Question B2: What is a galaxy? (Addendum on the relaxation time)

Background:

As introduced in the previous contribution to The Dark Matter Crisis, Question A: Galaxies do not work in LCDM, sociology and majority views, PK was recently contacted by a few people, and here are excerpts from some of the questions asked and the replies. These help to illustrate some of the issues at hand. The questions are

A) So the LCDM model fails on scales smaller than about 8 Mpc?

B1) What is a galaxy?

B2) What is a galaxy? (Addendum on the relaxation time) (this contribution)

C) What are the three best reasons for the failure of the LCDM model?

I: Incompatibility with observations

II: MOND works far too well !

III: Fundamental theoretical problems

 

D) What about the Bullet cluster?  And what about the Train-Wreck cluster Abell 520?

E) Why is the main stream community so reluctant to  go along with accepting the failure of LCDM?

This contribution deals with Question B2, while upcoming contributions will concentrate on the remaining questions.

 


 

Addendum on the relaxation time:

In the previous contribution “Question B: What is a galaxy?” was raised, asking readers to cast a vote after reading the Forbes & Kroupa (2011) paper on this problem.

One of the criteria suggested originially by Kroupa (1998) is to define a galaxy as a stellar-dynamical system of stars which has a  two-body relaxation time (TREL) that is longer than a Hubble time. A star cluster would be a system with TREL being shorter than the age of the universe.

To add a few clarifying  insights on this proposed definition:

This definition implies that a galaxy does not evolve noticeably by energy re-distribution within it over the age of the universe.

A simple well-known example:

Take a box, subdivide it into two equal volumes. Fill one volume with hot gas and the other with cold gas, and then remove the wall between the two volumes. One can measure the time it takes for both sub-volumes of the now one large volume to evolve towards equal temperature. The atoms of the gas bounce off each other thus exchanging their kinetic energy such that after some time the whole combined volume is at the same temperature. The gas has achieved a state of energy equipartition, and the time it takes for the temperature to change significantly in either sub-volume is the energy-equipartition time-scale, or in short TREL.

Now take a stellar-dynamical system (e.g. a star cluster or a galaxy).

Here there are stars moving rapidly and stars moving slowly. They can exchange energy through distant weak gravitational encounters (stars very very rarely collide physically because their separations are vast).  So the fast stars typically slow down, while the slows stars typically speed up, just like the gas atoms in the box.  But, in a gravitationally self-bound system the slowed-down stars fall towards the system center (a stone also falls towards the center of the Earht unless it is thrown with very high speed).  It speeds up as it falls, and is now faster again allowing it to shed its  surplus energy again (a dropped stone gets ever faster until it can do some real damage). This goes on and on, such that a stellar-dynamical system cannot achieve a stable configuration; it cannot achieve a state of energy equipartition – there is an instability which stellar-dynamicists refer to as a “gravo-thermal catastrophe”. The slow stars, on the other hand, typically gain speed and climb outwards thereby becoming slower (a stone thrown upwards also slows down). So they can again acquire kinetic enegy if they encounter a faster star. Thus, slow stars typically move outwards, and at some point they can be lost from the system. Note though that all of this is a statistical process: a fast star can become a slow star and vice versa. Mathematically, one treats these processes through studying the rate of energy diffusion.

A stellar-dynamical system such as a galaxy or a star-cluster thus looses stars through the process of energy equipartition. This happens on a TREL time scale.

Thus, over the age of the universe, a “galaxy” does not loose many stars though this process, while a star cluster does.

Mathematically,

when stellar-dynamicists study the evolution of a stellar-dynamical system, it is necessary to calculate every single gravitational encounter between two distant stars, if TREL is short. This requires extremely sophisticated and highly complex mathematical and algorithmic approaches and is highly computationally demanding. Such techniques have been under development over decades leading to sophisticated but non-trivial computer programmes, notably the Nbody4, Nbody5, Nbody6 codes by Dr. Sverre Aarseth in Cambridge. Thus, to compute the evolution of a small globular cluster with some 100,000 stars today requires the fastest super-computers. A large globular cluster with more stars is beyond current computational means.  A star cluster with a million stars requires a computer a thousand times faster to do the calculation in the same human time as for a cluster with 100,000 stars!

Thus, galaxies with many more times a million stars cannot be computed with this direct-N-body technique using current technology.

