The Universe Is Dark: Dark Matter and Dark Energy

Summary: Dark matter discovered in the 1930s makes up 27% of the universe, while dark energy makes 68% and observable matter makes up just 5% of it. The existence of dark matter is indicated through the gravitational lensing of galaxy clusters, galactic rotational curves, speed of rotation of constituent galaxies in a cluster and hence the calculated mass of the clusters. Dark matter is completely different for ordinary baryonic matter, and communicates through gravitational force only. Different candidate particles like WIMPs, MACHOs and Axions have been predicted. One theory to explain the observations without dark matter is MOND, but it fails for galaxy clusters. On the other hand, a new theory suggests that dark matter is actually in a superfluid state in the galaxies, and helps explain a lot of observed phenomena. Experimental verification still pending. Dark Energy on the other hand is an opposing force to gravity, it repels. Quantum theory suggests it could be the energy of the vacuum. Currently even less is known about it than dark matter. Just that it is enough to avoid collapse of universe due to gravity. It increases with the amount of vacuum. It is exactly the force predicted by the cosmological constant introduced by Einstein, which he called his greatest blunder.


A few days ago I posted about the courses I was undertaking on this online science website, WorldScienceU, an initiative by Brian Greene. One of the courses I took was on dark matter, lectured on by Justin Khoury. This is a post mostly on what I learnt from there, and, some from a couple of books.


Dark Matter: Discovery & Evidence

Universe is vast. No matter which direction you look in, you can see a number of stars, galaxies, and clusters. There are billions of galaxies in the universe, each containing a billion of stars. Contemplating on such huge numbers, you might think that they make up most of the mass of the universe. Shockingly, no. Baryonic matter, i.e. observable matter that you can see and interact with, makes up just 5% of the universe’s mass. The rest is made up by dark matter(27%) and dark energy (68%). Dark matter was discovered first as result of observations by a Caltech scientist, Fritz Zwicky. Zwicky in 1930’s was observing and studying the rotational speed of the constituent galaxies of the Coma cluster(30 million light years away from us), which is a part of the constellation Coma Berenices(hair of Berenices, queen of Egypt). Since orbital velocity depends on gravitation and hence on the amount of mass, studying these speeds, the mass of the cluster can be calculated. When Zwicky calculated this velocity, he found out it was exceedingly higher than the predicted value. Here I should mention that if the velocity of Earth was even 1.141 times higher than its present value, it would attain escape velocity and fling outside the solar system. Hence, due to higher velocities, the galaxies in the Coma cluster should have long separated out, but they haven’t. Coma cluster is one of the oldest clusters, almost from the very early stages of the universe. The only explanation is that gravity should be high, and hence the mass too. But when you add the mass of all the galaxies and the high-energy gases(i.e. the observable ‘normal’ matter) in the cluster, it lacks exceedingly behind. This missing mass has been credited to dark matter. In fact galaxies make up only 1% of the mass, and the high energetic gas makes up 9% of it. The remaining mass of a cluster is due to dark matter. We are a minority. The universe is dark.

coma
Coma cluster

There are other evidences that point towards the existence of dark matter. In 1976, Vera Rubin, of Carnegie Institution of Washington studied the rotation curves of galaxies. Since galaxies spin, and most of the mass(baryonic) is concentrated at the centres, as you move away from the centre, the orbital velocity should decrease monotonically. But to her surprise she found that the observed curve was more or less flat, indicating that the orbital velocity remained almost constant. This could only be possible if there was more mass in the outer regions, that we could see or detect. Rubin called her observation a result of dark matter halos around the galaxies. Another interesting evidence comes from the observed gravitational lensing in the Bullet cluster. This cluster is actually two galactic groups that collided long ago in the past. When they collided, the respective gas clouds of the groups collided and interacted, as normal matter does, and got accumulated around a region. But since dark matter doesn’t interact at all, but only through gravity, the respective dark matter halos passed through each other, and got a bit overshot beyond the gases. Since light bends on account of bending of space-time as predicted by general relativity, which is because of gravity, most of the observed lensing is due to an ’empty’ space separate from the gas clouds(in the image below, lensing is mostly due to the area beyond the blue regions). This is a strong evidence of existence of gravity due to something invisible, called dark matter.

GalaxyRotationCurve
A typical galactic rotation curve.

