Mr Dwyer, interesting work, well researched. I agree that dark matter is the symptom that we do not understand gravity. I believe this stems from our lack of understanding of space. And to think that not that long ago some were proposing that we had neared the end of physics! It appears we have hardly begun.
I especially value your selection of references and will follow up later on.
M. Vasilyeva, thanks very much for your consideration and very kind remarks.
I wholeheartedly agree that understanding the physical nature of spacetime is crucial to more completely understanding gravitation.
Best wishes in your future studies, Jim
Chris/James
The 'lock step' rotation isn't strictly flat, it's gently graded and has 'steps' at certain 'virial' radii, with dense shocks at the change in velocity (equivalent to the Unruh effect and the incresaed 'intensity' giving photoionization). So if the rotating body represents a coherent inertial frame in accordance with both Galilean relativity and SR, as we know it does with the ECI frame within the Barycentric frame, all falls into place.
It's a chicken and egg job, increased velocity at the boundary propagates an increased ion density (that's why a meteor becomes a comet above a certain relative speed through the vacuum - also the pe cloud propagates round the proton bunch in the LHC pipe). Look also at the high star production at the halo virial radii, at the ends of the bars in a barred spiral, and lower peak along the 'front' of the bar. None of which have yet been explained any other way as it's assumed space is empty so can have no assignable 'state of motion'.
James - I also re-post my reply under anon in my blog, below.
James,
You're right. If we considered 'visible' as only the optical em range the right hand image is also not strictly 'visible', same as as the left one. However, in astronomy we're almost never dealing with the optical range (which is a tiny part of observation), so 'visible' is shorthand for visible 'at' 'in' or 'by'...' i.e. it's synonymous with 'detectable'. It is a very anthropocentric view to think the 'visibly' range is more important than any other. Astronomy is by it's very nature NOT anthropocentric! The ring shown was 'detectable' by the standard lensing based mass estimation techniques that have been used for decades. The technique is not that complex, based largely on radius of curvature. Remember, our eyes use lensing, so even our visible image of the universe depends on it! Present astronomy is equivalent to 'bionic eyes', including taking lensed images and inferring both original image and lens characteristics.
The matter is indeed then rendered 'visible', and that sense it is better than just 'optical range' detection, but, I agree it is also open to as much or even more misinterpretation as other observation (certainly including optical!
I also agree that estimation of galaxy and cluster mass from lensing is faulty. It has always been to high, and I consider 'caustics' and 'gravity wells' are used too liberally as 'patches' to cover the cracks. The 'Curved space-time' basis is in any case still unexplained (however many claim it is!).
But consider this carefully; It is not just lensing that tells up of the IGM, and whether from 'space-time curved by gravity' or from simple diffraction by the (mainly) free electrons found, (with protons, positrons, CO and basic bound molecular gas) the lensing exists. (Look carefully at the optical image and you can see the many curved 'smears' around the centre which they used).
Now we know plasma DOES refract light, and very effectively, but has a refractive index very close to 1. That's why it normally isn't detectable optically. That does not mean it is not visible by other means (including first hand by Voyager 2, and other closer probes including Cluster).
Now I say the plasma etc. we find out there moves and diffracts just like plasma anywhere else, so acts like a giant lens, and propose that the fact that lensing can be quantitatively explained in this way, along with unexplained effects such as kSZ, Faraday Rotation, ellipticity, aberration, Chirality etc, is no accident. Nothing we have found contradicts this hypothesis, only current interpretation does so.
You have a different view, which I agree should be studied considered equally with all others, as the de Souza proposal. So I should then ask questions, such as do you agree there is diffuse plasma CO and molecular gas out there, and why that might not be expected to behave with the plasma we find locally. The question is one I have asked proponents of the mainstream interpretation, with, as yet, no credible answer.
I hope that fully answers your points.
Best wishes
Peter
Peter,
If I understand you correctly, in plain terms the "chicken and egg job" you describe refers to your scenario in which the galactic effects commonly attributed to dark matter halos are instead the products of plasma halos, similar to the x-ray emitting intracluster medium within galaxy clusters. Your description of "increased velocity at the boundary propagates an increased ion density" implies that the high velocity motions of galactic disk periphery ionizes gas to produce the plasma halo - correct?
