## Modified Newtonian Dynamics – Is there something to it?

You are constantly accelerating. The Earth’s gravity is pulling you downward at g = 9.8 meters per second per second. It wants to take your velocity up to about 10 meters per second after only the first second of free fall. Normally you don’t fall, because the floor is solid due to electromagnetic forces and also it is electromagnetic forces that give your body structural integrity and power your muscles, resisting the pull of gravity.

You are also accelerating due to the Earth’s spin and its revolution about the Sun.

International Space Station, image credit: NASA

Our understanding of gravity comes primarily from these large accelerations, such as the Earth’s pull on ourselves and on satellites, the revolution of the Moon about the Earth, and the planetary orbits about the Sun. We also are able to measure the solar system’s velocity of revolution about the galactic center, but with much lower resolution, since the timescale is of order 1/4 billion years for a single revolution with an orbital radius of about 25,000 light-years!

It becomes more difficult to determine if Newtonian dynamics and general relativity still hold for very low accelerations, or at very large distance scales such as the Sun’s orbit about the galactic center and beyond.

Modified Newtonian Dynamics (MOND) was first proposed by Mordehai Milgrom in the early 1980s as an alternative explanation for flat galaxy rotation curves, which are normally attributed to dark matter. At that time the best evidence for dark matter came from spiral galaxy rotation curves, although the need for dark matter (or some deviation from Newton’s laws) was originally seen by Fritz Zwicky in the 1930s while studying clusters of galaxies.

NGC 3521. Image Credit: ESA/Hubble & NASA and S. Smartt (Queen’s University Belfast); Acknowledgement: Robert Gendler

Galaxy Rotation Curve for M33. Public Domain, By Stefania.deluca – Own work,  https://commons.wikimedia.org/w/index.php?curid=34962949

If general relativity is always correct, and Newton’s laws of gravity are correct for non-relativistic, weak gravity conditions, then one expects the orbital velocities of stars in the outer reaches of galaxies to drop in concert with the fall in light from stars and/or radio emission from interstellar gas, reflecting decreasing baryonic matter density. (Baryonic matter is ordinary matter, dominated by protons and neutrons). As seen in the image above for M33, the orbital velocity does not drop, it continues to rise well past the visible edge of the galaxy.

To first order, assuming a roughly spherical distribution of matter, the square of the velocity at a given distance from the center is proportional to the mass interior to that distance divided by the distance (signifying the gravitational potential), thus

v² ~ G M / r

where G is the gravitational constant, and M is the galactic mass within a spherical volume of radius r. This potential corresponds to the familiar 1/r² dependence of the force of gravity according to Newton’s laws.  In other words, at the outer edge of a galaxy the velocity of stars should fall as the square root of the increasing distance, for Newtonian dynamics.

Instead, for the vast majority of galaxies studied, it doesn’t – it flattens out, or falls off very slowly with increasing distance, or even continues to rise, as for M33 above. The behavior is roughly as if gravity followed an inverse distance law for the force (1/r) in the outer regions, rather than an inverse square law with distance (1/r²).

So either there is more matter at large distances from galactic centers than expected from the light distribution, or the gravitational law is modified somehow such that gravity is stronger than expected. If there is more matter, it gives off little or no light, and is called unseen, or dark, matter.

It must be emphasized that MOND is completely empirical and phenomenological. It is curve fitted to the existing rotational curves, rather successfully, but not based on a theoretical construct for gravity. It has a free parameter for weak acceleration, and for very small accelerations, gravity is stronger than expected. It turns out that this free parameter, $a_0$, is of the same order as the ‘Hubble acceleration’ $c \cdot H$. (The Hubble distance is c / H and is 14 billion light-years; H has units of inverse time and the age of the universe is 1/H to within a few percent).

The Hubble acceleration is approximately .7 nanometers / sec / sec or 2 centimeters / sec / year  (a nanometer is a billionth of a meter, sec = second).

Milgrom’s fit to rotation curves found a best fit at .12 nanometers/sec/sec, or about 1/6 of $a_0$. This is very small as compared to the Earth’s gravity, for example. It’s the ratio between 80 years and one second, or about 2.5 billion. So you can imagine how such a variation could have escaped detection for a long time, and would require measurements at the extragalactic scale.

The TeVeS – tensor, vector, scalar theory is a theoretical construct that modifies gravity from general relativity. General relativity is a tensor theory that reduces to Newtonian dynamics for weak gravity. TeVeS has more free parameters than general relativity, but can be constructed in a way that will reproduce galaxy rotation curves and MOND-like behavior.

But MOND, and by implication, TeVeS, have a problem. They work well, surprisingly well, at the galactic scale, but come up short for galaxy clusters and for the very largest extragalactic scales as reflected in the spatial density perturbations of the cosmic microwave background radiation. So MOND as formulated doesn’t actually fully eliminate the requirement for dark matter.