 

Properties Of Dark Matter

Dark matter doesn’t respond to electromagnetic force, hence there are no dark matter atoms. Also they don’t respond to strong or weak forces. The only observed effect from them is the changes in space-time due to their gravity. One of the predicted particles that might make up dark matter are WIMPs( Weakly Interacting Massive Paricles), or Axions( Far lighter than WIMPs, can transform into photon and vice versa in a strong magnetic field). Neither has been detected yet. They might not even be the right answer and dark matter might be something else completely. The only requirement is that it should have the properties observed. Quite surprisingly, the dark matter required in theory to help in the formation of galaxies and clusters in the early stages after big bang, is six times the ordinary mass, which is almost what is observed. Computer simulations that only contain dark matter show that when it is let to homogeneously evolve, the dark matter clumps in clusters, interconnected by filaments, forming a sort of cosmic web(cover pic). These actually correspond to the galaxies and clusters observed in the universe. Dark matter in galaxies moves really slow, and so is called ‘cold dark matter’(Higher the speed, higher the average kinetic energy, and hence higher the temperature of the particles). Some people theorise that the mass is because of dark matter black holes, though none has been observed yet, these black holes, if any, are completely different from our normal ones as they are not formed by the gravitational collapse of an ordinary star, and hence have to be primordial black holes, i.e. existing since the big bang. How dark matter was created is a mystery. It cannot participate in nuclear reactions, and hence wasn’t formed in the sense ordinary matter was. Awkwardly, terming baryonic matter as ordinary is a misnomer, as it isn’t ordinary at all, it is a tiny part of a universe dictated by dark matter and dark energy, for we can say, they are ordinary, but for present let’s stick to calling baryonic matter as ordinary.

Theories, Relations & Explanations

According to an empirical relation, called the Tully-Fischer relation, the observed matter in a galaxy is directly proportional to the fourth power of the asymptotic orbital velocity(the velocity to which the flat part of the rotation curve extends to). But this velocity should depend on the dark matter in and around the galaxy, hence there must exist a relation between ordinary and dark matter. Simulations also show that around the dark matter clumps, there are orbiting ‘satellite’ clumps of dark matter too, which must correspond to dwarf satellite galaxies around the major galaxy. Accordingly, Milky Way must have hundreds of satellite galaxies spread isotropically (i.e. evenly in every direction), but we have found only 30 of them, and that too in a particular plane and not spread evenly all around. No explanation is available yet. 

5-09-milky-way-satellites
Observe the planar distribution of the dwarf galaxies and their number.

In a new theory, a modification of Newton’s theory of gravitation, correctly called MOND- Modified Newtonian Dynamics, introduced by Mordehai Milgrom,in the region of very low acceleration, like that in galaxies, the Newton’s force formula gets modified as:

F(n)­­= mµ(a/a’)a,

where m= mass of the galaxy/cluster, a= acceleration of the galaxy/cluster, a’= threshold acceleration [=10-10(m/s2), s= radius], and µ= interpolating function which relates Newtonian mechanics to MOND regime i.e. very low accelerations.

µ(a/a’) = √{1+(a/a’)²}

Interestingly, the MOND formula exactly predicts the Tully-Fischer relation. The drawback it suffers is that though it excellently fits the data for individual galaxies, it suffers a major blow when applied to clusters and the cosmic web. You should not mistake this theory and relation as the final correct theory to study dark matter, but this is certain that whatever the ‘right’ and ‘accurate’ formula and theory would be, it should have the same result, or behaviour, as the MOND formula and the empirical Tully-Fischer relation in their regimes. So this gives us a little insight into the nature of dark matter.