In that case, wouldn't this galactic plasma halo - large, massive clouds of (ionized or not) gasses be directly detectable from their emissions and/or interaction with photons? Again, any galactic halos providing compensatory mass, fitting observed flat or increasing galaxy rotation curves to Keplerian diminishing curve models would be required to increase total galactic mass up to ten-fold and increase the planar mass distribution by around three-fold. Surely such an enormous mass of gas clouds enveloping galaxies would be directly detectable via photon emissions.
The semantical argument that dark matter indirectly inferred by derived gravitational effects can be considered in any way 'visible' (referring of course to our extended discussion in your and other blogs) is an interesting maneuver. Honestly, I should probably simply accept your explanation, letting you off the hook for the "Visible 'dark matter'" misrepresentation. However, the reason I brought it up to begin with is the reason I cannot accept that compromise. Allowing such misrepresentations perpetuates the considerable confusion regarding dark matter.
Sorry, but I must insist that inference is not equivalent to the direct detection of photons. The rings of "Visible 'dark matter'" 'clouds' shown in the NASA image Hubble Finds Ghostly Ring of Dark Matter is no more real the artist's rendering of a dark matter halo surrounding the Milky Way in Serious Blow to Dark Matter Theories? (an ESO release - a very interesting read).
Perpetuation of such misrepresentations leads to inaccuracies such as the statement in your blog (1330) posting - Anonymous replied on Sep. 12, 2012 @ 11:34 GMT:
"We now estimate the rotational velocities of galaxies via the red and blue shift of the dark matter haloes."
I'm sorry if I seem inconsiderate, but there should be nothing personal about the pursuit of reality.
Sincerely, Jim
Dear James,
Of course the problem of dark matter up to now is not resolved and also needed in much attention. In the article: Cosmic Red Shift, Microwave Background, and New Particles. another possibility is studied for dark matter which arose in the Theory of Infinite Hierarchical Nesting of Matter (my essay). Nuons as new particles may be the reason for dark matter.
My reply, posted on the author's essay blog:
Caohoàng Hai thân men,
If I understand, then, you propose that the gravitational effects causing planets to orbit the Sun are not the same universal gravitation that causes moons to orbit planets? Since the law of universal gravitation can be very usefully applied to both realms, it seems to me unlikely that the two nearly identical effects would be caused by different processes.
As I tried to explain, I personally view gravitation as a 'push' from space contracted by a condensed mass. The appearance of attraction as described by Newton is the combined result of two opposingly directed 'pushing' fields of space.
I do not subscribe to the existence of a physical force of attraction, only the approximation of a net effect of attraction produced by the interaction of external fields produced by massive objects. That aside, I really don't know how many accidental granddaughters I have - I do think the two I know are quite attractive, but that's a different matter...
Jim
Jim
Emissions by CO receding will be redshifted, approaching blue shifted. The same is then true of free electrons, except that they only re-emit on or near the arrival 'vector' (as plasma is self focussing) so will only re-emit (so lens) the light from galaxies behind the plasma halo towards us, not widely 'scatter' light from all around.
This is important as it means we can obtain the rotational velocity from the CO, molecular gas etc, and the (normally outer) ion density from the DELAYS. Which are found up to 3 years so far (Abell) relative to the accelerated emissions from the other side of the halo. These 'lensing delays' are thus only kinetic (related again to the kSZ effect) as plasma n=1 so there is no dispersion delay.
This is very important, but not yet studied or accepted by the community though more observationally and logically consistent than current (recognised as inconsistent and 'poorly understood') interpretation.
I'm afraid your own interpretation of this element is less, not more, consistent with observation than current theory, however much you 'must insist' that mine is wrong. I agree of course that current theory is also wrong.
I don't take any scientific challenge or criticism personally, except when people abuse or ignore the data. With respect you are now edging towards that dangerous area! Proper science is surely about honest falsification, not cherry picking support. Yes?
Peter
Jim
Do you realize the term 'velocity dispersion' has nothing to do with 'direction'? It is a notional value of relative speed range 'spreads'. I repeat, and I'm sorry, but it seems both you and Mario have misinterpreted the terminology'; there is no implication of any but trivial radial motion in Ganda Fig 5a, and more disc plane inflow (jet 'feedback') than outflow in Sauron findings. A good intro overview to help is in this presentation. http://www-obs.univ-lyon1.fr/labo/perso/jeremy.blaizot/Presentations/emsellem.pdf my essay (and last years) fills in some missing gaps, but it's a good start. A more complete list is here; http://www.strw.leidenuniv.nl/sauron/publications.html
The kSZ is not just 'found in the...etc.' as you seem to assume, It is a common 'effect' consistent with all findings of galaxy kinetics.
