Is the Dark Matter Hypothesis Failing to Explain Galaxy Formation?

[Saul]

Which patterns are these?


The theory that ellipticals formed from the mergers of spirals (which is by no means universally accepted)...

I'm not quite sure what this is supposed to mean. The angular momentum of stars and gas is sensitive to the galaxy's merger and star formation history, including stellar and AGN feedback. Since such things are difficult to simulate, we can't be sure that such discrepancies are resulting from a problem with the dark matter paradigm.

What it says. Spirals to Elliptical (Not)
The question to answer is how do spirals remain as spirals after multiple mergers. I believe observationally the percentage of galaxies that are spirals does not vary significantly with redshift. Roughly 70%. (I am looking for a paper, that I thought I read that specifically discusses the survey results. See the paper I copied above Milky Way is an exceptionally quiet galaxy.)

Spiral Galaxy Properties:
Disney et al's finding that it appears multiple disk properties are correlated to a single unknown parameter is interesting.

The angular momentum catastrophe is only one of a multiple of problems with the dark matter hypothesis. The simulations show the spirals form too early and are hence too small (roughly an order of magnitude). In addition the simulated galaxy's bulge is too large and the angular momentum distribution of the simulated galaxy does not match physical galaxies.

http://arxiv.org/PS_cache/arxiv/pdf/0908/0908.1409v1.pdf

Galactic Disk Formation and the Angular Momentum Problem
Simulations of galactic disk formation suffer often from catastrophic angular momentum loss which leads to disks with unreasonably small scale lengths and surface densities that are too large. The origin might be strong clumping of the infalling gas which looses angular momentum by dynamical friction within the surrounding dark matter halo (Navarro & Benz 1991, Navarro & Steinmetz 2000), low numerical resolution (Governato et al. 2004, 2007), substantial and major mergers (d’Onghia et al. 2006) and artificial secular angular momentum transfer from the cold disk to its hot surrounding (Okamoto et al. 2003). It has been argued that this problem might be solved by including star formation and energetic feedback (e.g. Sommer-Larsen et al. 2003, Abadi et al. 2003, Springel & Hernquist 2003, Robertson et al. 2004, Oppenheimer & Dave 2006, Dubois & Teyssier 2008). No reasonable, universally applicable feedback prescription has however yet been found that would lead to the formation of large-sized, late-type disks, not only for special cases, but in general.

http://arxiv.org/PS_cache/astro-ph/pdf/0208/0208524v1.pdf

New problems for the Formation of Disk Galaxies
Because of the overall success of these models in explaining a wide range of observed properties of disk galaxies, it has generally been assumed that the aforementioned assumptions are correct. However, several recent results have started to cast some doubt as to the validity of this standard framework. First of all, detailed hydro-dynamical simulations of disk formation in a cold dark matter (CDM) Universe yield disks that are an order of magnitude too small (e.g., Steinmetz & Navarro 1999). This problem, known as the angular momentum catastrophe, is a consequence of the hierarchical formation of galaxies which causes the baryons to lose a large fraction of their angular momentum to the dark matter.

Secondly, under assumption (iii) the density distribution of disks is a direct reflection of the AMD in the proto-galaxy. Bullock et al.(2001, hereafter B01) determined the AMDs of individual dark matter halos, which according to assumption (ii) should be identical to that of the gas, and thus to that of the disk. However, these distributions seem to have far too much low angular momentum material for consistency with the typical exponential density distributions of disk galaxies (B01; van den Bosch 2001).

 

[twofish-quant]

[The angular momentum catastrophe is only one of a multiple of problems with the dark matter hypothesis.

Yup. Got an interesting mystery here, which lots of people are trying to figure out.

Any ideas how to fix it? The problem with tossing dark matter is that at that point you end up not explaining large scale structure.

The thing about galaxy formation is that you are dealing with lots of interesting physics, and we don't really understand how galaxies form, so right now the general belief is that we are missing something fundamental in the way that galaxies form. Or we could just be calculating things wrong. There's enough wiggle room right now that you can't say the angular momentum problem comes anywhere close to killing dark matter. This won't be the case in five to ten years.

Again, process of elimination. You come up with about twenty different things that it could be, and over the next few years you rule them out one by one. The trouble is that there is some really weird stuff that you can invoke. Who says for example that dark matter has to be stable (well there are limits)? Also you have invoke my favorite tooth fairy for these situations, magnetic fields.

