Tag Archives: clusters of galaxies

Emergent Gravity: Verlinde’s Proposal

In a previous blog entry I give some background around Erik Verlinde’s proposal for an emergent, thermodynamic basis of gravity. Gravity remains mysterious 100 years after Einstein’s introduction of general relativity – because it is so weak relative to the other main forces, and because there is no quantum mechanical description within general relativity, which is a classical theory.

On reason that it may be so weak is because it is not fundamental at all, that it represents a statistical, emergent phenomenon. There has been increasing research into the idea of emergent spacetime and emergent gravity and the most interesting proposal was recently introduced by Erik Verlinde at the University of Amsterdam in a paper “Emergent Gravity and the Dark Universe”.

A lot of work has been done assuming anti-de Sitter (AdS) spaces with negative cosmological constant Λ – just because it is easier to work under that assumption. This year, Verlinde extended this work from the unrealistic AdS model of the universe to a more realistic de Sitter (dS) model. Our runaway universe is approaching a dark energy dominated dS solution with a positive cosmological constant Λ.

The background assumption is that quantum entanglement dictates the structure of spacetime, and its entropy and information content. Quantum states of entangled particles are coherent, observing a property of one, say the spin orientation, tells you about the other particle’s attributes; this has been observed in long distance experiments, with separations exceeding 100 kilometers.

400px-SPDC_figure.pngIf space is defined by the connectivity of quantum entangled particles, then it becomes almost natural to consider gravity as an emergent statistical attribute of the spacetime. After all, we learned from general relativity that “matter tells space how to curve, curved space tells matter how to move” – John Wheeler.

What if entanglement tells space how to curve, and curved space tells matter how to move? What if gravity is due to the entropy of the entanglement? Actually, in Verlinde’s proposal, the entanglement entropy from particles is minor, it’s the entanglement of the vacuum state, of dark energy, that dominates, and by a very large factor.

One analogy is thermodynamics, which allows us to represent the bulk properties of the atmosphere that is nothing but a collection of a very large number of molecules and their micro-states. Verlinde posits that the information and entropy content of space are due to the excitations of the vacuum state, which is manifest as dark energy.

The connection between gravity and thermodynamics has been around for 3 decades, through research on black holes, and from string theory. Jacob Bekenstein and Stephen Hawking determined that a black hole possesses entropy proportional to its area divided by the gravitational constant G. String theory can derive the same formula for quantum entanglement in a vacuum. This is known as the AdS/CFT (conformal field theory) correspondence.

So in the AdS model, gravity is emergent and its strength, the acceleration at a surface, is determined by the mass density on that surface surrounding matter with mass M. This is just the inverse square law of Newton. In the more realistic dS model, the entropy in the volume, or bulk, must also be considered. (This is the Gibbs entropy relevant to excited states, not the Boltzmann entropy of a ground state configuration).

Newtonian dynamics and general relativity can be derived from the surface entropy alone, but do not reflect the volume contribution. The volume contribution adds an additional term to the equations, strengthening gravity over what is expected, and as a result, the existence of dark matter is ‘spoofed’. But there is no dark matter in this view, just stronger gravity than expected.

This is what the proponents of MOND have been saying all along. Mordehai Milgrom observed that galactic rotation curves go flat at a characteristic low acceleration scale of order 2 centimeters per second per year. MOND is phenomenological, it observes a trend in galaxy rotation curves, but it does not have a theoretical foundation.

Verlinde’s proposal is not MOND, but it provides a theoretical basis for behavior along the lines of what MOND states.

Now the volume in question turns out to be of order the Hubble volume, which is defined as c/H, where H is the Hubble parameter denoting the rate at which galaxies expand away from one another. Reminder: Hubble’s law is v = H \cdot d where v is the recession velocity and the d the distance between two galaxies. The lifetime of the universe is approximately 1/H.


The value of c / H is over 4 billion parsecs (one parsec is 3.26 light-years) so it is in galaxies, clusters of galaxies, and at the largest scales in the universe for which departures from general relativity (GR) would be expected.

Dark energy in the universe takes the form of a cosmological constant Λ, whose value is measured to be 1.2 \cdot 10^{-56} cm^{-2} . Hubble’s parameter is 2.2 \cdot 10^{-18} sec^{-1} . A characteristic acceleration is thus H²/ Λ or 4 \cdot 10^{-8}  cm per sec per sec (cm = centimeters, sec = second).

One can also define a cosmological acceleration scale simply by c \cdot H , the value for this is about 6 \cdot 10^{-8} cm per sec per sec (around 2 cm per sec per year), and is about 15 billion times weaker than Earth’s gravity at its surface! Note that the two estimates are quite similar.

This is no coincidence since we live in an approximately dS universe, with a measured  Λ ~ 0.7 when cast in terms of the critical density for the universe, assuming the canonical ΛCDM cosmology. That’s if there is actually dark matter responsible for 1/4 of the universe’s mass-energy density. Otherwise Λ could be close to 0.95 times the critical density. In a fully dS universe, \Lambda \cdot c^2 = 3 \cdot H^2 , so the two estimates should be equal to within sqrt(3) which is approximately the difference in the two estimates.

So from a string theoretic point of view, excitations of the dark energy field are fundamental. Matter particles are bound states of these excitations, particles move freely and have much lower entropy. Matter creation removes both energy and entropy from the dark energy medium. General relativity describes the response of area law entanglement of the vacuum to matter (but does not take into account volume entanglement).

Verlinde proposes that dark energy (Λ) and the accelerated expansion of the universe are due to the slow rate at which the emergent spacetime thermalizes. The time scale for the dynamics is 1/H and a distance scale of c/H is natural; we are measuring the time scale for thermalization when we measure H. High degeneracy and slow equilibration means the universe is not in a ground state, thus there should be a volume contribution to entropy.