Horseshoe shaped Einstein Ring

Image credit: ESA/Hubble and NASA

Any alternative to general relativity also must explain gravitational lensing, for which there are a large number of examples. Typically a background galaxy image is distorted and magnified as its light passes through a galaxy cluster, due to the large gravity of the cluster. MOND proponents do claim to reproduce gravitational lensing in a suitable manner.

Our conclusion about MOND is that it raises interesting questions about gravity at large scales and very low accelerations, but it does not eliminate the requirement for dark matter. It is also very ad hoc. TeVeS gravity is less ad hoc, but still fails to reproduce the observations at the scale of galaxy clusters and above.

Nevertheless the rotational curves of spirals and irregulars are correlated with the visible mass only, which is somewhat strange if there really is dark matter dominating the dynamics. Dark matter models for galaxies depend on dark matter being distributed more broadly than ordinary, baryonic, matter.

In the third article of this series we will take a look at Erik Verlinde’s emergent gravity concept, which can reproduce the Tully-Fisher relation and galaxy rotation curves. It also differs from MOND both in terms of being a theory, although incomplete, rather than empiricism, and apparently in being able to more successfully address the dark matter issues at the scale of galaxy clusters.

References

Wikipedia MOND entry: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics

M. Milgrom 2013, “Testing the MOND Paradigm of Modified Dynamics with Galaxy-Galaxy Gravitational Lensing” https://arxiv.org/abs/1305.3516

R. Reyes et al. 2010, “Confirmation of general relativity on large scales from weak lensing and galaxy velocities” https://arxiv.org/abs/1003.2185

“In rotating galaxies, distribution of normal matter precisely determines gravitational acceleration” https://www.sciencedaily.com/releases/2016/09/160921085052.htm

## Dark Gravity: Is Gravity Thermodynamic?

This is the first in a series of articles on ‘dark gravity’ that look at emergent gravity and modifications to general relativity. In my book Dark Matter, Dark Energy, Dark Gravity I explained that I had picked Dark Gravity to be part of the title because of the serious limitations in our understanding of gravity. It is not like the other 3 forces; we have no well accepted quantum description of gravity. And it is some 33 orders of magnitude weaker than those other forces.
I noted that:

The big question here is ~ why is gravity so relatively weak, as compared to the other 3 forces of nature? These 3 forces are the electromagnetic force, the strong nuclear force, and the weak nuclear force. Gravity is different ~ it has a dark or hidden side. It may very well operate in extra dimensions… http://amzn.to/2gKwErb

My major regret with the book is that I was not aware of, and did not include a summary of, Erik Verlinde’s work on emergent gravity. In emergent gravity, gravity is not one of the fundamental forces at all.

Erik Verlinde is a leading string theorist in the Netherlands who in 2009 proposed that gravity is an emergent phenomenon, resulting from the thermodynamic entropy of the microstates of quantum fields.

In 2009, Verlinde showed that the laws of gravity may be derived by assuming a form of the holographic principle and the laws of thermodynamics. This may imply that gravity is not a true fundamental force of nature (like e.g. electromagnetism), but instead is a consequence of the universe striving to maximize entropy. – Wikipedia article “Erik Verlinde”

This year, Verlinde extended this work from an unrealistic anti-de Sitter model of the universe to a more realistic de Sitter model. Our runaway universe is approaching a dark energy dominated deSitter solution.

He proposes that general relativity is modified at large scales in a way that mimics the phenomena that have generally been attributed to dark matter. This is in line with MOND, or Modified Newtonian Dynamics. MOND is a long standing proposal from Mordehai Milgrom, who argues that there is no dark matter, rather that gravity is stronger at large distances than predicted by general relativity and Newton’s laws.

In a recent article on cosmology and the nature of gravity Dr.Thanu Padmanabhan lays out 6 issues with the canonical Lambda-CDM cosmology based on general relativity and a homogeneous, isotropic, expanding universe. Observations are highly supportive of such a canonical model, with a very early inflation phase and with 1/3 of the mass-energy content in dark energy and 2/3 in matter, mostly dark matter.

And yet,

1. The equation of state (pressure vs. density) of the early universe is indeterminate in principle, as well as in practice.

2. The history of the universe can be modeled based on just 3 energy density parameters: i) density during inflation, ii) density at radiation – matter equilibrium, and iii) dark energy density at late epochs. Both the first and last are dark energy driven inflationary de Sitter solutions, apparently unconnected, and one very rapid, and one very long lived. (No mention of dark matter density here).

3. One can construct a formula for the information content at the cosmic horizon from these 3 densities, and the value works out to be 4π to high accuracy.

4. There is an absolute reference frame, for which the cosmic microwave background is isotropic. There is an absolute reference scale for time, given by the temperature of the cosmic microwave background.

5. There is an arrow of time, indicated by the expansion of the universe and by the cooling of the cosmic microwave background.