But, because they have a TREL longer than the age of the universe, astrophysicists can use a different mathematical approach altogether to compute galaxies. Instead of solving the 6N coupled first-order differential equations they can solve the Collisionless Boltzmann Equation. Here N is the number of stars in the system, and “collisionless” means that the gravitational encounters between stars are not important, which is the case when TREL is very long.

By being able to ignore the many distant weak gravitational encountes between two stars, astrophysicists can treat each star as moving in the average smooth gravitational field generated by all the other stars. This is like calculating the trajectory of a cannon ball in Earth’s gravitational field. So the computational problem becomes significantly easier and astrophysicists can calculate the evolution and the interactions of galaxies with modern computers.

In fact, some of the mathematical methods being used, e.g. in the Stellar-Populations and -Dynamics Research Group in Bonn are so fast that present-day laptops can be used to compute the evolution of a few galaxies over the time of the universe, taking no longer than a few hours, if at all, of human time.

But this is only possible for systems of stars with TREL longer than the age of the universe.

Now, what happens when the universe is twice its age (about 28 Gyr)? Not much: what we call a galaxy today will still be a galaxy then, except that the transition mass where TREL is about the age of the universe, will have shifted by a factor of four.

What happens when the universe is ten times older? Well, then the objects we today call transition-type objects or ultra compact dwarf (UCD) galxies will have evolved partially through the energy equipartition process, similarly to the present-day massive globular clusters.

 

By Pavel Kroupa and Marcel Pawlowski (23.01.2011): “Question B2: What is a galaxy?  (Addendum on the relaxation time)” on SciLogs. See the overview of topics in  The Dark Matter Crisis.

Question B1: What is a galaxy?


Question B1: “What is a galaxy?  – vote here!”

 

Answer: The astronomical object we commonly call a “galaxy” has no formal definition yet. This issue is now raised to a more formal problem by Forbes & Kroupa (2011)(F&K).

Here is the associated press release.

Science and New Scientist also report on this question.

Your vote is of interest: Being motivated by the vote at the General Assembly of the International Astronomical Union in Prague in the year 2006 on Pluto’s status in the Solar System and given the lack of a formal definition of what constitutes a “galaxy”, Prof. Duncan Forbes from Swinburne University in Melbourne has organised a poll to seek if a consensus may emerge how a galaxy could perhaps be defined. To contribute to the poll, feel free to cast your vote here as to what you think a galaxy is. But please read the above F&K paper first.

And, feel free to post your own views on what a galaxy is in the comments section below.

The results of the poll and of the discussion will be reported at conferences.

 


 

Background:

As introduced in the previous contribution to The Dark Matter Crisis, Question A: Galaxies do not work in LCDM, sociology and majority views, PK was recently contacted by a few people, and here are excerpts from some of the questions asked and the replies. These help to illustrate some of the issues at hand. The questions are

A) So the LCDM model fails on scales smaller than about 8 Mpc?

B1) What is a galaxy? (this contribution)

B2) What is a galaxy? (Addendum on the relaxation time) 

C) What are the three best reasons for the failure of the LCDM model?

I: Incompatibility with observations

II: MOND works far too well !

III: Fundamental theoretical problems

 

D) What about the Bullet cluster?  And what about the Train-Wreck cluster Abell 520?

E) Why is the main stream community so reluctant to  go along with accepting the failure of LCDM?

This contribution deals with Question B1, while upcoming contributions will concentrate on the remaining questions.

 

Traditional ideas seen from a modern perspective:

The word “galaxy” comes from the Greek word for “milky circle”. The discovery of galaxies as extra-galactic objects is a fascinating part of science history and is outlined for example in the Wikipedia article on Galaxy.

In the standard LCDM model galaxies are the central typically 0.2-40kpc large region weighing a few per cent of mass of a vast dark matter halo which is about ten times larger in extend. Each galaxy has a distinct and typically violent formation history as a result of the coalescence and merging of smaller dark-matter halos. It is part of a complex dynamic environment. A large range of properties of galaxies is thus expected, with the more massive galaxies being expected to appear later in time and in denser environments.