When the surface mass density falls below c \cdot H / (8 \pi \cdot G) things change and Verlinde states the spacetime medium becomes elastic. The effective additional ‘dark’ gravity is proportional to the square root of the ordinary matter (baryon) density and also to the square root of the characteristic acceleration c \cdot H.

This dark gravity additional acceleration satisfies the equation g _D = sqrt  {(a_0 \cdot g_B / 6 )} , where g_B is the usual Newtonian acceleration due to baryons and a_0 = c \cdot H is the dark gravity characteristic acceleration. The total gravity is g = g_B + g_D . For large accelerations this reduces to the usual g_B and for very low accelerations it reduces to sqrt  {(a_0 \cdot g_B / 6 )} .

The value a_0/6 at 1 \cdot 10^{-8} cm per sec per sec derived from first principles by Verlinde is quite close to the MOND value of Milgrom, determined from galactic rotation curve observations, of 1.2 \cdot 10^{-8} cm per sec per sec.

So suppose we are in a region where g_B is only 1 \cdot 10^{-8} cm per sec per sec. Then g_D takes the same value and the gravity is just double what is expected. Since orbital velocities go as the square of the acceleration then the orbital velocity is observed to be sqrt(2) higher than expected.

In terms of gravitational potential, the usual Newtonian potential goes as 1/r, resulting in a 1/r^2 force law, whereas for very low accelerations the potential now goes as log(r) and the resultant force law is 1/r. We emphasize that while the appearance of dark matter is spoofed, there is no dark matter in this scenario, the reality is additional dark gravity due to the volume contribution to the entropy (that is displaced by ordinary baryonic matter).


Flat to rising rotation curve for the galaxy M33

Dark matter was first proposed by Swiss astronomer Fritz Zwicky when he observed the Coma Cluster and the high velocity dispersions of the constituent galaxies. He suggested the term dark matter (“dunkle materie”). Harold Babcock in 1937 measured the rotation curve for the Andromeda galaxy and it turned out to be flat, also suggestive of dark matter (or dark gravity). Decades later, in the 1970s and 1980s, Vera Rubin (just recently passed away) and others mapped many rotation curves for galaxies and saw the same behavior. She herself preferred the idea of a deviation from general relativity over an explanation based on exotic dark matter particles. One needs about 5 times more matter, or about 5 times more gravity to explain these curves.

Verlinde is also able to derive the Tully-Fisher relation by modeling the entropy displacement of a dS space. The Tully-Fisher relation is the strong observed correlation between galaxy luminosity and angular velocity (or emission line width) for spiral galaxies, L \propto v^4 .  With Newtonian gravity one would expect M \propto v^2 . And since luminosity is essentially proportional to ordinary matter in a galaxy, there is a clear deviation by a ratio of v².


 Apparent distribution of spoofed dark matter,  for a given ordinary (baryonic) matter distribution

When one moves to the scale of clusters of galaxies, MOND is only partially successful, explaining a portion, coming up shy a factor of 2, but not explaining all of the apparent mass discrepancy. Verlinde’s emergent gravity does better. By modeling a general mass distribution he can gain a factor of 2 to 3 relative to MOND and basically it appears that he can explain the velocity distribution of galaxies in rich clusters without the need to resort to any dark matter whatsoever.

And, impressively, he is able to calculate what the apparent dark matter ratio should be in the universe as a whole. The value is \Omega_D^2 = (4/3) \Omega_B where \Omega_D is the apparent mass-energy fraction in dark matter and \Omega_B is the actual baryon mass density fraction. Both are expressed normalized to the critical density determined from the square of the Hubble parameter, 8 \pi G \rho_c = 3 H^2 .

Plugging in the observed \Omega_B \approx 0.05 one obtains \Omega_D \approx 0.26 , very close to the observed value from the cosmic microwave background observations. The Planck satellite results have the proportions for dark energy, dark matter, ordinary matter as .68, .27, and .05 respectively, assuming the canonical ΛCDM cosmology.

The main approximations Verlinde makes are a fully dS universe and an isolated, static (bound) system with a spherical geometry. He also does not address the issue of galaxy formation from the primordial density perturbations. At first guess, the fact that he can get the right universal \Omega_D suggests this may not be a great problem, but it requires study in detail.

Breaking News!

Margot Brouwer and co-researchers have just published a test of Verlinde’s emergent gravity with gravitational lensing. Using a sample of over 33,000 galaxies they find that general relativity and emergent gravity can provide an equally statistically good description of the observed weak gravitational lensing. However, emergent gravity does it with essentially no free parameters and thus is a more economical model.

“The observed phenomena that are currently attributed to dark matter are the consequence of the emergent nature of gravity and are caused by an elastic response due to the volume law contribution to the entanglement entropy in our universe.” – Erik Verlinde


Erik Verlinde 2011 “On the Origin of Gravity and the Laws of Newton” arXiv:1001.0785

Stephen Perrenod, 2013, 2nd edition, “Dark Matter, Dark Energy, Dark Gravity” Amazon, provides the traditional view with ΛCDM  (read Dark Matter chapter with skepticism!)

Erik Verlinde 2016 “Emergent Gravity and the Dark Universe arXiv:1611.02269v1

Margot Brouwer et al. 2016 “First test of Verlinde’s theory of Emergent Gravity using Weak Gravitational Lensing Measurements” arXiv:1612.03034v


Galaxy Clusters Probe Dark Energy

Rich (large) clusters of galaxies are significant celestial X-ray sources. In fact, large clusters of galaxies typically contain around 10 times as much mass in the form of very hot gas as is contained in their constituent galaxies.