6. The universe has, rather uniquely for physical systems, made a transition from quantum behavior to classical behavior.

“The evolution of spacetime itself can be described in a purely thermodynamic language in terms of suitably defined degrees of freedom in the bulk and boundary of a 3-volume.”

Now in fluid mechanics one observes:

“First, if we probe the fluid at scales comparable to the mean free path, you need to take into account the discreteness of molecules etc., and the fluid description breaks down. Second, a fluid simply might not have reached local thermodynamic equilibrium at the scales (which can be large compared to the mean free path) we are interested in.”

Now it is well known that general relativity as a classical theory must break down at very small scales (very high energies). But also with such a thermodynamic view of spacetime and gravity, one must consider the possibility that the universe has not reached a statistical equilibrium at the largest scales.

One could have reached equilibrium at macroscopic scales much less than the Hubble distance scale c/H (14 billion light-years, H is the Hubble parameter) but not yet reached it at the Hubble scale. In such a case the standard equations of gravity (general relativity) would apply only for the equilibrium region and for accelerations greater than the characteristic Hubble acceleration scale of  $c \cdot H$ (2 centimeters per second / year).

This lack of statistical equilibrium implies the universe could behave similarly to non-equilibrium thermodynamics behavior observed in the laboratory.

The information content of the expanding universe reflects that of the quantum state before inflation, and this result is 4π in natural units by information theoretic arguments similar to those used to derive the entropy of a black hole.

The black hole entropy is  $S = A / (4 \cdot Lp^2)$ where A is the area of the black hole using the Schwarzschild radius formula and Lp is the Planck length, $G \hbar / c^3$ , where G is the gravitational constant, $\hbar$ is Planck’s constant.

This beautiful Bekenstein-Hawking entropy formula connects thermodynamics, the quantum world  and gravity.

This same value of the universe’s entropy can also be used to determine the number of e-foldings during inflation to be 6 π² or 59, consistent with the minimum value to enforce a sufficiently homogeneous universe at the epoch of the cosmic microwave background.

If inflation occurs at a reasonable ~ $10^{15}$ GeV, one can derive the observed value of the cosmological constant (dark energy) from the information content value as well, argues Dr. Padmanhaban.

This provides a connection between the two dark energy driven de Sitter phases, inflation and the present day runaway universe.

The table below summarizes the 4 major phases of the universe’s history, including the matter dominated phase, which may or may not have included dark matter. Erik Verlinde in his new work, and Milgrom for over 3 decades, question the need for dark matter.

Epoch  /  Dominated  /   Ends at  /   a-t scaling  /   Size at end

Inflation /  Inflaton (dark energy) / $10^{-32}$ seconds / $e^{Ht}$ (de Sitter) / 10 cm

Radiation / Radiation / 40,000 years / $\sqrt t$ /  10 million light-years

Matter / Matter (baryons) Dark matter? /  9 billion light-years / $t^{2/3}$ /  > 100 billion light-years

Runaway /  Dark energy (Cosmological constant) /  “Infinity” /  $e^{Ht}$ (de Sitter) / “Infinite”

In the next article I will review the status of MOND – Modified Newtonian Dynamics, from the phenomenology and observational evidence.

References

E. Verlinde. “On the Origin of Gravity and the Laws of Newton”. JHEP. 2011 (04): 29 http://arXiv.org/abs/1001.0785

T. Padmanabhan, 2016. “Do We Really Understand the Cosmos?” http://arxiv.org/abs/1611.03505v1

S. Perrenod, 2011. Dark Matter, Dark Energy, Dark Gravity 2011  http://amzn.to/2gKwErb

S. Carroll and G. Remmen, 2016, http://www.preposterousuniverse.com/blog/2016/02/08/guest-post-grant-remmen-on-entropic-gravity/

## Axions, Inflation and Baryogenesis: It’s a SMASH (pi)

Searches for direct detection of dark matter have focused primarily on WIMPs (weakly interacting massive particles) and more precisely on LSPs (the lightest supersymmetric particle). These are hypothetical particles such as neutralinos that are least massive members of the hypothesized family of supersymmetric partner particles.

But supersymmetry may be dead. There have been no supersymmetric particles detected at the Large Hadron Collider at CERN as of yet, leading many to say that this is a crisis in physics.

At the same time as CERN has not been finding evidence for supersymmetry, WIMP dark matter searches have been coming up empty as well. These searches keep increasing in sensitivity with larger and better detectors and the parameter space for supersymmetric WIMPs is becoming increasingly constrained. Enthusiasm unabated, the WIMP dark matter searchers continue to refine their experiments.

LUX dark matter detector in a mine in Lead, South Dakota is not yet detecting WIMPs. Credit: Matt Kapust/ Sanford Underground Research Facility

What if there is no supersymmetry? Supersymmetry adds a huge number of particles to the particle zoo. Is there a simpler explanation for dark matter?