Modern research however is indicating galaxies to be more like true island universes, as originally thought by Immanuel Kant in the middle of the 18th century. Indeed, the large fraction of all major galaxies are large thin disk galaxies, in which stars and gas move about a common center of gravity on near-circular orbits. In disk galaxies new stars can form from the cold gas. In the seminal paper “Galaxies appear simpler than expected“, Disney et al. (2008, Nature) demonstrate the followig:

Disk galaxies are  observed to look las if they formed and evolved largely isolated, one galaxy loooking more or less like another (thin disk, nobulge, typical profile with a scalelength that can be predicted approximately if the luminosity is known). Ony the minority show evidence for strong interactions and important influence from the environment.  Galaxies form a one-parameter family, meaning that there is one parameter which defines most of the appearance of the galaxy. Based on the sample of about 560 galaxies in the Local Volume Peebels & Nusser (2010, Nature), in their paper on “Nearby galaxies as pointers to a better theory of cosmic evolution“, also describe galaxies to be “island universes”.

But, as one goes to lower masses, at which point does one enter the regime of star clusters? Can a galaxy be composed of merely 1000 stars? Can a star cluster be composed of ten million stars? A disc galaxy today consists mostly of stars with about 10-20 % of mass in gas. But there are also dwarf and massive elliptical galaxies, in which star formation is not proceeding any longer. They look red as they are composed mostly of older stars which orbit on randomly oriented orbits about a common center of mass.

It is the low-mass, faint end which is now challenging our understanding of what a galaxy actually is.

Does a stellar population consisting of say, 100,000  stars, which is called a “galaxy” have different  properties to a “star cluster” which consists of 100,000 stars? Or is there a regime where such a distinction between galaxy and star cluster is no longer possible?

 

Some modern ideas:

How to define a galaxy is becoming an issue given that the large modern telescopes and the simultaneous spectroscopic observations of many sources in large fields of view have lead to the discovery of small stellar-populations, which can be called large star clusters or small galaxies.

The observational break-through came with the PhD thesis of Dr. Michael Hilker (PhD thesisHilker et al. 1999), who was then working in Bonn with Dr. Tom Richtler and Prof. Klaas S. de Boer. Nearly simultaneously an Autralian-British-American team made the same discovery as documented by their paper “Compact stellar systems in the Fornax Cluster: Super-massive star clusters or extremely compact dwarf galaxies?” (Drinkwater et al. 2000). They were later named “ultra compact dwarf galaxies” (UCDs) by Phillips et al. (2001).

Tradionally, an astronomer would refer to a star cluster as being a population of stars which are gravitationally bound to each other and all of which have the same age and chemical composition. But, today we know that “star clusters” exist that contain stars which do not have the same chemical composition, nor the same age. A prime example is Omega Centauri, which is traditionally known as the most massive star cluster in the Milky Way weighing about 3 million solar masses. Hilker & Richtler (2000) have done a seminal study of this object demonstrating that it seems to contain stars with ages that differ by up to 6 Gyr. That is, star formation seems to have gone on for 6 Gyr in this “star cluster”. Until then it was thought that only galaxies could do this. Furthermore some of the satellite “dwarf spheroidal (dSph) galaxies” around the MilkyWay appear to have only a few thousand stars (Strigari et al. 2008, Nature). Remember that the star cluster Pleiades contains only about a thousand stars.

That the distinction between star clusters and spheroidal dwarf galaxies was becoming blurred was actually realised somewhat earlier by Pavel Kroupa. Having seen the amasing HST images of the interacting pair of Antennae galaxies where the inner parts of the extensive tidal arms  are littered with thousands of newly formed star clusters, it was immediately apparent that many of the clusters were clustered into larger aggregates, groups, complexes or superclusters of star clusters. The star clusters in the cluster complexes must be interacting gravitationally. What sort of object evolves if the many clusters in a complex merge? Kroupa (1998) quantified the resulting objects showing that spheroidal dwarf galaxies emerge from the merging star clusters.

This research lead to many follow-on papers dealing with the evolution of star-cluster complexes under various conditions (see PhD thesis of Michael Fellhauer, and Fellhauer et al. 2002). It has emerged that Omega-Centauri-type objects, that dSph-galaxy-type objects and UCD-type objects can be formed, depending on the mass, size and tidal field. Also, “star clusters” which also have a large radius can be explained as merged superclusters (Fellhauer & Kroupa 2002, Bruens & Kroupa 2010).

A formal definition between a galaxy and a star cluster was introduced by Kroupa (1998) who defined a galaxy to be a stellar-dynamical system of stars which has a median two-body relaxation time longer than a Hubble time. Mathematically this is equivalent to stating that a galaxy has a smooth potential, that is, that there are no irregularities in the potential for the stars to scatter on significantly over the age of the universe.

