter is 330 times more massive than the Earth.
The Sun is 1,000 times more massive than Jupiter.
LEO I STABLE ORBIT?
There was no claim by Ken Crowell or Sohn et al that Leo was in a stable orbit around the MW. Read last sentence of 2nd paragraph of this article. In the Sohn paper they give the escape velocities at the distance r = 260.6 kpc of Leo I are 182, 222, and 256 km/s for the models with masses of 1.0 × 10^12, 1.5 × 10^12, and 2.0 × 10^12 solar masses, respectively.
Velocity of Leo I is v = 196.0 +/- 19.4 km/s.
Up to 1 billion years ago Leo was heading toward the Milky Way. Not straight at us like M31, but in our direction. See Figures 10-12. I think of it as performing a slingshot maneuver the same way Voyager (I) made around Jupiter. The purpose of the study, as you should recall, was to determine the mass of the Milky Way -- which they estimated to be 1.6 trillon solar masses -- not the orbit of Leo. They are simply providing the best estimate of the mass that best determines the proper motion of Leo I over a five year period.
jtdwyer,
Reply | Report Abuse | Link to thisYou are unable to find your own quotes? Here's what you said at 07:48 AM 12/10/12 (comment #29):
"However, since the history of these mergers is not practically determinable, nor the mass or positions of the now merged galaxies prior to merger, reasonably determining the gravitational influence of M31 and its progenitors of the motions of Leo I over the past 8 billion years is not possible."
If you say determining the influence of M31 is not possible, you can NOT say that Sohn is wrong when they claim that the contribution of M31 to the influence on Leo I is irrelevant.
CONSTANT MASS OF LOCAL GROUP:
Reply | Report Abuse | Link to thisIf anyone is interested why Sohn et al assumed the mass of the Local Group is constant, look up the "local group timing argument." The first paper on this was Kahn & Woltjer (1959).
"LEO I STABLE ORBIT?"
Reply | Report Abuse | Link to thisThis estimate of MW mass presumes that the velocity of Leo I is entirely the product of the MW's gravitational acceleration. I contend that other factors almost certainly contribute Leo I's velocity, rendering this MW mass estimation invalid.