Alternative candidates under consideration for dark matter, including sterile neutrinos, axions, and primordial black holes, and are now getting more attention.

From a prior blog I wrote about axions as dark matter candidates:

Axions do not require the existence of supersymmetry. They have a strong theoretical basis in the Standard Model as an outgrowth of the necessity to have charge conjugation plus parity conserved in the strong nuclear force (quantum chromodynamics of quarks, gluons). This conservation property is known as CP-invariance. (While CP-invariance holds for the strong force, the weak force is CP violating).

In addition to the dark matter problem, there are two more outstanding problems at the intersection of cosmology and particle physics. These are baryogenesis, the mechanism by which matter won out over antimatter (as a result of CP violation of Charge and Parity), and inflation. A period of inflation very early on in the universe’s history is necessary to explain the high degree of homogeneity (uniformity) we see on large scales and the near flatness of the universe’s topology. The cosmic microwave background is at a uniform temperature of 2.73 Kelvins to better than one part in a hundred thousand across the sky, and yet, without inflation, those different regions could never have been in causal contact.

A team of European physicists have proposed a model SMASH that does not require supersymmetry and instead adds a few particles to the Standard Model zoo, one of which is the axion and is already highly motivated from observed CP violation. SMASH (Standard Model Axion Seesaw Higgs portal inflation) also adds three right-handed heavy neutrinos (the three known light neutrinos are all left-handed). And it adds a complex singlet scalar field which is the primary driver of inflation although the Higgs field can play a role as well.

The SMASH model is of interest for new physics at around 10^11 GeV or 100 billion times the rest mass of the proton. For comparison, the Planck scale is near 10^19 GeV and the LHC is exploring up to around 10^4 GeV (the proton rest mass is just under 1 GeV and in this context GeV is short hand for GeV divided by the speed of light squared).

Figure 1 from Ballesteros G. et al. 2016. The colored contours represent observational limits from the Planck satellite and other sources regarding the tensor-to-scalar power ratio of primordial density fluctuations (r, y-axis) and the spectral index of these fluctuations (ns, x-axis). These constraints on primordial density fluctuations in turn constrain the inflation models. The dashed lines ξ = 1, .1, .01, .001 represent a key parameter in the assumed slow-roll inflation potential function. The near vertical lines labelled 50, 60, 70, 80 indicate the number N of e-folds to the end of inflation, i.e. the universe inflates by a factor of e^N in each of 3 spatial dimensions during the inflation phase.

So with a single model, with a few extensions to the Standard Model, including heavy right-handed (sterile) neutrinos, an inflation field, and an axion, the dark matter, baryogenesis and inflation issues are all addressed. There is no need for supersymmetry in the SMASH model and the axion and heavy neutrinos are already well motivated from particle physics considerations and should be detectable at low energies. Baryogenesis in the SMASH model is a result of decay of the massive right-handed neutrinos.

Now the mass of the axion is extremely low, of order 50 to 200 μeV (millionths of an eV) in their model (by comparison, neutrino mass limits are of order 1 eV), and detection is a difficult undertaking.

There is currently only one active terrestrial axion experiment for direct detection, ADMX. It has its primary detection region at lower masses than the SMASH model is suggesting, and has placed interesting limits in the 1 to 10 μeV range. It is expected to push its range up to around 30 μeV in a couple of years. But other experiments such as MADMAX and ORPHEUS are coming on line in the next few years that will explore the region around 100 μeV, which is more interesting for the SMASH model.

Not sure why the researchers didn’t call this the SMASHpie model (Standard Model Axion Seesaw Higgs portal inflation), because it’s a pie in the face to Supersymmetry!

It would be wonderfully economical to explain baryogenesis, inflation, and dark matter with a handful of new particles, and to finally detect dark matter particles directly.

Reference

“Unifying inflation with the axion, dark matter, baryogenesis and the seesaw mechanism” Ballesteros G., Redondo J., Ringwald A., and Tamarit C. 2016  https://arxiv.org/abs/1608.05414

## Supernovae Destroy Dwarf Galaxies: Dark Matter is Safe

The existence of dark matter has not exactly been under threat – the ratio of dark matter to ordinary matter in the universe is well established, at about 5:1 in favor of dark matter. Consistent results are found between observations of the cosmic microwave background, observations of clusters of galaxies, and observations of the rotation curves of galaxies. (The MOND theory as an alternative to dark matter does not do well at scales greater than that of individual galaxy rotation curves.)

But there has been an issue around galaxy formation. It has been expected that many more dwarf galaxies should be seen in our Local Group, which is dominated by the Andromeda Galaxy (#1) and our Milky Way Galaxy (#2, sorry folks), along with the aptly named Triangulum Galaxy (#3).

Where are the Dwarfs?