Moreover, the dark matter content of clusters is even greater than the gas content; typically it amounts to 80% to 90% of the cluster mass. In fact, the first detection of dark matter’s gravitational effects was made by Fritz Zwicky in the 1930s. His measurements indicated that the galaxies were moving around much faster than expected from the known galaxy masses within the cluster.


Image credit: X-ray: NASA/CXC/Univ. of Alabama/A. Morandi et al; Optical: SDSS, NASA/STScI (X-ray emission is shown in purple)

The dark matter’s gravitational field controls the evolution of a cluster. As a cluster forms via gravitational collapse, ordinary matter falling into the strong gravitational field interacts via frictional processes and shocks and thermalizes at a high temperature in the range of 10 to 100 million degrees (Kelvins). The gas is so hot, that it emits X-rays due to thermal bremsstrahlung.

Recently, Drs. Morandi and Sun at the University of Alabama have implemented a new test of dark energy using the observed X-ray emission profiles of clusters of galaxies. Since clusters are dominated by the infall of primordial gas (ordinary matter) into dark matter dominated gravitational wells, then X-ray emission profiles – especially in the outer regions of clusters – are expected to be similar, after correcting for temperature variations and the redshift distance. Their analysis also considers variation in gas fraction with redshift; this is found to be minimal.

Because of the self similar nature of the X-ray emission profiles, X-ray clusters of galaxies can serve as cosmological probes, a type of ‘standard candle’. In particular, they can be used to probe dark energy, and to look at the possibility of the variation of the strength of dark energy over multi-billion year cosmological time scales.

The reason this works is that cluster development and mass growth, and corresponding temperature increase due to stronger gravitational potential wells, are essentially a tradeoff of dark matter and dark energy. While dark matter causes a cluster to grow, dark energy inhibits further growth.

This varies with the redshift of a cluster, since dark energy is constant per unit volume as the universe expands, but dark matter was denser in the past in proportion to (1 + z)^3, where z is the cluster redshift. In the early universe, dark matter thus dominated, as it had a much higher density, but in the last several billion years, dark energy has come to dominate and impede further growth of clusters.

The table below shows the percentage of the mass-energy of the universe which is in the form of dark energy and in the form of matter (both dark and ordinary) at a given redshift, assuming constant dark energy per unit volume. This is based on the best estimate from Planck of 68% of the total mass-energy density due to dark energy at present (z = 0). Higher redshift means looking farther back in time. At z = 0.5, around 5 billion years ago, matter still dominated over dark energy, but by around z = 0.3 the two are about equal and since then (for smaller z) dark energy has dominated. It is only since after the Sun and Earth formed that the universe has entered the current dark energy dominated era.

Table: Total Matter & Dark Energy Percentages vs. z 


Dark Energy percent

Matter percent



















The authors analyzed data from a large sample consisting of 320 clusters of galaxies observed with the Chandra X-ray Observatory. The clusters ranged in redshifts from 0.056 up to 1.24 (almost 9 billion years ago), and all of the selected clusters had temperatures measured to be equal to or greater than 3 keV (above 35 million Kelvins). For such hot clusters, non-gravitational astrophysical effects, are expected to be small.

Their analysis evaluated the equation of state parameter, w, of dark energy. If dark energy adheres to the simplest model, that of the cosmological constant (Λ) found in the equations of general relativity, then w = -1 is expected.

The equation of state governs the relationship between pressure and energy density; dark energy is observed to have a negative pressure, for which w < 0, unlike for matter.

Their resulting value for the equation of state parameter is

w = -1.02 +/- 0.058,

equal to -1 within the statistical errors.

The results from combining three other experiments, namely

  1. Planck satellite cosmic microwave background (CMB) measurements
  2. WMAP satellite CMB polarization measurements
  3. optical observations of Type 1a supernovae

yield a value

w = -1.09 +/- 0.19,

also consistent with a cosmological constant. And combining both the X-ray cluster results with the CMB and optical results yields a tight constraint of

w = -1.01 +/- 0.03.

Thus a simple cosmological constant explanation for dark energy appears to be a sufficient explanation to within a few percent accuracy.

The authors were also able to constrain the evolution in w and find, for a model with

w(z) = w(0) + wa * z / (1 + z), that the evolution parameter is zero within statistical errors:

wa = -0.12 +/- 0.4.

This is a powerful test of dark energy’s existence, equation of state, and evolution, using hundreds of X-ray clusters of galaxies. There is no evidence for evolution in dark energy with redshift back to around z = 1, and a simple cosmological constant model is supported by the data from this technique as well as from other methods.


  1. Morandi, M. Sun arXiv:1601.03741v3 [astro-ph.CO] 4 Feb 2016, “Probing dark energy via galaxy cluster outskirts”
  2. http://chandra.harvard.edu/photo/2016/clusters/

Dusty Star-Forming Galaxies Brightened by Dark Matter

The first galaxies were formed within the first billion years of the Universe’s history. Our Milky Way galaxy contains very old stars with ages indicating formation around 500 or 600 million years after the Big Bang.

Astronomers are very eager to study galaxies in the early universe, in order to understand galaxy formation and evolution. They can do this by looking at the most distant galaxies. With the expanding universe of the Big Bang, the farther away a galaxy is, the farther back in time we are looking. Astronomers often use redshift to measure the distance, and hence age, of a galaxy. The larger the redshift, z, the farther back in time, and the closer to a galaxy’s birth and the universe’s birth.

The interstellar medium of a galaxy consists of gas and dust. The gas can be hot or cold, and in atomic or molecular form. Atomic gas may be ionized by ultraviolet starlight, or X-radiation from neutron stars or black holes (not the black holes themselves, but hot matter near the black hole), from cosmic rays or from other astrophysical mechanisms. Our Milky Way galaxy is rich in gas and dust, and contains thousands of molecular clouds. These are very cold clouds composed mainly of molecular hydrogen but also many other molecular species. Molecular clouds are the primary sites of new star formation. The Horsehead Nebula is an example of a molecular cloud in the constellation of Orion.