Yes, very familiar with collisions and bullet cluster, and the lensing CANNOT be explained without the distorted clouds, as the text in the link confirms. Your comments don't make sense, I assume as based on misunderstandings. The affected ion densities of ALL collisions (there are really not that many) studied affect lensing patterns. Yes it is assumed as 'dark matter', but no, though it DOES have to be something with gravitational potential matching halo interaction evolution it may just as well be plasma because plasma n=1. There are still many different opinions on what that unidentified ('dark') matter is, including many agreeing baryonic including MACHO's. Yes, most do assume the matter is there, but for much more sound reasons than you seem to realise. Your suggestion would need to show how it can fit the data to offer your proposal any support. It certainly looks unable to do so at present, so you have to show how with some pretty detailed data analysis not to be laughed off.
I can see the free link was 'no value' to your thesis, but it is of truth value! I looked at your link to the M51 Density Wave paper, which again finds no net radial outflow, confirming (1141) the "CONTOURS of the projected velocity field are purely radial." Also, as I said; "that out-of-plane motions are significant."and suggesting (1157) "the input spiral pattern vanishes in less than one orbital timescale (~200 Myr)" Supporting the evolution sequence of spiral to lenticular (SO) which I identify.
Sorry Mario, but it is also in response to your false accusations that I was 'wrong'. I'll re-post this on Jim's string in case there are more questions. Time to face facts about the cited 'evidence', but I repeat, I agree there are very many fundamentally wrong assumptions in astronomy, and 'patch' atop 'patch,' most from trying to be consistent with SR. All attempts to challenge assumptions should be encouraged, but also well evidenced.
Best wishes
Peter
I repost here my response to Peter's comment, originally posted at Mario de Souza's essay blog...
Peter,
I can only take offense to statements such as "Your comments don't make sense, I assume as based on misunderstandings." I will respond more rationally.
In relation to my comments (about the Bullet Cluster), they are entirely consistent with the referenced text, including the concluding statements:
"But the dark matter present has not interacted with the cluster gas except by gravity. The clear separation of dark matter and gas clouds is considered direct evidence that dark matter exists."
In fact, those statements conflict with your assertion that the gravitational lensing effects identified can easily be produced by the separated gas.
IMO, the established interpretation falsifies your thesis that the effects attributed to dark matter are actually the product of dense plasmas. This interpretation is confirmed in a recent research reported in the ApJ states in its abstract:
"Weak-lensing results for A1758N agree with previous weak-lensing results for clusters 1E0657-558 (Bullet cluster) and MACS J0025.4-1222, whose X-ray gas components were found to be largely separated from their clusters' gravitational potentials."
Ref.: B. Ragozzine et al. "WEAK-LENSING RESULTS FOR THE MERGING CLUSTER A1758." ApJ 744 94 (Jan 10 2012). doi:10.1088/0004-637X/744/2/94. arXiv:1111.4983v2.
The consensus explanation for the separation of colliding galaxy clusters' gaseous intracluster mediums (ICM) from their galaxies and (presumedly WIMP) dark matter (normally coincident with the ICM prior to collision) is that, when the relatively high velocity clusters meet, their effectively non-interacting sparse galaxies and (WIMP) dark matter proceed in the independent directions of their established momentum, while the disperse gaseous ICMs physically interact, producing "ram pressure" that largely absorbs their momentum.
The separation of lensing effects from the gaseous ICMs (but not their galaxies) seems to falsify your assertion that the lensing effects are produced by the gaseous ICMs. BTW, It does not preclude the possibility that the clusters' galactic masses have been systematically underestimated, and that their gravitational potential alone produces the weak lensing effects.
I'm aware that I do not have the expertise to fully evaluate Mario's thesis that the gaseous arms of spiral galaxies are produced from outflows of gas from the galactic center. That's why I've asked you to explain the data to me. However, you seem intent on merely dismissing any interpretation of observational data indicating that there are any outflows except the perpendicular polar jets produced by AGN. That, taken with your questionable assessment of other data convinces me that your evaluations cannot be relied upon.
I'm sorry that I had to bring up important observational evidence that conflicts with you own proposal. However, insulting me is not appropriate - even if you cannot respond appropriately.