Our Milky Way has only around 30 dwarf galaxies as companions, the best known of which are the Large and Small Magellanic Clouds. While a few more have been discovered only recently, simulations of galaxy formation have previously suggested this number ought to be more than 1000! This posed a problem for both our understanding of dark matter and our understanding of galaxy formation.

Now, from CalTech comes a much more detailed simulation of how galaxies similar to the Milky Way are formed. The researchers used over 700,000 CPU hours of supercomputer time to create the most detailed simulation ever of the galaxy formation and evolution processes.

“In a galaxy, you have 100 billion stars, all pulling on each other, not to mention other components we don’t see like dark matter. To simulate this, we give a supercomputer equations describing those interactions and then let it crank through those equations repeatedly and see what comes out at the end.”  – Caltech’s Phil Hopkins, associate professor of theoretical astrophysics.

Death by Supernova

Postdoc Andrew Wetzel and Prof. Hopkins paid special attention to the effects of supernovae. When supernovae explode they release tremendous amounts of kinetic energy. They generate powerful winds that reach speeds of over a thousand kilometers per second.

In a dwarf galaxy an individual supernova can have substantial effect. The researchers’ simulations indicate that dwarf galaxies can actually be destroyed by the effect of even a single supernova during their early history. Stars and gas that would form future stars can both be blown out of the dwarf galaxies. In addition, many dwarf galaxies in the Milky Way’s neighborhood would have been destroyed by the gravitational tidal forces of the Milky Way, the simulations show.

These advanced galaxy evolution simulations appear to solve the dark matter and dwarf galaxy problem. The authors plan to refine their results and develop even greater understanding of galaxy formation with simulations of even greater power in the future.

Simulated View of Milky Way Galaxy
The formation and evolution of the galaxy were done on a supercomputer. Credit: Hopkins Research Group/Caltech

References:

https://www.caltech.edu/news/recreating-our-galaxy-supercomputer-51995

https://youtu.be/e7KuwjGGxBw

## Dark Matter Clumps Tear up Clusters

What is destroying globular clusters?

Globular clusters were formed early in the history of our Milky Way’s history; the 150 or so globular clusters in our galaxy contain many of its oldest stars. Globular clusters are round (hence their name), dense, gravitationally bound collections of stars and can contain hundreds of thousands of stars.

What’s older than globular clusters? Dark matter subhalos! Our galaxy is dominated by dark matter distributed in a halo. Massive supercomputer simulations have shown that regions of higher dark matter density known as subhalos were the seeds for the formation of the galaxy. These subhalos, with millions of solar masses, formed first and supplied the gravity necessary for galaxies to subsequently begin their formation.

Palomar 5 is smaller than most globulars. It was detected only in 1950, in part due to its low mass of only 16,000 solar masses. Palomar 5 is far above the Milky Way’s disk, residing in the dark matter dominated halo, and has been heavily influenced tidally over the past 11 billion years. In its next encounter with the disk, some 100 million plus years into the future, it may even be  completely torn apart by tidal interactions.

Palomar 5 shows significant tidal disruption, with a very long stream of stars trailing out of the cluster, pulled out by tidal forces. The length of the stream is several tens of degrees across the sky, some 30,000 light-years in extent. This is greater than the distance from the Sun to the center of the Milky Way. The stream’s mass is 5000 times that of the Sun.

Of great significance are two well defined gaps in the stream. These gaps are very intriguing to astrophysicists, because they may be probes of the nature of the dark matter in our galaxy’s halo.

Upper portion of Figure 9 from Erkal et al. (referenced below). The two gaps are centered on the dotted lines.

Recently three astrophysicists from the Institute of Astronomy at Cambridge University have modeled the stream and these two gaps and described three main possible causes of the gaps: the Milky Way’s bar (our galaxy has spiral arms leading into a central bar), giant molecular clouds, and/or dark matter halos. (Erkal et al. paper in References below).

They find that gravitational interaction from giant molecular clouds might explain the smaller gap, but not the larger one. Interaction from the Milky Way’s bar is another possibility, but might not be the best for producing such clean gaps, that on the face of it, seem to be due to discrete encounters with smaller structures.

Because of the well defined nature of the gaps, the researchers’ preliminary conclusion is that dark matter halos caused both, and especially so in the case of the larger gap. The smaller gap could be caused by giant molecular clouds, but probably not the larger gap.

The leading tail of the star stream (shown on the left side of the figure) has a two degree gap; this is consistent with an interaction from a dark matter subhalo of 1 to 10 million solar masses. The trailing tail has a nine degree gap that is consistent with perturbation of the stream due to a dark matter subhalo of 10 to 100 million solar masses.

Additional data from several planned experiments should allow better discrimination between the possible causes of the gaps. It is very interesting to note that if the smaller gap is due to a sub halo of a few million solar masses, that knowledge in turn can be used to constrain the mass of the dark matter particles to be greater than 2% of the electron rest mass. This would rule out axions as the dominant contributor to dark matter; the axion mass is expected to be much less than 1 electron-Volt (eV) whereas the electron mass is 511,000 eV.