What is a two-body relaxation time?  In any self-gravitating stellar population the stars constantly exchange gravitational and kinetic energy with each other. When two stars pass each other, they give each other tiny gravitational nudges. This is also happening in the Solar System between its planets – as a result of the ongoing gravitational pulls the planets are changing their orbital eccentricities and periods all the time. In a stellar system, these tiny nudges between the stars cause the system to evolve towards energy equipartition as a result of which it changes its overall morhpology (its radius, and the radial distribution of its stars). The time-scale over which the system re-arranges itself significantly is measured in terms of the median two body relaxation time. One can say that after a relaxation time, a stellar system has “relaxed”, that is, that it has significantly evolved towards energy equipartition.

Note that defining a galaxy to be a stellar-dynamical system with a median two-body relaxation time longer than the age of the universe is the same as defining it to be a system in which the time-scale for energy-equipartition is longer than a Hubble time. Energy equipartition between stars is therefore not an important process in a galaxy. A star cluster, on the other hand, has an energy-equipartition time-scale shorter than the age of the universe. Thus, energy equipartition plays a significant role in the evolution of a star cluster.

Note that a system of stars being “relaxed” is not synonymous with the system being in dynamical equilibium. A system achieves dynamical equilibrium within a few crossing times, but it may not be relaxed. The crossing time is the time a typical star needs to cross through the system (e.g. it is about 200 Myr for the Milky Way near the Solar radius) and it is much shorter than the two-body relaxation time which is many times 13 Gyr for the Milky Way. A system in dynamical equilibrium means that the star cluster or galaxy does not “wobble”, that is, its radius for example, does not evolve or change, unless one is looking at it over time-scales similar to a relaxation time.

Thus, according to Kroupa’s definition, a galaxy has not had enough time to relax. A star cluster, on the other hand, being defined to be a stellar system with a median two-body relaxation time which is shorter than a Hubble time, does relax. And, in the process of relaxation, a star cluster evaporates its stars, and thus looses mass. If the relaxation time is sufficiently short, e.g. if it is only a small fraction of the age of the universe, then a star cluster will completely evaporate leaving not more than a few stars in orbit about each other. Globular clusters have a two-body relaxation time of roughly 100 Myr to a few Gyr, so they are still around. Open star clusters, such as the Pleiades or Hyades, have a two-body relaxation time of a few tens Myr such that they dissolve as they age, both having in fact already lost the majority of their stars which they were born with.

Now, it emerges that Kroupa’s definition of a galaxy implies that every known object which has so far been called a galaxy remains a galaxy, while Omega Centauri would formally be a star cluster, but can also be viewed as a low-mass UCD galaxy. Omega Cen is a transition-type object, with properties between those of a star cluster (two-body relaxation time slightly shorter than a Hubble time) and those of a true galaxy (complex stellar population).

Noteworthy is however that dark matter only appears in systems with a median two-body relaxation time longer than a Hubble time, as is demonstrated by Dabringhausen, Hilker & Kroupa (2008). That is, according to Kroupa, dark matter only appears  in “galaxies”.

But why should dark matter care about the relaxation time of a stellar system?

Or, is a “galaxy” simply a system which behaves according to Milgrom’s law of dynamics?

What do you think constitutes a galaxy? Vote here! and discuss below.

By Pavel Kroupa and Marcel Pawlowski (19.01.2011): “Question B1: What is a galaxy?” on SciLogs. See the overview of topics in  The Dark Matter Crisis.

Question A: Galaxies do not work in LCDM, sociology and majority views

Independently of any dark-matter detections or the success or failure of dark-matter searches

(it is notable that the originally favoured dark matter particles have long ago been excluded through direct searches, as summarised by Prof. Stacy McGaugh),

it is a well known problem that galaxies cannot be reproduced in the standard cosmological (i.e. the LCDM) scenario. In the LCDM model, the mass of the universe consists to about 4 % out of normal (baryonic) matter which we observe, while 96% is in an unknown dark form (about 22 % being the exotic cold dark matter and about 74% being in dark energy).

Since the large fraction of astronomers (about 95 % as is often stated) and physicists are convinced that the LCDM model is the correct description of the cosmological universe, a vast industry has been established world-wide to try to solve the failure of LCDM on galaxy scales. Each year hundreds of research papers are spurned out by excellently funded reseach groups claiming to solve some aspect of the problem.