Sincerely, Jim
Jim
If someone resists accessing actual evidence but proposes something contrary that's fine, but that's called speculation not science and I'm sure you can judge how its veracity is viewed.
You now 'urge me to consider' evidence assuming I have not done so for both that and far better evidence very closely for some years. You assumption is incorrect. But I also still don't agree your characterisation (last para). I'll do my best again to explain, as long as you don't call it 'lecturing'!
When galaxies and clusters collide, let's say the 'fine structure' (whatever) surrounds them is disturbed. This is invariably found as more dense CO and molecular gas towards the barycentre and a more diffuse electron based plasma (when detectable) towards the outer halo (or IGM/ICM). (They overlap because one begets the other!) Now I'm sorry, but if you've studied as much data and research as I have over the years you will find a clear pattern, consistent with the following description (and I'm not just spouting any mainstream 'dark matter' theories).
The molecular gas clouds are only concentrated in different parts of space to the plasma because they 'started' in different parts of space so are affected differently. Now the lensing found does not 'JUST' correlate with the visible molecular gas, at WHATEVER wavelength it scatters light (normally investigated at multiple frequencies). All the condensed matter there is assumed to have gravitational potential according to it's mass just like it does in our back yard. The change in motions of the visible matter correlates with this basis and provides an approximation of density of the NON visible 'clouds'. These are normally thus considered as 'dark matter', either as some exotic new particles or not. I propose not, because the densities are consistent with electron densities found locally (The Kingsley Figure 2 I referred you to, and the international standard ionospheric model at up to 10^14 particles/cm^-3 at shocks).
Now there is also other evidence, quite complex, but lensing is the main and largely independent second 'check'. It quite simply does not correlate with the visible gas, at least 'alone'. But now we get into interpretation'. Mainstream uses 'curved space-time' to estimate galaxy mass, but gets anomalously high masses. More and more (inconsistent with relativity) use my method of diffraction by matter for lensing (as smaller lenses) which is more consistent with the REAL data (Sauron, Atlas 3D etc).
The lensing then simply implies spatial distribution and density. Most of mainstream just call it 'dark matter density', but that just means it's not visible and includes a broad church of options. Plasma 'scatters' far better directionally than gas (that's what 'self focussing' means). So that's why the gas visible at X ray has no effect on lensing, which is indeed a proof of the plasma thesis. (Unless you really believe the nearby galaxy cluster 'bends' a pure vacuum - as current mainstream expects us to, but that gas does not).
Now I've tried other models which don't work, and tried for some time to falsify (NOT verify!) this, but failed. Yet I still have an open mind.
Now none of this has much to do with my essay, which just exposes the underlying quantum mechanism the 'particle' based lensing implies, and more than a handful of other anomalies. But you did ask.
I'm sorry if your beliefs and Mario's thesis are different, that's fine let them be if you prefer, and as I recall I have no problem with any other parts, but I don't believe in hiding from inconvenient scientific truths, and hope you're the same.
Peter
(reposted from my string in response to Jim's reply)
Jim
Open access for particle physics in UK announced (IOP). All journal articles are to be free access, (as the work is mainly government funded). It's a start at least, perhaps for astronomy as well in ~13.7Gyr.!
Peter
I've reposted my response to Peter from his essay's blog below.
Peter,
We're now discussing my claim that the separation of lensing effects and x-ray emitting intracluster media falsifies your assertion that the effects attributed to dark matter can be attributed to plasmas. Please do Mario the favor of excluding remarks about him from this discussion, as he has made no such claims and in fact I've had no discussions with Mario about this claim of mine. He has nothing to do with this discussion - this is just between you and me.
Secondly, as I have provided several sources that conclude that the separation of lensing effects from x-ray emitting gases in high velocity galaxy collisions provides evidence for the existence of enormous masses of not just 'non-visible' matter but effectively non-interacting non-baryonic, weakly interacting massive particles (WIMPs). Please see Chandra posting. This is not just 'little old me' making this claim, it seems to be the consensus "mainstream" astrophysical community.
As I understand, 'undisturbed' galaxy cluster morphology can be generalized as tending towards a spherical distribution of mass centered around a common center of mass, generally coincident with the geometric center of the cluster. There the gaseous intracluster medium is densest and hottest, emitting high energy x-rays. There is also often an enormous galaxy located near the center of mass.
The consensus interpretation of collided galaxy clusters, as I understand, is that the disperse gasses comprised of baryonic particles physically interact upon collision, absorbing their momentum slowing their forward motion.