References:

Erkal, D., Koposov S., and Belokurov V. 2016 “A sharper view of Pal 5’s tails” http://arxiv.org/pdf/1609.01282v1.pdf

Kupper, A. et al. 2015 “Globular Cluster Streams as Galactic High-Precision Scales” https://arxiv.org/abs/1502.02658

Kuzma, P. et al. 2014 “Palomar 5 and its Tidal Tails” https://arxiv.org/abs/1411.0776

http://www.dailygalaxy.com/my_weblog/2016/09/-gigantic-compared-to-our-solar-system-two-massive-holes-caused-by-dark-matter-observed-just-outside.html

https://darkmatterdarkenergy.com/2014/02/09/axions-as-cold-dark-matter/

## WIMPs or MACHOs or Primordial Black Holes

A decade or more ago, the debate about dark matter was, is it due to WIMPs (weakly interacting massive particles) or MACHOs (massive compact halo objects)? WIMPs would be new exotic particles, while MACHOs are objects formed from ordinary matter but very hard to detect due to their limited electromagnetic radiation emission.

Schwarzenegger (MACHO), not Schwarzschild (Black Holes)

Image credit: Georges Biard, CC BY-SA 3.0

Candidates in the MACHO category such as white dwarf or brown dwarf stars have been ruled out by observational constraints. Black holes formed in the very early universe, dubbed primordial black holes, were thought by many to have been ruled out as well, at least across many mass ranges, such as between the mass of the Moon and the mass of the Sun.

The focus during recent years, and most of the experimental searches, has shifted to WIMPs or other exotic particles (axions or sterile neutrinos primarily). But the WIMPs, which were motivated by supersymmetric extensions to the Standard Model of particle physics, have remained elusive. Most experiments have only placed stricter and stricter limits on their possible abundance and interaction cross-sections. The Large Hadron Collider has not yet found any evidence for supersymmetric particles.

Have primordial black holes (PBHs) as the explanation for dark matter been given short shrift? The recent detections by the LIGO instruments of two gravitational wave events, well explained by black hole mergers, have sparked new interest. A previous blog entry addressed this possibility:

The black holes observed in these events have masses in a range from about 8 to about 36 solar masses, and they could well be primordial.

There are a number of mechanisms to create PBHs in the early universe, prior to the very first second and the beginning of Big Bang nucleosynthesis. At any era, if there is a total mass M confined within a radius R, such that

2*GM/R > c^2 ,

then a black hole will form. The above equation defines the Schwarzschild limit (G is the gravitational constant and c the speed of light). A PBH doesn’t even have to be formed from matter whether ordinary or exotic; if the energy and radiation density is high enough in a region, it can also result in collapse to a black hole.

Cosmic Strings

Image credit: David Daverio, Université de Genève, CSCS supercomputer simulation data

The mechanisms for PBH creation include:

1. Cosmic string loops – If string theory is correct the very early universe had very long strings and many short loops of strings. These topological defects intersect and form black holes due to the very high density at their intersection points. The black holes could have a broad range of masses.
2. Bubble collisions from symmetry breaking – As the very early universe expanded and cooled, the strong force, weak force and electromagnetic force separated out. Bubbles would nucleate at the time of symmetry breaking as the phase of the universe changed, just as bubbles form in water as it boils to the surface. Collisions of bubbles could lead to high density regions and black hole formation. Symmetry breaking at the GUT scale (for the strong force separation) would yield BHs of mass around 100 kilograms. Symmetry breaking of the weak force from the electromagnetic force would yield BHs with a mass of around our Moon’s mass ~ 10^25 kilograms.
3. Density perturbations – These would be a natural result of the mechanisms in #1 and #2, in any case. When observing the cosmic microwave background radiation, which dates from a time when the universe was only 380,000 years old, we see density perturbations at various scales, with amplitudes of only a few parts in a million. Nevertheless these serve as the seeds for the formation of the first galaxies when the universe was only a few hundred million years old. Some perturbations could be large enough on smaller distance scales to form PBHs ranging from above a solar mass to as high as 100,000 solar masses.

For a PBH to be an effective dark matter contributor, it must have a lifetime longer than the age of the universe. BHs radiate due to Hawking radiation, and thus have finite lifetimes. For stellar mass BHs, the lifetimes are incredibly long, but for smaller BHs the lifetimes are much shorter since the lifetime is proportional to the cube of the BH mass. Thus a minimum mass for PBHs surviving to the present epoch is around a trillion kilograms (a billion tons).