For example, many research papers deal with the question why there are only about two dozen satellite galaxies around the Milky Way, while there ought to be many thousands of satellite dark matter halos around the Milky Way (the Missing Satellite Problem). Why are the satellite galaxies of the Milky Way distributed so unevenly about the Milky Way, forming a giant disk-like distribution which is nearly perpendicularly oriented to the disk of the Milky Way (the Satellite Anisotropy Problem)? Another issue of focuss is why the dark matter halos inferred from observations have cores, while the LCDM model predicts them to have dense central regions, i.e. cusps (the Core-Cusp Problem). Another issue being worked on in much detail is why there are large thin disk galaxies with no bulges (the Angular-Momentum Problem). Why are disk galaxies, which by the way are the majority of all galaxies, all so simple (the Invariant Galaxy Problem)?  Why do large elliptical galaxies appear so rapidly after the Big Bang even though they must have been build-up from pre-existing galaxies in the LCDM model, according to which galaxies form through myriads of mergers of smaller dark matter halos that already have a normal-matter content in the form of stars and gas. Why are the predicted building blocks (these dwarf galaxies) observed to be younger than the large elliptical galaxies, although they should be older because the small dark matter halos form before the large ones (the Downsizing Probem)? Or, why is there an observed strong conspiracy between the distribution of normal (baryonic) matter and dark matter in all disk galaxies? This Conspiracy Problem has not been solved although it is known since decades. And, related to this, why is there no observational evidence for dark matter in dwarf-elliptical galaxies and large elliptical galaxies within their visible regions? Why does dark matter always only appear when the surface density of normal matter falls below a critical level? The surface density is but the gravitational acceleration – so, why should dark matter decide to appear when the acceleration falls below a critical threshold, which happens to be the same for all galaxies (the Dark Matter Emergence Probem)? Note that this is a purely observationally established fact, highlighted recently by Gentile et al.(2009, Nature) without any implication, as yet, of hidden deeper physics.

 

There is a very large number of research papers dealing with each of these aspects, and by adjusting various parts of the modelling, certain problems can be reduced. Each year many new research papers appear attempting to deal with some of the problems. But the real issue is whether a proposed solution to any one of the problems is consistent with the solution to any one of the other problems.

For example, the formation of stars in small dark matter halos can be delayed by introducing re-ionisation at a special time in the universe. Re-ionisation means the re-heating of the cooled gas after the Big Bang through radiation which is intense enough to knock electrons from the hydrogen nuclei. When an electron gets knocked out, the nucleus and electron depart with much energy, the resulting ionised gas being heated to 10000 Kelvin. This may indeed have happened because luminous sources like the first massive stars or active galactic nuclei or quasars appear. The gas, or more correctly the plasma, is then too hot to be captured by the dwarf dark matter halos existing at that time.

But, is this resulting model then able to explain elliptical galaxies, or, the observed cores of dwarf galaxies, at the same time? And, are the observed ages of stars in dwarf galaxies consistent with this delay through re-ionisation?

So while there is a vast research literature claiming success on individual problems, the large picture is usually not addressed, the cross-referencing to other problems affected by the particular solution is rarely if ever attempted. Given this situation, we decided to approach this issue of consistency by testing the excellent observational data that is available for the Local Group of galaxies.

A view sometimes voiced is that the LCDM model is right and that galaxies are merely non-linear small-scale weather phenomenawhich cannot be computed adequately so it is not surprising that there are problems. It is sometimes stated that these problems are not major and that the LCDM model does excellently on larger-than-galaxy scales.

There is some truth to these statements, because going from a full cosmological computer simulation down to what happens in individual galaxies requires a tremendous numerical resolution, ranging from Gpc down to pc scales. So often computational short-cuts are required.

It is therefore necessary to devise tests of the theory which capture the essence of the LCDM model. That is, any scrutiny of the LCDM model must not test issues that rely on the details of the star-formation recipes used, but must deal with general aspects related to overall conservation laws which must be valid in the LCDM model as in any other. Such tests lead to the realisation that the failure of the LCDM model on galaxy scales is, figuratively speaking, akin to a weather model which predicts constant snowfall in the Sahara.

PK was recently contacted by a few people, and here are excerpts from some of the questions asked and the replies. These help to illustrate some of the issues at hand. The questions are

A) So the LCDM model fails on scales smaller than about 8 Mpc? (this contribution)

B1) What is a galaxy?

B2) What is a galaxy? (Addendum on the relaxation time)

C) What are the three best reasons for the failure of the LCDM model?