"Hubble Sees a Horsehead of a Different Color" by ESA/Hubble. Licensed under CC BY 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Hubble_Sees_a_Horsehead_of_a_Different_Color.jpg#/media/File:Hubble_Sees_a_Horsehead_of_a_Different_Color.jpg

“Hubble Sees a Horsehead of a Different Color” by ESA/Hubble. Licensed under CC BY 3.0 via Wikimedia Commons 

During their most active phase of star formation, a large galaxy might give birth to over 1000 solar masses worth of stars per year. By comparison, in the Milky Way galaxy, the new star formation rate is only of order 1 solar mass per year, the equivalent of 1 Sun, or, say, 2 stars with half the mass of our Sun, per annum. Over its entire 13 billion year life the Milky Way has formed many hundreds of billions of stars, so clearly the star formation rate was higher in the past.

Before the first stars and galaxies form, the universe contains only hydrogen and helium, and no heavier elements. Those are produced by thermonuclear reactions in stellar interiors. This is a wonderful thing, because carbon, oxygen and other heavy elements are essential to life.

After a galaxy produces its first generation of massive stars, its interstellar medium will begin to contain carbon, nitrogen, oxygen and other heavy elements (heavy means anything above helium, in this context). Massive stars (above a few solar masses) evolve rapidly, with timescales in the millions of years, rather than billions, and explode as supernovae at the end of their lives. A large portion of their material, now containing heavy elements as well as hydrogen and helium, is expelled at high velocity and mixed into the interstellar medium. The carbon, nitrogen and oxygen which is then in the respective galaxy’s interstellar medium can be detected in atomic (including ionized) or molecular forms. The relative abundance of heavy elements grows with time as more stars are formed, evolve, and recycle matter into the interstellar medium.

High-redshift (z > 2) galaxies with active star formation are best observed in the infrared. The gas and dust in molecular clouds is quite cold, usually less than 100 K (100 degrees above absolute zero). And their radiation is shifted further toward the far infrared and sub-millimeter portions of the spectrum by the redshift factor of 1+z. So radiation emitted at 100 microns is detected at the Earth at 400 microns for a source at z = 3.

These are difficult measurements to make, because if the galaxy is very distant, it is also very faint. However the possibility of getting good measurements is helped by two things. One is that galaxies with very active star formation are intrinsically brighter.

And the other reason is that intervening clusters of galaxies are massive and contain mostly dark matter. As we look far back through the universe toward an early galaxy, there is a good chance that the line of sight passes through a cluster of galaxies. Clusters of galaxies contain hundreds or even thousands of galaxies, and are dominated by dark matter. Most of the infrared radiation can pass through the intracluster medium – the space between galaxies – without being absorbed; it does not interact with dark matter. The clusters are sufficiently massive to bend the light, however, according to general relativity. As the background galaxy’s light passes through the cluster during its multi-billion year journey to the Earth and our telescopes, the cluster’s gravitational potential modifies the light ray’s path. Actually the intervening cluster of galaxies does more than displace the light, it acts as a lens, causing the image to brighten by as much as 10 times or more. This makes it much easier to gather enough photons from the target galaxy to obtain good quality results.

An international research team with participants from Germany, the U.S., Chile, the U.K. and Canada has identified 20 high redshift “dusty star forming galaxies” at very high redshift (DSFG is a technical term for galaxies with high star formation rates and lots of dust) from the South Pole Telescope infrared galaxy survey. They have been able to further elucidate the nature of 17 of these early galaxies by measuring C II emission from singly ionized atomic carbon, and CO emission from carbon monoxide molecules for 11 of those. They have also determined the total far infrared luminosity for these target galaxies. Their results allow them to place constraints on the nature of the interstellar medium and the properties of molecular clouds.

The galaxies’ high redshifts, ranging from z = 2.1  to 5.7, actually makes it possible to make Earth-bound measurements in most cases. At lower redshifts the observations would not be possible from Earth because the Earth’s atmosphere is highly opaque at the observation frequencies. But it is much more transparent at longer wavelengths, so as the redshift exceeds z = 3, Earth-based observations are possible from favorable locations, in this case the Chilean desert. For three sources with redshifts around 2 the atmosphere prohibits ground-based observations and the team therefore made observations from the orbiting Herschel Space Telescope, designed for infrared work.

The figure labelled Figure 3 below is taken from their paper. It indicates the redshift z on the x-axis (logarithmically) and the far infrared luminosity of the galaxy on the y-axis (as the log) as well. The 17 galaxies studied by the authors are indicated with red dots and labelled “SPT DSFGs”. Their very high luminosities are in the range of 10 to 100 trillion times the Sun’s luminosity. Note that the luminosities must be very high for detection at such a high redshift (distance from Earth). Also these luminosities are uncorrected for the lensing magnification, so the true luminosities are around an order of magnitude lower.


The redshift range covered in this research corresponds to ages for the universe of around 1 billion years old (z = 5.7) to a little over 3 billion years old (z = 2.1). So the lookback time is roughly 11 to 13 billion years.

For those of us interested in dark matter, their findings regarding the degree of magnification by dark matter are also interesting. They find “strong lensing” or magnification in the range of 5 to 21 times for 4 sources that allowed for lens modeling. The other sources do not have magnifications measured, but they are presumed to be of the same order of magnitude of around 10 times or so, to within a factor of 2 either way.