Carr et al. (paper referenced below) summarized the constraints on what fraction of the matter content of the universe could be in the form of black holes. Traditional black holes, of several solar masses, created by stellar collapse and detectable due to their accretion disks, do not provide enough matter density. Neither do supermassive black holes of over a million solar masses found at the centers of most galaxies. PBHs may be important in seeding the formation of the supermassive black holes, however.

Limits on the PBH abundance in our galaxy and its halo (which is primarily composed of dark matter) are obtained from:

1. Cosmic microwave background measurements
2. Microlensing measurements (gravitational lensing)
3. Gamma-ray background limits
4. Neutral hydrogen clouds in the early universe
5. Wide binaries (disruption limits)

Microlensing surveys such as MACHO and EROS have searched for objects in our galactic halo that act as gravitational lenses for light originating from background stars in the Magellanic Clouds or the Andromeda galaxy. The galactic halo is composed primarily of dark matter.

A couple of dozen of objects with less than a solar mass have been detected.  Based on these surveys the fraction of dark matter which can be PBHs with less than a solar mass is 10% at most. The constraints from 1 solar mass up to 30 solar masses are weaker, and a PBH explanation for most of the galactic halo mass remains possible.

Similar studies conducted toward distant quasars and compact radio sources address the constraint in the supermassive black hole domain, apparently ruling out an explanation due to PBHs with from 1 million to 100 million solar masses.

Lyman-alpha clouds are neutral hydrogen clouds (Lyman-alpha is an important ultraviolet absorption line for hydrogen) that are found in the early universe at redshifts above 4. Simulations of the effect of PBH number density fluctuations on the distribution of Lyman-alpha clouds appear to limit the PBH contribution to dark matter for a characteristic PBH mass above 10,000 solar masses.

Distortions in the cosmic microwave background are expected if PBHs above 10 solar masses contributed substantially to the dark matter component. However these limits assume that PBH masses do not change. Merging and accretion events after the recombination era, when the cosmic microwave background was emitted, can allow a spectrum of PBH masses that were initially less than a solar mass before recombination evolve to one dominated by PBHs of tens, hundreds and thousands of solar masses today. This could be a way around some of the limits that appear to be placed by the cosmic microwave background temperature fluctuations.

Thus it appears could be a window in the region 30 to several thousand solar masses for PBHs as an explanation of cold dark matter.

As the Advanced LIGO gravitational wave detectors come on line, we expect many more black hole merger discoveries that will help to elucidate the nature of primordial black holes and the possibility that they contribute substantially to the dark matter component of our Milky Way galaxy and the universe.

References

B. Carr, K. Kohri, Y. Sendouda, J. Yokoyama, 2010 arxiv.org/pdf/0912.5297v2 “New cosmological constraints on primordial black holes”

S. Cleese and J. Garcia-Bellido, 2015 arxiv.org/pdf/1501.07565v1.pdf “Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the Seeds of Galaxies”

P. Frampton, 2015 arxiv.org/pdf/1511.08801.pdf “The Primordial Black Hole Mass Range”

P. Frampton, 2016 arxiv.org/pdf/1510.00400v7.pdf “Searching for Dark Matter Constituents with Many Solar Masses”

Green, A., 2011 https://www.mpifr-bonn.mpg.de/1360865/3rd_WG_Green.pdf “Primordial Black Hole Formation”

P. Pani, and A. Loeb, 2014 http://xxx.lanl.gov/pdf/1401.3025v1.pdf “Exclusion of the remaining mass window for primordial black holes as the dominant constituent of dark matter”

NEW BOOK just released:

S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)

## Primordial Black Holes as Dark Matter?

LIGO Gravitational Wave Detection Postulated to be Due to Primordial Black Holes

Dark matter remains elusive, with overwhelming evidence for its gravitational effects, but no confirmed direct detection of exotic dark matter particles.

Another possibility which is being re-examined as an explanation for dark matter is that of black holes that formed in the very early universe, which in principle could be of very small mass, or quite large mass. And they may have initially formed at smaller masses and then aggregated gravitationally to form larger black holes.

Recently gravitational waves were discovered for the first time, by both of the LIGO instruments, located in Louisiana and in Washington State. The gravitational wave signal (GW150914) indicates that the source was a pair of black holes, of about 29 and 36 solar masses respectively, spiraling together into a single black hole of about 62 solar masses. A full 3 solar masses’ worth of gravitational energy was radiated way in the merger. Breaking news: LIGO has just this month announced gravitational waves from a second black hole binary of 22 solar masses total. One solar mass of energy was radiated away in the merger.

Image credit: NASA/JPL, http://www.nasa.gov/jpl/nustar/pia18842

Most of the black holes that we detect (indirectly, from their accretion disks) are stellar-sized in the range of 10 to 100 solar masses and are believed to be the evolutionary endpoints of massive stars. We detect them when they are surrounded by accretion disks of hot luminous matter outside of their event horizons. The other main category of black holes exceeds a million solar masses and can even be more than a billion solar masses, and are known as supermassive black holes.