It is thought that the colliding clusters' sparse galaxies do not physically interact - their momentum allows each group of galaxies to continue their established relative motion until gravitation eventually slows their progress.
The gravitational lensing effects of collided galaxy clusters are typically coincident with the location of the two separated groups of galaxies. However, since the collective mass estimated for the galaxies is thought to be insufficient to produce the identified weak gravitational lensing effects, it is presumed that enormous amounts of dark matter coincident with the galaxies is contributing most of the mass necessary to produce the identified gravitational lensing effects.
It is crucial to understand that the inferred dark matter could only be coincident with the two groups of non-interacting galaxies if the dark matter was also non-interacting. The only interaction that could have occurred between the two groups of galaxies and any possible dark matter was gravitational.
The principal requirement for the inferred dark matter is that it could only have gravitationally interacted with any of the clusters' mass upon collision. As I understand, the p[articles of colliding plasma clouds would physically interact much like the hot gases in the intracluster medium - their forward progress could not have continued such that they would located coincidentally with the sparse, non-interacting galaxies.
If you can explain how ionized gas or plasma particles within the two colliding galaxy clusters could have avoided all physical interaction with other disperse particles, allowing their momentum to carry them along with the clusters' galaxies, I'd be very happy to try to understand.
Sincerely, Jim
Peter,
Yes - this is great news! I hope this or some similar model suppoting free access is adopted by all other fields of study.
Thanks, Jim
Hi Jim, we met on the Sciam blog about two years ago and I see this is like me already your second participation with the FQXi contest. I read your essay with much attention and think that when you mention "I am just a "layman" it is not a bad proposition (from your point of view). Please as a layman listen attentively to proffessionals like Peter Jackson, besides that he is a professional that has a very open mind and a lot of intriguing new visions, all based on the facts that astronomy has put up untill today.
About dark matter which represents 95% of our visual universe (but is not visible) , I have no specific ideas only that the forces that are attributed to it are "emergent" from Total Simultaneity (TS).
If you are interested pls read/rate and/or comment "THE CONSCIOUSNESS CONNECTION", which is quite another approach of our "reality".
I look forward for your opinion.
Wilhelmus
Hi Wilhelmus,
Whether my status as a layperson in the field of physics is or isn't a bad "proposition" for me, I'm compelled to make that honest disclosure up front so that others might realize might level of expertise. As to my professional standing, I worked exceedingly hard for several decades as a highly accomplished information systems analyst. When I raise a very specific technical issue I expect a professional response, not a lecture on my demeanor. Thank you for your personal advice...
I see you have no specific thoughts regarding my essay. Thanks for your comment.
Jim
After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.
Cood luck.
Sergey,
Thanks for your notification, I guess. Not that it makes any real difference, since, unlike some others, I haven't been mass marketing my essay to the rest of the community, soliciting ratings (some even hinting at Quid pro quo). As a result I could see that mine would not be in the top 35 essays as rated by the community.
However I should inform you that, with my background in information systems analysis, I find that my essay's position within the list ordered by community rating dropped precipitously following you rating notice. That indicates two conditions: my essay had not been rated by many members of the community and your rating was substantially lower than previous ratings.
Again, all this rating stuff is meaningless since my essay would not have ever been one of the finalists (unless perhaps I had very successfully supported it with an intense marketing effort). However, more important to me than knowing you rated my essay would be to better understand why you might have given it a low rating, presuming that your rating was based on some specific evaluations of my essay. With no animosity, I would be very interested in understanding your assessment of my essay. Please do explain further!
Sincerely, Jim
Dear Jim,
I enjoyed with your interesting Essay, hence, I am going to give you an high score.
Notice that, even admitting that Galaxy Rotation Problem could represent a fundamental falsification of Newton's law of universal gravitation (this is the issue on which you disagree in your Essay) there is a problem which is even greater. The existence of Dark Matter is admitted in order to justify Newtonian theory. But the most precise theory of gravitation that we have at the present time is general relativity rather than Newtonian theory! In the framework of general relativity the energy is coordinate dependent, hence we CANNOT speak of Dark Matter!!!
You could be interested to another approach to solve the Dark Matter in this paper that I wrote with two colleagues: http://arxiv.org/abs/1105.0147
Cheers,
Ch.
Dear Jim,
Sorry if you thought that I was correcting you, I am not at all the one that is able for that.