It is only because the lensing is so substantial that they are able to measure these galaxies with sufficient fidelity to arrive at their results. So not only is dark matter key to galaxy formation and evolution, it is key to allowing us to study galaxies in the early universe. Dark matter forms galaxies and then helps us understand how they form!


B. Gullberg et al. 2015, ”The nature of the [CII] emission in dusty star-forming galaxies from the SPT survey” to be published, Monthly Notices of the Royal Astronomical Society, http://arxiv.org/pdf/1501.06909v2.pdf

C.M. Casey, D. Narayanan, A. Cooray 2015, “Dusty Star-Forming Galaxies at High Redshift”, http://arxiv.org/abs/1402.1456

The Supervoid

The largest known structure in the universe goes by the name of the Supervoid. It is an enormously large under-dense region about 1.8 billion light-years in extent. Voids (actually low density regions) in galaxy and cluster density have been mapped over several decades.

The cosmic microwave background radiation map from the Planck satellite and earlier experiments is extremely uniform. The temperature is about 2.7 Kelvins everywhere in the universe at present. There are small microKelvin scale fluctuations due to primordial density perturbations. The over-dense regions grow over cosmic timescales to become galaxies, groups and clusters of galaxies, and superclusters made of multiple clusters. Under-dense regions have fewer galaxies and groups per unit volume than the average.

The largest inhomogeneous region detected in the cosmic microwave background map is known as the Cold Spot and has a very slightly lower temperature by about 70 microKelvins (a microKelvin being only a millionth of a degree). It may be partly explained by a supervoid of radius 320 Megaparsecs, or around 1 billion light-years radius.

Superclusters heat cosmic microwave background photons slightly when they pass through, if there is significant dark energy in the universe. Supervoids cool the microwave background photons slightly. The reason is that, once dark energy becomes significant, during the second half of the universe’s expansion to date, it begins to smooth out superclusters and supervoids. It pushes the universe back towards greater uniformity while accelerating the overall expansion.

A photon will gain energy (blueshift) when it heads into a supercluster on its way to the Earth. This is an effect of general relativity. And as it leaves the other side of the supercluster as it continues its journey, it will lose energy (redshift) as it climbs out of the gravitational potential well. But while it is passing through the supercluster, that structure is spreading out due to the Big Bang overall expansion, and its gravitational potential is weakening. So the redshift or energy loss is smaller than the original energy gain or blueshift. So net-net, photons gain energy passing through a supercluster.

The opposite happens with a supervoid. Photons lose energy on the way in. They gain  energy on the way out, but less than they lost. Net-net photons lose energy, become colder, when passing through supervoids. Now all of this is relative to the overall redshift that all photons experience as they travel from the Big Bang last scattering surface to the Earth. During each period that the universe doubles in size, the Big Bang radiation doubles in wavelength, or halves in temperature.

In a newly published paper titled “Detection of a Supervoid aligned with the Cold Spot in the Cosmic Microwave Background”, astronomers looked at the distribution of galaxies in the direction of the well-established Cold Spot. The supervoid core redshift distance is in the range z = 0.15 to z = 0.25, corresponding to a distance of roughly 2 to 3 billion light-years from Earth.

They find a reduction in galaxy density of about 20%, and of dark matter around 14%, in the supervoid, relative to the overall average density values in the universe. The significance of the detection is high, around 5 standard deviations. The center of the low density region is well aligned with the position of the Cold Spot in the galactic Southern Hemisphere.

Both the existence of this supervoid and its alignment with the Cold Spot are highly significant. The chance of the two being closely aligned to this degree is calculated as just 1 chance in 20,000. The image below is Figure 2 from the authors’ paper and maps the density of galaxies in the left panel and the temperature differential of the microwave background radiation in the right panel. The white dot in the middle of each panel marks the center of the Cold Spot in the cosmic microwave background.


A lower density of galaxies is indicated by a blue color in the left panel. Red and orange colors denote a higher density of galaxies. The right panel shows slightly lower temperature of the cosmic microwave background in blue, and slightly higher temperature in red.

The authors have calculated the expected temperature reduction due to the supervoid; using a first-order model it is about 20 microKelvins. While this is not sufficient to explain the entire Cold Spot temperature decrease, it is a significant portion of the overall 70 microKelvin reduction.

Dark Energy is gradually smearing out the distinction between superclusters and supervoids. Dark Energy has come to dominate the universe’s mass-energy balance fairly recently, since about 5 billion years ago. If there is no change in the Dark Energy density, over many billions of years it will push all the galaxies so far apart from one another that no other galaxies will be detectable from our Milky Way.


I. Szapudi et al, 2015 M.N.R.A.S., Volume 450, Issue 1, p. 288, “Detection of a supervoid aligned with the cold spot of the cosmic microwave background” – http://mnras.oxfordjournals.org/content/450/1/288.full

S. Perrenod and M. Lesser, 1980, P.A.S.P. 91:764, “A Redshift Survey of a High-Multiplicity Supercluster” http://www.jstor.org/discover/10.2307/40677683?uid=2&uid=4&sid=21106121183081


Super Colliders in Space: Dark Matter not Colliding

What’s bigger and more powerful than the Large Hadron Collider at CERN? Why colliding galaxy clusters of course.

A cluster of galaxies consists of hundreds or even thousands of galaxies bound together by their mutual gravitation. Both dark matter and ordinary matter in and between galaxies is responsible for the gravitational field of a cluster. And typically there is about 5 times as much dark matter as ordinary matter. The main component of ordinary matter is hot intracluster gas; only a small percentage of the mass is locked up in stars.

One stunning example of dark matter detection is the Bullet Cluster. This is the canonical example found revealing dark matter separation from ordinary matter in a pair of clusters colliding and merging. The dark matter just passes right through, apparently unaffected by the collision. The hot gas (ordinary matter) is seen through its X-ray emission, since the gas is heated by collisions to of order 100 million degrees. The Chandra X-ray Observatory (satellite) provided these measurements.