 

[Saul]

Not quite. The neutrino is only required if you demand that laws of physics obey the conservation of energy and momentum.

The predictions you're talking about here are contingent on the details of the physics implemented in enormous computer simulations. But, as has already been pointed out in this thread, it's a know fact that the baryonic physics in those simulations isn't good enough to capture everything going on with the baryonic matter. And, without knowing exactly how the results would be affected if those shortcomings could be fixed, you can't know whether the discrepancies with observations are shortcomings in the simulations or shortcomings in the basic physical models underlying the simulations.

One other point, eliminating dark matter would completely unravel the extremely good agreement that cosmological (rather than astrophysical) modeling has found with observational data.

Look at the problem from a different perspective. Assume it is a fact that dark matter does not exist. How effective and how useful is the theoretical work trying to construct models to explain galaxy formation using dark matter if dark matter does not exist?

It takes insight to identify a faulty theory. Good science identifies theories that are on the ropes. Can the theory be saved? Should it be saved? The theoretical problems with dark matter seem to be significantly deeper than a lack of computing power.

When a theory appears to be in crisis it is helpful to re-look at the observational data without prejudice and with different assumptions.

What else could physically cause what is observed? What are the fundamental assumptions of the field? Observationally what convinces us the fundamental assumptions are correct? Could any of the assumptions be incorrect? Any other anomalies?

The observational data appears to be pointing to a specific physical cause which is not dark matter, nor is it a modification of the laws of physics. There is a pattern of peculiar connected anomalies and observations. What causes or more accurately triggers star burst galaxies? What is the unknown parameter that Disney et al's paper is discussing?

 

[twofish-quant]

Look at the problem from a different perspective. Assume it is a fact that dark matter does not exist. How effective and how useful is the theoretical work trying to construct models to explain galaxy formation using dark matter if dark matter does not exist?

Very. If it turns out that we spend lots of effort trying to create models of galaxy formation with dark matter, and it just doesn't work, then this is a hugely useful activity. We don't know right now, that we can't get a usable galaxy formation model with dark matter. We'll know more in a few years.

It takes insight be able identify a faulty theory.

It takes observations and calculation. We don't know for a fact that dark matter is fundamentally flawed when it comes to galaxy formation. Give it some time, and either we will find some fundamental flaw that we can't work around or we won't.

Science is hard. It takes time.

The theoretical problems with dark matter seem to be significantly deeper than a lack of computing power.

Right now they aren't very deep problems. There's no smoking gun. There may or may not be in a few years. The type of "smoking gun" argument that would toss a theory into crisis is if you should that dark matter would somehow violate conservation of energy by 15 orders of magnitude. Right now we just have computer simulations.

When a theory appears to be in crisis it is helpful to re-look at the observational data without prejudice and with different assumptions.

Sure. The trouble is that this also takes time. Something that someone should be doing is to run a galaxy evolution simulation without dark matter and with modified gravity. The trouble is that it takes about a year to run this simulation. Also, if someone has run the simulation and it doesn't solve the problem, then it's not publishable.

What else could physically cause what is observed? What are the fundamental assumptions of the field? Observationally what convinces us the fundamental assumptions are correct? Could any of the assumptions be incorrect? Any other anomalies?

First of all, it's not either/or. You could have a mix of dark matter, magnetic fields, modified gravity, radiation pressure, shock waves, turbulence, electrostatic fields, star formation, dark energy, GR effects, numerical effects, selection effects, and something else that we have no clue about.

The trouble with galaxy formation is that you can come up with about a dozen different explanations for what is going on. That's why no one is quite willing to declare dark matter dead because of galaxy formation. There are just too many unknowns.

The observational data appears to be pointing to a specific physical cause which is not dark matter, nor is it a modification of the laws of physics. There is a pattern of peculiar connected anomalies and observations. What causes or more accurately triggers star burst galaxies? What is the unknown parameter that Disney et al's paper is discussing?

It could be one of about twenty things. Or it could be a combination of five different things. Or it could be an observational selection effect. Right now the going assumption is that as we figure out what is going on, it's probably going to be something that manages to work with dark matter. I'm a theorist. If you give me an hour I can come up with about a dozen things that it could be (dark matter creates clusters of black holes with magnetic fields that spin up as the swallow each other. Population III stars create shock waves that combine to increase angular momentum. Dark matter has non-linear properties that create shocks. There is no dark matter, it's all modified gravity.)