A very interesting view-point is offered by Dr. Justin Khoury. His theory suggests that the dark matter in galaxies actually behaves like a superfluid. Superfluids are a state of matter, near absolute zero (o Kelvin), when the atoms don’t freeze but are in a liquid state, with zero viscosity or friction. For example Helium-3 and Helium-4 at 3K become superfluids. When the container containing a superfluid is rotated, the fluid stays still, but when the rate of rotation is increased, unlike ordinary fluids which would spin along, superfluids form tiny vortices in them, and the number of vortices increases with the rotation rate. For dark matter to be in a superfluid state, two conditions must be satisfied. Firstly, the dark matter should aggregate at higher densities. Since the calculated mass of dark matter is very high, the dark matter particles should be very light( around 1% the mass of a proton), in order to accumulate and have high densities. This rules out WIMPs as a possible candidate. Secondly, the dark matter must have a temperature below a critical value. This critical temperature comes out to be around 1K. Assuming the first condition is satisfied, for individual galaxies calculation show that the cold dark matter(i.e. slow moving dark matter) has a temperature of 0.1K and thus satisfy the second condition. The dark matter can certainly exist in a superfluid state. Using superfluid counterparts, research shows that superfluids have a force resembling the MOND force, similar to the one that results in the observed satisfaction of the MOND formula. On the other hand, in clusters, the dark matter moves a bit fast and the calculated temperature is 10K, which is quite high than the critical value. Hence, the dark matter particles are not in a state of superfluidity, and MOND force isn’t observed which explains why the MOND formula fails for clusters and cosmic web. In a superfluid all atoms work coherently i.e in unison. They lose their individuality. Any excitation travels like a longitudinal wave in the superfluid, similar to sound waves, and these excitations are called ‘phonons’. Simulations show that two dark matter blobs when pass through each other, they interfere and form fringes which points to the possible quantum behaviour. Though the existence of fringes can also be explained by conventional models. Superfluid nature of dark matter offers explanation to as why the galaxies in the core of the Fornax dwarf cluster haven’t fused in the centre. If dark matter wasn’t in a superfluid state, when two galaxies collided, they would slowly merge into each other instead of slinging away because of the dynamical friction offered by dark matter due to its gravity, which would pull them to the area of higher concentration. Instead, in a superfluidity state, there is no viscousity, and hence no friction, and the galaxies don’t merge into each other. Similar is the case for the Fornax dwarf cluster. Direct evidence for this superfluid state can be found by detecting the vortices formed in the dark matter cores of galaxies due to their rotation, though this would be really hard because there would be justa few hundreds of them that too in a size of approximately 1mm. The similarity of the mathematical model required for explaining MOND force to the model of superfluidic systems encouraged Dr. Khoury to come up with this theory.

 

Dark Energy

An awfully less is known about dark energy compared to dark matter. Einstein introduced the cosmological constant in his field equations of general relativity to account for a stable, uniform universe. But when Edwin Hubble (or quite infamously Vesto Sipher, whose research went unnoticed) found that the universe was expanding through the red-shifts in the spectra of distant galaxies, Einstein called his cosmological constant his biggest blunder. Years later it was found that the universe’s expansion was accelerating. This was confusing. There had to be some force pushing against the gravitational pull. The answer to this, ironically was found in Einstein’s blunder, his cosmological constant (Λ), which correctly accounted for this force. There is a constant called ‘omega’ (Ω) which is equal to the ratio of the total mass of the universe to the critical mass (i.e. the mass for which the universe would be stable). A value less than one meant the universe was expanding, like a saddle, whereas a value greater than one meant a collapsing universe, while a value of one meant a stationary one. Calculations showed that the value of Ω to be 0.3, which meant the universe was expanding really fast. Research by MIT’s Alan Guth to modify the big bang theory to explain some of the observed data, showed that when the big bang took place as explained by him to result in a universe, as homogenous and isotropic as ours, it accounts for the presence of the accelerated expansion. But for this the mass had to be very very very high. Almost 68% of the predicted mass was unaccounted for even when you add the mass of dark matter with ordinary matter. This mass was the result of ‘dark energy’. Einstein’s mass-energy relation shows that energy is equivalent to mass. Interestingly, using this data, the value of Ω comes out to be just a bit less than one, which excellently fits the data. What exactly is dark energy is a much more difficult question than its counterpart for dark matter. This energy only exists for vacuum. As the vacuum increases, this energy increases. Hence, as the universe expands, the vacuum created increases the dark energy’s value, which accelerates the expansion. Quantum mechanics points that the production of matter-antimatter pairs accounts for this outward pressure, but this results in a 10¹²° higher value than observed. There is no other valid explanation yet to explain this energy.

Conclusion

After more than 2000 words, all we can say is that there exist evidence for something increasing the mass of universe and expanding it. Perhaps our current models and predictions are wrong, but what is certain is that there is something. This something has been called dark matter ( which increases the mass and gravity) and dark energy ( accelerates expansion). They might be particles not yet detected, processes not yet discovered, forces not yet understood, but they are very real, and make up the majority of our universe. They make the universe invisible. They make the universe dark. Happy Reading!

-The Cosmogasmic Person

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