Image courtesy of Chandra X-ray Observatory

Bullet Cluster. The blue color shows the distribution of dark matter, which passed through the collision without slowing down. The purple color shows the hot X-ray emitting gas. Image courtesy of Chandra X-ray Observatory

The distribution of matter overall in the Bullet Cluster or other clusters is traced by gravitational lensing effects; general relativity tells us that  background galaxies will have their images displaced, distorted, and magnified as their light passes through a cluster on its way to Earth. The magnitude of these effects can be used to “weigh” the dark matter. These measurements are made with the Hubble Space Telescope.

In the Bullet Cluster the dark matter is displaced from the ordinary matter. The interpretation is that the ordinary matter from the two clusters, principally in the form of hot gas, is slowed by frictional, collisional processes as the clusters interact and form a larger single cluster of galaxies. Another six or so examples of galaxy clusters showing the displacement between the dark matter and the ordinary matter in gas and stars have been found to date.

Now, a team of astrophysicists based in the U.K. and Switzerland have examined 30 additional galaxy clusters with data from both Chandra and Hubble, and with redshifts typically 0.2 to 0.6. In aggregate there are 72 collisions in the 30 systems, since some have more than two subclusters. The offsets between the gas and dark matter are quite substantial, and in aggregate indicate the existence of dark matter in these clusters with over 7 standard deviations of statistical significance (probability of the null hypothesis of no dark matter is 1 in 30 trillion).

They then look at the possible drag force on the dark matter due to dark matter particles colliding with other dark matter particles. There are already much more severe constraints on ordinary matter – dark matter interactions from Earth-based laboratory measurements. But the dark matter mutual collision cross section could potentially be large enough to result in a drag. They measure the relative positions of hot gas, galaxies, and dark matter for all of the 72 subclusters.

From paper "The non-gravitational interactions of dark matter in colliding galaxy clusters"

From paper “The non-gravitational interactions of dark matter in colliding galaxy clusters” D. Harvey et al. 2015

The gas should and does lag the most, relative to the direction of the galaxies in a collision. If there is a dark matter drag, then dark matter should lag behind the positions of the stars. They find no lag of the dark matter average position, which allows them to place a new, tighter constraint on the mutual interaction cross-section for dark matter.

Their constraint is σ(DM)/m < 0.47 cm^2/g at 95% confidence level, where σ (sigma) is the cross-section and m is the mass of a single dark matter particle. This limit is over twice as tight as that previously obtained from the Bullet Cluster. And some dark matter models predict a cross section per unit mass of 0.6 cm^2/g, so these models are potentially ruled out by these new measurements.

In summary, using Nature’s massive particle colliders, the authors have found further highly significant evidence for the existence of dark matter in clusters of galaxies, and they have placed useful constraints on the dark matter self-interaction cross-section. Dark matter continues to be highly elusive.


D. Harvey et al. 2015 “The non-gravitational interactions of dark matter in colliding galaxy clusters” http://arxiv.org/pdf/1503.07675v1.pdf

Dark Matter: Made of Sterile Neutrinos?


Composite image of the Bullet Group showing galaxies, hot gas (shown in pink) and dark matter (indicated in blue). Credit: ESA / XMM-Newton / F. Gastaldello (INAF/IASF, Milano, Italy) / CFHTLS 

What’s more elusive than a neutrino? Why a sterile neutrino, of course. In the Standard Model of particle physics there are 3 types of “regular” neutrinos. The ghost-like neutrinos are electrically neutral particles with 1/2 integer spins and very small masses. Neutrinos are produced in weak interactions, for example when a neutron decays to a proton and an electron. The 3 types are paired with the electron and its heavier cousins, and are known as electron neutrinos, muon neutrinos, and tau neutrinos (νe, νμ, ντ).

A postulated extension to the Standard Model would allow a new type of neutrino, known as a sterile neutrino. “Sterile” refers to the fact that this hypothetical particle would not feel the standard weak interaction, but would couple to regular neutrino oscillations (neutrinos oscillate among the 3 types, and until this was realized there was consternation around the low number of solar neutrinos detected). Sterile neutrinos are more ghostly than regular neutrinos! The sterile neutrino would be a neutral particle, like other neutrino types, and would be a fermion, with spin 1/2. The number of types, and the respective masses, of sterile neutrinos (assuming they exist) is unknown. Since they are electrically neutral and do not feel the standard weak interaction they are very difficult to detect. But the fact that they are very hard to detect is just what makes them candidates for dark matter, since they still interact gravitationally due to their mass.

What about regular neutrinos as the source of dark matter? The problem is that their masses are too low, less than 1/3 of an eV (electron-Volt) total for the three types. They are thus “too hot” (speeds and velocity dispersions too high, being relativistic) to explain the observed properties of galaxy formation and clumping into groups and clusters. The dark matter should be “cold” or non-relativistic, or at least no more than “warm”, to correctly reproduce the pattern of galaxy groups, filaments, and clusters we observe in our Universe.

Constraints can be placed on the minimum mass for a sterile neutrino to be a good dark matter candidate. Observations of the cosmic microwave background and of hydrogen Lyman-alpha emission in quasar spectra have been used to set a lower bound of 2 keV for the sterile neutrino’s mass, if it is the predominant component of dark matter. A sterile neutrino with this mass or larger is expected to have a decay channel into a photon with half of the rest-mass energy and a regular (active) neutrino with half the energy.