The trouble is that is that to develop anyone of those ideas would take about six months to a year.

You are never going to figure it out by just staring at the data. You just need to make some guesses, take more data and do more calculations. And it's fine to guess wrong.

 

[Chronos]

There are more than a few theories that almost, but, not quite cut the mustard. There are more than a few papers that have not been published on this account. Close is not good enough when theory conflicts with overwhelming observational evidence.

 

[Saul]

Multiple papers by different authors concerning different fundamental aspects of the dark matter hypothesis all support the assertion that dark matter does not exist.

Is it possible the dark matter theory could be revived? How long does one continue to beat a dead horse?

Re-read Disney et al's paper from the perspective that dark matter does not exist. What Disney et al have found is a significant observational clue. Why are a set of galaxy parameters tightly correlated, if galaxies are formed by random mergers, the hierarchical formation hypothesis?

What is causing the rotational anomaly, if dark matter does not exist? How do spiral galaxies avoid becoming elliptical galaxies from mergers. (70% of current galaxies are spiral.) Why is spiral rotational velocity very tightly correlated with galaxy luminosity?

Space Tiger's above comment concerned the observation that high red shift galaxies are very dense and compact. As the authors of this paper ask what mechanism causes the compact massive galaxy to expand? Mergers cannot be the mechanism as mergers destroy the spirals.

Confirmation of the remarkable compactness of massive quiescent galaxies at z~2.3: early-type galaxies did not form in a simple monolithic collapse

http://arxiv.org/abs/0802.4094v1http://arxiv.org/PS_cache/astro-ph/pdf/0208/0208524v1.pdf

New problems for the Formation of Disk Galaxies
Because of the overall success of these models in explaining a wide range of observed properties of disk galaxies, it has generally been assumed that the aforementioned assumptions are correct. However, several recent results have started to cast some doubt as to the validity of this standard framework. First of all, detailed hydro-dynamical simulations of disk formation in a cold dark matter (CDM) Universe yield disks that are an order of magnitude too small (e.g., Steinmetz & Navarro 1999). This problem, known as the angular momentum catastrophe, is a consequence of the hierarchical formation of galaxies which causes the baryons to lose a large fraction of their angular momentum to the dark matter.

Secondly, under assumption (iii) the density distribution of disks is a direct reflection of the AMD in the proto-galaxy. Bullock et al.(2001, hereafter B01) determined the AMDs of individual dark matter halos, which according to assumption (ii) should be identical to that of the gas, and thus to that of the disk. However, these distributions seem to have far too much low angular momentum material for consistency with the typical exponential density distributions of disk galaxies (B01; van den Bosch 2001).

http://arxiv.org/abs/0811.1554

http://www.nature.com/nature/journal/v455/n7216/abs/nature07366.html

Galaxies appear (my comment Non random) simpler than expected

Galaxies are complex systems the evolution of which apparently results from the interplay of dynamics, star formation, chemical enrichment and feedback from supernova explosions and supermassive black holes (1). The hierarchical theory of galaxy formation holds that galaxies are assembled from smaller pieces, through numerous mergers of cold dark matter (2, 3, 4). The properties of an individual galaxy should be controlled by six independent parameters including mass, angular momentum, baryon fraction, age and size, as well as by the accidents of its recent haphazard merger history. Here we report that a sample of galaxies that were first detected through their neutral hydrogen radio-frequency emission, and are thus free from optical selection effects (5), shows five independent correlations among six independent observables, despite having a wide range of properties. This implies that the structure of these galaxies must be controlled by a single parameter, although we cannot identify this parameter from our data set. Such a degree of organization appears to be at odds with hierarchical galaxy formation, a central tenet of the cold dark matter model in cosmology (6).

Primarily Zeon100 results are negative for the detection of dark matter.