I: Incompatibility with observations

II: MOND works far too well ! 

III: Fundamental theoretical problems

 

D) What about the Bullet cluster?  And what about the Train-Wreck cluster Abell 520?

E) Why is the main-stream community so reluctant to go along with accepting the failure of LCDM?

This contribution deals with Question A, while upcoming contributions will concentrate on the other questions.


Question A: “So, in your view, LCDM fails on the local level, i.e. on scales below about 8 Mpc in the local universe?”

Answer: Indeed, and with high significance. Do remember that I had worked happily within this framework, that is,  I find the original hypothesis of LCDM (i.e. there is cold dark matter) as being reasonable, although I had never bothered to check on inflation or dark energy.

The argument comes two-fold. First there are  the properties of the Local Volume of Galaxies. Then there are the properties of the Local Group of galaxies, the latter being contained in the former and providing, not surprisingly, much better data on the individual-galaxy scale.

The Local Volume of galaxies consists of the local region of the universe within a sphere around the Sun with a radius of about 8 Mpc. It contains about 560 known galaxies which are distributed in a large sheet. It also contains a void which is far too empty in comparison with the expectations from the LCDM model. Near the edge of the Local Sheet of galaxies which we inhabit are three major disk galaxies that ought not to be in such isolated regions. In their paper “Nearby galaxies as pointers to a better theory of cosmic evolutionPeebles & Nusser (2010, Naure) write “… the properties of nearby galaxies that can be observed in greatest detail suggest that a better theory would describe a mechanism by which matter is more rapidly gathered into galaxies and groups of galaxies. This more rapid growth occurs in some theoretical ideas now under discussion.” On p.568 they state :

The variety of problems we have considered in the interpretation of
the present baseline motivates serious consideration of adjustments of
the fundamental theory. Any adjustment would have to preserve the
properties of the standard cosmology that agree with the cosmological
tests but that allow new physics operating on the scale of galaxies. The
evidence for more-rapid structure formation agrees with what happens
in modifications of the gravity physics of the general theory of relativity
and in general relativity with a long-range force acting only on
the dark matter.”

Effectively these authors state that: Either gravity needs to be modified – for example, in MOND structures do grow more rapdily as has been explicitly computed by Claudio Llinares et al. (2008). Or, an additional “dark force (DF1)” needs to be postulated to act only between dark matter particles leading to the GR+I+DM+DE+DF1 model (a model based on the general theory of relativity + inflation + cold dark matter + dark energy + dark force). A “second dark force (DF2)” must, however, also exist, in order to account for the observed fact that dark matter arranges itself according to the distribution of normal (baryonic) matter  –  the observed strong conspiracy between baryonic and dark matter is one of the very well known and hitherto not solved problems in LCDM – see  Pfenniger & Combes (1994). Following the line of thought of Peebles & Nusser, we would then arrive at the  GR+I+DM+DE+DF1+DF2 model. Note that this model of the universe is then made essentially only of unkown stuff. Pfenniger & Combes try to solve the conspiracy by suggesting that the dark matter is in the form of cold molecular-hydrogen clouds which cannot be observed. Needless to say, the Conspiracy Problem (CP) is naturally resolved by MOND – in MOND the CP does not even appear.

The Local Group of galaxies is the local region of the universe within a sphere around the Sun with a radius of about 1.5 Mpc. It contains two major disk galaxies (the Milky Way and Andromeda), two smaller disk galaxies (Triangulum or M33 and the Large Magellanic Cloud) and about 40 known dwarf galaxies most of which are satellites of the two major disks. The Local Group is a gravitationally bound, that is, it is a region which has decoupled from the cosmologically expanding Hubble flow.

Our work shows that the satellite galaxies around Andromeda and the Milky Way cannot be accounted for by the LCDM model, and that Andromeda and the Milky Way are too similar given the large variation of galaxies expected in the LCDM model. This is covered in depth by “Local-Group tests of dark-matter concordance cosmology. Towards a new paradigm for structure formation(Kroupa et al. 2010)  in which the large body of recently published research, which claims that the LCDM model can account for the Local Group satellite galaxies, is scrutinised carefully using a variety of tests.

By Pavel Kroupa and Marcel Pawlowski (17.01.2011): “Question A: Galaxies do not work in LCDM, sociology and majority views” on SciLogs. See the overview of topics in  The Dark Matter Crisis.