A recent suggestion is that an X-ray emission feature seen at 3.56 keV (kilo-electron Volts) from galaxy clusters is a result of the decay of sterile neutrinos into photons with that energy plus active (regular) neutrinos with similar energy. This X-ray emission line has been seen in a data set from the XMM-Newton satellite that stacks results from 73 clusters of galaxies together. The line was detected in 2 different instruments with around 4 or 5 standard deviations significance, so the existence of the line itself is on a rather strong footing. However, it is necessary to prove that the line is not from an atomic transition from argon or some other element. The researchers argue that an argon line should be much, much weaker than the feature that is detected.

In addition, a second team of researchers, also using XMM-Newton data have claimed detection of lines at the same 3.56 keV energy in the Perseus cluster of galaxies as well as our neighbor, the Andromeda galaxy.

There are no expected atomic transition lines at this energy, so the dark matter decay possibility has been suggested by both teams. An argon line around 3.62 KeV is a possible influence on the signal, but is expected to be very much weaker. Confirmation of these XMM-Newton results are required from other experiments in order to gain more confidence in the reality of the 3.56 keV feature, regardless of its cause, and to eliminate with certainty the possibility of an atomic transition origin. Analysis of stacked galaxy cluster data is currently underway for two other X-ray satellite missions, Chandra and Suzaku. In addition, the astrophysics community eagerly awaits the upcoming Astro-H mission, a Japanese X-ray astronomy satellite planned for launch in 2015. It should be able to not only confirm the 3.56 keV X-ray line (if indeed real), but also detect it within our own Milky Way galaxy.

Thus the hypothesis is for dark matter composed primarily of sterile neutrinos of a little over 7.1 keV in mass (in E = mc^2 terms), and that the sterile neutrino has a decay channel to an X-ray photon and regular neutrino. Each decay product would have an energy of about 3.56 keV. Such a 7 keV sterile neutrino is plausible with respect to the known density of dark matter and various cosmological and particle physics constraints. If the dark matter is primarily due to this sterile neutrino, then it falls into the “warm” dark matter domain, intermediate between “cold” dark matter due to very heavy particles, or “hot” dark matter due to very light particles.

The abundance of dwarf satellite galaxies found in the Milky Way’s neighborhood is lower than predicted from cold dark matter models. Warm dark matter could solve this problem. As Dr. Abazajian puts in in his recent paper “Resonantly Produced 7 keV Sterile Neutrino Dark Matter Models and the Properties of Milky Way Satellites”

the parameters necessary in these models to produce the full dark matter density fulfill previously determined requirements to successfully match the Milky Way galaxy’s total satellite abundance, the satellites’ radial distribution, and their mass density profile..


Dark Energy Survey First Light!

Last month the Dark Energy Survey project achieved first light from its remote location in Chile’s Atacama Desert. The term first light is used by astronomers to refer to the first observation by a new instrument.

And what an instrument this is! It is in fact the world’s most powerful digital camera. This Dark Energy Camera, or DECam, is a 570 Megapixel optical survey camera with a very wide field of view. The field of view is over 2 degrees, which is rather unusual in optical astronomy. And the camera requires special CCDs that are sensitive in the red and infrared parts of the spectrum. This is because distant galaxies have their light shifted toward the red and the infrared by the cosmological expansion. If the galaxy redshift is one,  the light travels for about 8 billion years and the wavelength of light that the DECam detects is doubled, relative to what it was when it was originally emitted.

Dark Energy Camera

Image: DECam, near center of image, is deployed at the focus of the 4-meter Victor M. Blanco optical telescope in Chile (Credit: Dark Energy Survey Collaboration)

The DECam has been deployed to further our understanding of dark energy through not just one experimental method, but in fact four different methods. That’s how you solve tough problems – by attacking them on multiple fronts.

It’s taken 8 years to get to this point, and there have been some delays, as normal for large projects. But now this new instrument is mounted at the focal plane of the existing 4-meter telescope of the National Science Foundation’s Cerro Tololo Inter-American observatory in Chile. It will begin its program of planned measurements of several hundred million galaxies starting in December after several weeks of testing and calibration. Each image from the camera-telescope combination can capture up to 100,000 galaxies out to distances of up to 8 billion light years. This is over halfway back to the origin of the universe almost 14 billion years ago.

In a previous blog entry I talked about the DES and the 4 methods in some detail. In brief they are based on observations of:

  1. Type 1a supernova (the method used to first detect dark energy)
  2. Very large scale spatial correlations of galaxies separated by 500 million light-years (this experiment is known as Baryon Acoustic Oscillations since the galaxy separations reflect the imprint of sound waves in the very early universe, prior to galaxy formation)
  3. The number of clusters of galaxies as a function of redshift (age of the universe)
  4. Gravitational lensing, i.e. distortion of background images by gravitational effects of foreground clusters in accordance with general relativity

NGC 1365

Image: NGC 1365, a barred spiral galaxy located in the Fornax cluster located 60 million light years from Earth (Credit: Dark Energy Survey Collaboration)

What does the Dark Energy Survey team, which has over 120 members from over 20 countries, hope to learn about dark energy? We already have a good handle on its magnitude, at around 73% presently of the universe’s total mass-energy density.

The big issue is does it behave as a cosmological constant or as something more complex? In other words, how does the dark energy vary over time and is there possibly some spatial variation as well? And what is its equation of state, or relationship between its pressure and density?

With a cosmological constant explanation the relationship is Pressure = – Energy_density, a negative pressure, which is necessary in any model of the dark energy, in order for it to drive the accelerated expansion seen for the universe. Current observations from other experiments, especially those measuring the cosmic microwave background, support an equation of state parameter within around 5% of the value -1, as represented in the equation in the previous sentence. This is consistent with the interpretation as a pressure resulting from the vacuum. Dark energy appears also to have a constant or nearly constant density per unit volume of space. It is unlike ordinary matter and dark matter, that both drop in mass density (and thus energy density) as the volume of the universe grows. Thus dark energy becomes ever more dominant over dark matter and ordinary matter as the universe continues to expand.