XENON 100 is in a class all its own. It uses around 50 kilograms of a liquid xenon compound that is supposed to emit a flash of light if it gets knocked by a passing dark matter particle. It's the size of the detector that really makes it stand out from the crowd: most dark matter experiments to date measure the size of their detectors in grams rather than kilos. More mass makes an interaction more likely and so even after just 11 days of running XENON 100 has something to say about dark matter.

http://arxiv.org/abs/astro-ph/0702585v1

“The Milky Way: An Exceptionally Quiet Galaxy; Implications for the formation of spiral galaxies”, by F. Hammer, M. Puech, L. Chemin, H. Flores, M. Lehnert

However, there are several outstanding difficulties with this standard scenario. One such difficulty is the so-called angular momentum problem. That is, simulated galaxies cannot reproduce the large angular momentum observed in nearby spiral galaxies (e.g., Steinmetz & Navarro 1999). Another is the assumed absence of collisions during and after the gas condensation process. Indeed, the hierarchical nature of the _CDM cosmology predicts that galaxies have assembled a significant fraction of their masses through collisions with other galaxies. It is likely that such collisions would easily destroy galactic disks (e.g., Toth & Ostriker 1992).

The widely accepted assumption that a major merger would unavoidably lead to an elliptical is perhaps no longer tenable: accounting for the large number of major mergers that have apparently occurred since z=3 would imply that all present day galaxies should be ellipticals. (My comment. Yes what is the explanation that all galaxies are not elliptical and what is causing the spiral galaxy rotational anomaly.) This is obviously not the case. So it is likely that disks either can survive or are “rebuilt” after a major merger, through whatever mechanism as yet perhaps unknown in detail (see, for example, Robertson et al. 2006).

 

[Chronos]

'many' paper calling dark matter into question does not offset the many more papers favoring dark matter. Little observational evidence is conclusive in cosmology - there are too many uncertainties. Uncertainty opens the door for fringe theories, but, is otherwise less that compelling. I am admittedly concerned by your fixation with Disney, et al. It is a fringe paper that cherry picks excerpts from a mix of papers of varying quality. It is no secret we poorly understand galactic evolution. That is not a persuasive argument for, or against, anything.

 

[twofish-quant]

Multiple papers by different authors concerning different fundamental aspects of the dark matter hypothesis all support the assertion that dark matter does not exist.

No they don't.

At best that reveal a conflict between dark matter and models of galaxy formation (and it's not even clear that they do that). Since we don't have a good model for galaxy formation, it's really, really premature to say that there is a problem with dark matter.

One problem is that it's not clear that any of the problems go away if you assume no dark matter.

Re-read Disney et al's paper from the perspective that dark matter does not exist. What Disney et al have found is a significant observational clue. Why are a set of galaxy parameters tightly correlated, if galaxies are formed by random mergers, the hierarchical formation hypothesis?

Because maybe they aren't formed by random mergers, and maybe the hierarchical formation hypothesis is totally, totally wrong.

What's any of that got to do with dark matter? Let's suppose that galaxies *aren't* formed by random mergers. How does that kill or even wound dark matter? Suppose you take away dark matter, can you show that any of these problems go away?

What is causing the rotational anomaly, if dark matter does not exist?

Modified Newtonian Dynamics. There is a huge amount of literature based on the idea that the discrepancies in rotation curves are due to modified gravity. The big problem with those models is that to get results that match observations, you have to assume that gravity behaves differently around each galaxy.

It would be really, really interesting if you could show that MOND gives you better galaxies formation dynamics than dark matter. The trouble is that since we really don't understand galaxy formation, no one has been able to show that.

How do spiral galaxies avoid becoming elliptical galaxies from mergers. (70% of current galaxies are spiral.) Why is spiral rotational velocity very tightly correlated with galaxy luminosity?

No clue. What's that got to do with dark matter?

Seriously, you seem to be quoting random papers, most of whom have little to do with dark matter. The one big problem with dark matter that is valid (i.e. the angular momentum problem) can be explained right now by pointing out that we really don't understand galaxy formation. This may not be tenable in five to ten years, but that's scientific progress.

If you have some grand theory that proposes to tie together all of these unexplained phenomenon, then put something on the table, so we can talk about it. The obvious line of research is to see what modified gravity does to galaxy formation, and if you want to pursue that line of research, put that on the table and let's discuss what needs to be done. What you will find is that once you get past "picking at flaws" and try to come up with an actual alternative, you'll find that it's quite hard, but that is what science is all about.

The problem is that even a flawed hypothesis is better than no hypothesis. We have a guess as to what is going on. We look at how the guess is wrong, and over time that hopefully gets us to a better understanding of what is going on. If you think that there is something fundamentally missing, then please suggest something. If you think that there is some basic blind spot that people are missing, I'd really be interested in knowing what it is.