I reread yor essay and indeed it is indicating as I understood it now, the old ways of regarding the complex movement of galaxies. You mention that the Keplerian rotation curves cannot be applied on structures like galaxies, and I fully agree. There is indeed a vast distribution of massive objects and perhaps we should regard it as a fluid with all the mechanics and formula's that goes with fluid mechanics, this is just perhaps a wrong idea, but it can change the way of thinking about dark matter, as in your well written essay.
Good luck in the contest.
Wilhelmus
Dear Chris,
Thanks so much for reading my essay - and especially your kind remarks!
I understand (in principle) that general relativity is fundamentally more accurate than classical physics and at least more correctly and more completely describes the physical effects of gravitation. However, I must take exception to the statement that "The existence of Dark Matter is admitted in order to justify Newtonian theory." IMO, a more correct statement would be that 'The existence of Dark Matter is admitted in order to justify the misapplication of overly-simplistic methods of approximation based on pre-Newtonian physics.'
Reading your paper, "High-energy scalarons in R^2 gravity as a model for Dark Matter in galaxies" (which I found very interesting, to the extent that I could comprehend), I think I should explain that, in my view, the fundamental issue with galaxy gravitational evaluations is not (when correctly applied) Newtonian physics, it is the expedient misapplication of even simpler methods of approximation by astronomers and others. There are several references to research in my 'Supplemental Info." and "Cited Works" sections (the latter correcting one erroneous URL) that more correctly represent galactic mass configurations using Newtonian dynamics and gravitation to successfully represent observed galaxy rotation. There is also a reference using general relativity - Fred Cooperstock also takes the view that the failing is inherent in Newtonian physics.
In my information systems analyst view, the application overly-simplistic methods of gravitational approximation to more complex structures introduces scale variant errors in the estimation of both non-luminous masses and the effects of gravitational interactions among discrete objects within very large composite structures. As I think is inherent in gravitational evaluation methods prescribed in general relativity, galactic disks are self-gravitating aggregations of massive objects, avoiding at least the errant evaluation of gravitational effects.
I have a lot of thoughts regarding gravitational lensing effects attributed to dark matter, especially through the compound lens that must be presented by galaxies within galaxy clusters. While certainly a 'localized' large scale structure such as a galaxy cluster must produce a collective curvature of spacetime, each relatively compact galaxy must also produce a more intensive, if more localized, curvature of spacetime. I suspect that generalizing the magnitude of lensing effects produced to consider only the overall structure in order to facilitate evaluation may introduce large scale errors into the results. I think (not comprehending math) I may have detected some perhaps over-generalizations in your equations - is that possible?
I've had some very long and tedious discussions with Peter Jackson attempting to explain that the Bullet Cluster's separation of gas and non-interacting masses does falsify his assertion that ionized gasses produce the effects attributed to dark matter. While I agree with him that non-detectable gasses represent an under-appreciated quantity at all scales, the decelerated gasses comprising intracluster media apparently cannot produce galaxy cluster lensing effects.
I think it's much more telling that dark matter is almost always coincidentally located with galaxies. Perhaps, in a literary sense, it is dark matter that cannot exist without galaxies! I think the method often used to estimate 'ordinary' galaxy mass based on luminosity is a perfect fit for main sequence stars, whose mass directly produces luminosity. However, applying that method to galaxies generally ignores a significant independently contributing factor of non-numinous (and often luminosity obscuring disperse) masses. As I understand, it's generally resulted in spiral galaxies often requiring large amount of compensatory dark matter - they also contain relatively large volumes of dust and gas. This, in conjunction with simplified methods of approximating gravitation relying too much on a compound object's center of mass and not considering the effects of so many discretely interacting objects, often produces underestimated masses for large scale composite masses.
To conclude all of this, I think that if the original requirement truly establishing the existence of dark matter in galaxies was a product of improper analysis, as I think I've established, and galactic rotation can be explained in the context of existing physics, then it should follow that galactic dark matter does not exist, at least in significant amounts. While I agree that this does not preclude its existence throughout the rest of the universe, I think that cosmologists rely entirely on galactic dark matter estimates for their presumptive universal proportion of dark matter to 'ordinary' matter. To that extent, if there's no requirement for galactic dark matter it should follow that there's no justification for cosmological dark matter, no matter how expedient it might be for cosmological analyses. At least that's the way this information systems analyst sees it...
Thanks again, Jim