We can’t wait to see the first publication of results from research into the nature of dark energy using the DECam.


http://www.noao.edu/news/2012/pr1204.php – Press release from National Optical Astronomical Observatory on DECam first light


http://www.ctio.noao.edu/noao/ – Cerro Tololo Inter-American Observatory page

http://lambda.gsfc.nasa.gov/product/map/dr4/pub_papers/sevenyear/basic_results/wmap_7yr_basic_results.pdf – WMAP 7 year results on cosmic microwave background


Dark Matter Bridge Discovered

A team of astronomers claims to have detected an enormous bridge or filament of dark matter, with a mass estimated to be of order 100 trillion solar masses, and connecting two clusters of galaxies. The two clusters, known as Abell 222 and Abell 223, are about 2.8 billion light-years away and separated from one another by 400 million light-years. Each cluster has around 150 galaxies; actually one of the pair is itself a double cluster.

Clusters of galaxies are gravitationally bound collections of hundreds to a thousand or more galaxies. Often a cluster will be found in the vicinity of other clusters to which it is also gravitationally bound. The universe as a whole is gravitationally unbound – the matter, including the dark matter – is insufficient to stop the continued expansion, which is driven to acceleration in fact, by dark energy.

Dark matter bridge

Figure: Subaru telescope optical photo with mass density shown in blue and statistical significance contours superimposed. In the filament area found near the center of the image, the contours indicate four standard deviations of significance in the detection of dark matter. The cluster Abell 222 is in the south, and Abell 223 is the double cluster in the north of the image. The distance between the two clusters is about 14 arc-minutes, or about ½ the apparent size of the Moon.

Dark matter was originally called “missing matter”, and was first posited by Fritz Zwicky (http://en.wikipedia.org/wiki/Fritz_Zwicky) in the 1930s because of his studies of the kinematics of galaxies and galaxy clusters. He measured the velocities of galaxies moving around inside a cluster and found they were significantly greater than expected from the amount of ordinary matter seen in the galaxies themselves. This implied there was more matter than seen in galaxies because the velocities of the galaxies would be determined by the total gravitational field in a cluster, and the questions have been where is, and what is, the “missing matter” inferred by the gravitational effects. X-ray emission has been detected from most clusters of galaxies, and this is due to an additional component of matter outside of galaxies, namely hot gas between galaxies. But it is still insufficient to explain the total mass of clusters as revealed by both the galaxy velocities and the temperature of the hot gas itself, since both are a reflection of the gravitational field in the cluster.

Dark matter is ubiquitous, found on all scales and is generally less clumped than ordinary matter, so it is not surprising that significant dark matter would be found between two associated galaxy clusters. In fact the researchers in this study point out that “It is a firm prediction of the concordance Cold Dark Matter cosmological model that galaxy clusters live at the intersection of large-scale structure filaments.”

The technique used to map the dark matter is gravitational lensing, which is a result of general relativity. The gravitational lensing effect is well established; it has been seen in many clusters of galaxies to date. In gravitational lensing, light is deflected away from a straight-line path by matter in its vicinity.

In this case the gravitational field of the dark matter filament and the galaxy clusters deflect light passing nearby. The image of a background galaxy located behind the cluster will be distorted as the light moves through or nearby the foreground cluster. The amount of distortion depends on the mass of the cluster (or dark matter bridge) and how near the line of sight passes to the cluster center.

There is also a well-detected bridge of ordinary matter in the form of hot X-ray emitting gas connecting the two clusters and in the same location as the newly discovered dark matter bridge.  The scientists used observations from the XMM-Newton satellite to map the X-ray emission from the two clusters Abell 222 and Abell 223 and the hot gas bridge connecting them. Because of the strong gravitational fields of galaxy clusters, the gas interior to galaxy clusters (but exterior to individual galaxies within the cluster) is heated to very high temperatures by frictional processes, resulting in thermal X-ray emission from the clusters.

The research team, led by Jörg Dietrich at the University of Michigan, then performed a gravitational lensing analysis, focusing on the location of the bridge as determined from the X-ray observations. The gravitational lensing work is based on optical observations obtained from the Subaru telescope (operated by the Japanese government, but located on the Big Island of Hawaii) to map the total matter density profile around and between the two clusters. This method detects the sum of dark matter and ordinary matter.

They analyzed the detailed orientations and shapes of over forty thousand background galaxies observable behind the two clusters and the bridge. This work allowed them to determine the contours of the dark matter distribution. They state a 98% confidence in the existence of a bridge or filament dominated by dark matter.

The amount of dark matter is shown to be much larger than that of ordinary matter, representing over 90% of the total in the filament region, so the gravitational lensing effects are primarily due to the dark matter. Less than 9% of the mass in the filament is in the form of hot gas (ordinary matter). The estimated total mass in the filament is about 1/3 of the mass of either of the galaxy clusters, each of which is also dominated by dark matter.

Observations of galaxy distributions show that galaxies are found in groups, clusters, and filaments connecting regions of galaxy concentration. Cosmological simulations of the evolution of the universe on supercomputers indicate that the distribution of dark matter should have a filamentary structure as well. So although the result is in many ways not surprising, it represents the first detection of such a structure to date.



http://ns.umich.edu/new/releases/20623-dark-matter-scaffolding-of-universe-detected-for-the-first-time – press release from the University of Michigan

http://www.gizmag.com/dark-matter-filaments-found/23281/ “Dark matter filaments detected for the first time”

J. Dietrich et al. 2012 http://arxiv.org/abs/1207.0809 “A filament of dark matter between two clusters of galaxies”