People are working on the assumption that dark matter is right, because it's a good guess that fits a lot of things. It's not the whole story, and it's got problems. Can you come up with anything better? In particular, I'm interested if you can come up with a *type* of theory that doesn't fall into either dark matter or modified gravity (including fifth force).

 

[twofish-quant]

'Little observational evidence is conclusive in cosmology - there are too many uncertainties.

I'd disagree with that somewhat. There isn't that much room for observational uncertainty in CMB measurements. When you go to galaxy counts, then you are talking about really messy statistics

It is no secret we poorly understand galactic evolution. That is not a persuasive argument for, or against, anything.

Also I don't think that the spending all of your time with fringe ideas is a good idea for an interesting reason. There is admittedly a perverse thrill at beating up on the "establishment" but if you focus on those areas, you miss the areas where there is standard model or theory. For example, right now there simply is no standard model of galactic evolution. People are guessing, but there is nothing approaching a firm theory.

If you focus on beating up on the establishment, you miss the areas were there is no establishment, and you waste a lot of your time trying to prove that 2+2=3 rather than thinking about how populations III stars might or might not work or how supernova explode. There are a lot of mysteries of the universe. No one quite understands how to model smoke rings or the Earth's magnetic field.

 

[twofish-quant]

Also you have to figure out how the pieces fit. Suppose it turns out that hierarchical galaxy formation was totally, totally wrong. That wouldn't kill dark matter, and I think you could without too much trouble salvage cold dark matter. All you need is some mechanism by which galaxy counts more or less track dark matter.

Cold dark matter is only one of several dark matter ideas. There's hot dark matter and baryonic dark matter. Cold dark matter won because of galaxy counts. There are a *lot* of differences between CDM and the galaxies statistics you expect to see. But HDM and baryonic dark matter look *NOTHING* like observed galaxy counts, and if you assume no dark matter then deuterium abundances and CDM falls apart. CDM has problems but compared to the alternatives, it's "close enough" that most people think that we'll be better off refining CDM and galaxy evolution then trying something really, really different.

If you can show that modified gravity gives you better galaxy evolution than CDM, you've got a paper, and if you are lucky then you've lots of awards. If...

Personally, I'd be really excited if someone came up with a smoking gun argument that says that dark matter can't possibly work. It's no fun if you seem to understand everything, which is why I didn't go into particle physics. But coming up with a real argument rather than just cherry picking papers is quite hard.

All models are wrong. Some models are useful.

 

[Saul]

No they don't.

At best that reveal a conflict between dark matter and models of galaxy formation (and it's not even clear that they do that). Since we don't have a good model for galaxy formation, it's really, really premature to say that there is a problem with dark matter.

The simulations produce galaxies that are 1/10 the size of physical galaxies with bulges that are too big and with an angular momentum profile that does not match observations. The reason for the discrepancy between observation and modeling is due to fundamental properties of dark matter.

One problem is that it's not clear that any of the problems go away if you assume no dark matter.

The solution is not dark matter. As I said there are multiple fundamental astronomical assumptions that are incorrect. When dark matter is removed, a physical explanation of the observations is required. This is physics not magic.

A year working at model construction will not help to solve the problem. The observations are clues to the solution. The key is removing the incorrect assumptions and adding the new mechanisms. The observations are patterned not random. See my next comment.

Because maybe they aren't formed by random mergers, and maybe the hierarchical formation hypothesis is totally, totally wrong.

What's any of that got to do with dark matter? Let's suppose that galaxies *aren't* formed by random mergers. How does that kill or even wound dark matter? Suppose you take away dark matter, can you show that any of these problems go away?

The observations are explained by the mechanisms. They are no longer problems.

Modified Newtonian Dynamics. There is a huge amount of literature based on the idea that the discrepancies in rotation curves are due to modified gravity. The big problem with those models is that to get results that match observations, you have to assume that gravity behaves differently around each galaxy.

It would be really, really interesting if you could show that MOND gives you better galaxies formation dynamics than dark matter. The trouble is that since we really don't understand galaxy formation, no one has been able to show that.

The solution is not MOND.

Seriously, you seem to be quoting random papers, most of whom have little to do with dark matter. The one big problem with dark matter that is valid (i.e. the angular momentum problem) can be explained right now by pointing out that we really don't understand galaxy formation. This may not be tenable in five to ten years, but that's scientific progress.

You are not thinking about the observations.

Imagine you enter a very large out door parking lot. You see all of the cars stacked in group of threes, with each group of three cars stacked one on top of the other. A scientist tells you the explanation is a strong wind storm caused what you see.

Why do you know that it is physically not possible for the wind to have caused what is observed. Would you suggest modeling to determine if the wind caused what is observed.

If you read a paper that stated that wind was not capable of causing what you observed, would you suggest that perhaps additional computer time or a larger more powerful computer would show that a wind storm could stack a few thousand cars in separate stacks of threes.

If you have some grand theory that proposes to tie together all of these unexplained phenomenon, then put something on the table, so we can talk about it. The obvious line of research is to see what modified gravity does to galaxy formation, and if you want to pursue that line of research, put that on the table and let's discuss what needs to be done. What you will find is that once you get past "picking at flaws" and try to come up with an actual alternative, you'll find that it's quite hard, but that is what science is all about.

Let the observations guide. That was one of the points of the MECO thread. We do not know what are the properties of very, very, massive objects. There is a very interesting set of peculiar quasar anomalies that provide some hints.

Do not be so quick to guess. What do the observations tell you? Analysis and discuss the observations.

The problem is that even a flawed hypothesis is better than no hypothesis. We have a guess as to what is going on. We look at how the guess is wrong, and over time that hopefully gets us to a better understanding of what is going on. If you think that there is something fundamentally missing, then please suggest something. If you think that there is some basic blind spot that people are missing, I'd really be interested in knowing what it is.

If dark matter does not exist, the dark matter hypothesis has delayed any scientific progress for a decade. During the decade astronomers have been busy gathering and analyzing observations. The answers are to be found in the observations.

 

[Saul]

Read and think about what Disney et al has discovered. I repeat what Disney has discovered.

One more time. What Disney has discovered.

http://arxiv.org/ftp/arxiv/papers/0811/0811.1554.pdf

Galaxies appear simpler than expected (My comment why? There is a physical solution this is not magic.)

If, as we have argued, galaxies come from at most a six-parameter set, then for gaseous galaxies to appear as a one-parameter set, as observed here, the theory of galaxy formation and evolution must supply five independent constraint equations to constrain the observations. This is such a stringent set of requirements that it is hard to imagine any theory, apart from the correct one, fulfilling them all. For instance, consider heirarchical galaxy formation in the dark matter model, which has been widely discussed in the literature3,4. Even after extensive simplification, it still contains four parameters per galaxy: mass, spin, halo-concentration index and epoch of formation.

Consider spin alone, which is thought to be the result of early tidal torquing. Simulations produce spins, independent of mass, with a log-normal distribution. Higher-spin discs naturally cannot contract as far; thus, to a much greater extent than for low-spin discs, their dynamics is controlled by their dark halos, so it is unexpected to see the nearly constant dynamical-mass/luminosity ratio that we and others14 actually observe. Heirarchical galaxy formation simply does not fit the constraints set by the correlation structure in the Equatorial Survey.

Higher-spin discs naturally cannot contract as far; thus, to a much greater extent than for low-spin discs, their dynamics is controlled by their dark halos, so it is unexpected to see the nearly constant dynamical-mass/luminosity ratio that we and others actually observe. Heirarchical galaxy formation simply does not fit the constraints set by the correlation structure in the Equatorial Survey.

More generally, a process of hierarchical merging, in which the present properties of any galaxy are determined by the necessarily haphazard details of its last major mergers, hardly seems consistent with the very high degree of organization revealed in this analysis. Hierarchical galaxy formation does not explain the commonplace gaseous galaxies we observe. So much organization, and a single controlling parameter—which cannot be identified for now—argue for some simpler model of formation.

In other words they form a one-parameter set lying on a single fundamental line. Such simplicity was unpredicted and is noteworthy when galaxies might well have been controlled by any six of the seven potentially independent physical parameters listed earlier. It is even more significant considering the enormous variety amongst the galaxies in the sample.

If, as we have argued, galaxies come from at most a six-parameter set, then for gaseous galaxies to appear as a one-parameter set, as observed here, the theory of galaxy formation and evolution must supply five independent constraint equations to constrain the observations. This is such a stringent set of requirements that it is hard to imagine any theory, apart from the correct one, fulfilling them all.