It is possible that some of the stellar-sized and even elusive intermediate black holes were formed in the Big Bang. Such black holes are referred to as primordial black holes. There are a variety of theoretical formation mechanisms, such as cosmic strings whose loops in all dimensions are contained within the event horizon radius (Schwarzschild radius). In general such primordial black holes (PBHs) would be distributed in a galaxy’s halo, would interact rarely and not have accretion disks and thus would not be detectable due to electromagnetic radiation. That is, they would behave as dark matter.

Dr. Simon Bird and coauthors have recently proposed that the gravitational wave event (GW150914) could be due to two primordial black holes encountering each other in a galactic halo, radiate enough of their kinetic energy away in gravity waves to become bound to each other and inspiral to a single black hole with a final burst of gravitational radiation. The frequency of events is estimated to be of order a few per year per cubic Gigaparsec (a Gigaparsec is 3.26 billion light years), if the dark matter abundance is dominated by PBHs.

While low-mass PBHs have been ruled out for the most part, except of a window around one one-hundred millionth of a solar mass, the authors suggest a window also remains for PBHs in the range from 20 to 100 solar masses.

Dr. A. Kashlinsky has gone further to suggest that the cosmic infrared background (CIB) of unresolved 2 to 5 micron near-infrared sources is due to PBHs. In this case the PBHs would be the dominant dark matter component in galactic halos and would mediate early star and galaxy formation. Furthermore there is an unresolved soft cosmic X-ray background which appears to be correlated with the CIB.

This would be a trifecta, with PBHs explaining much or most of the dark matter, the CIB and the soft-X-Ray CXB! But at this point it’s all rather speculative.

The LIGO instruments are now upgraded to Advanced LIGO and as more gravitational wave events are detected due to black holes, we can gain further insight into this possible explanation for dark matter, in whole or in part. Improved satellite born experiments to further resolve the CIB and CXB will also help to explore this possibility of PBHs as a major component to dark matter.

References:

S. Bird et al. arXiv:1603.00464v2 “Did LIGO detect Dark Matter”

A. Kashlinksy arXiv:1605.04023v1 “LIGO gravitational wave detection, primordial black holes and the near-IR cosmic infrared background anisotropies”

http://www.space.com/26857-medium-size-black-hole-discovery-m82.html – “It’s Confirmed! Black Holes Do Come in Medium Sizes”

Video (artist’s representation) of inspiral and merger of binary black hole GW151226 (second gravitational wave detection): https://youtu.be/KwbXxzgAObU

NEW BOOK just released:

S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)

## 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

 Redshift Dark Energy percent Matter percent 0 68 32 0.25 52 48 0.5 39 61 0.75 28 72 1.0 21 79 1.5 12 88

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.

References:

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/

## Gamma Rays from Dark Matter at the Center of the Galaxy: Stronger Evidence

Evidence has been growing for the detection of dark matter more directly – at the center of the Milky Way Galaxy. Normally, we detect dark matter through its gravitational effects only, although there have been many attempts to detect it more directly, both through laboratory experiments here on Earth and from astronomical measurements. The Earthbound experiments are inconclusive at best, with some claims of detection being contradicted by other experiments.

But the evidence for astronomical detection of dark matter is growing. Expected sources include dwarf galaxies https://darkmatterdarkenergy.com/tag/dwarf-galaxies/ that are found near our Milky Way. The low luminosity of dwarf galaxies due to stars and supernovae can make it easier to extract evidence of dark matter due to its self annihilation.

Our own Milky Way Galaxy has a higher concentration of normal matter at the center, and is expected to have a higher concentration of dark matter as well. For the past 5 years or so, there has been evidence for possible dark matter annihilation at the Galactic Center. See http://www.sciencedirect.com/science/article/pii/S0370269311001742.

The mechanism is dark matter self-annihilation, resulting in the creation of decay products of ordinary matter and gamma rays (highly energetic photons). See one of my prior blogs at: https://darkmatterdarkenergy.com/tag/dark-matter-annihilation/.

The leading dark matter candidate is some sort of WIMP (weakly interacting massive particle). WIMPs interact only via gravity and perhaps the weak nuclear force. WIMP self-annihilations can produce quarks, neutrinos, gamma rays and other ordinary matter particles.

There is a known gamma ray signal in the Galactic Center (the center of our Milky Way) that extends to 5 degrees away from the center, corresponding to roughly a kiloparsec in extent (a kiloparsec is 3260 light-years, and our Sun is 8 kiloparsecs from the Center). The major alternatives for this signal appear to be dark matter annihilation, cosmic ray interactions with interstellar gas, or emission from rapidly rotating neutron stars (millisecond pulsars).

A recent paper from T. Daylan and co-authors from Harvard, MIT, Princeton, the University of Chicago and the Fermi Laboratory is titled “The Characterization of the Gamma-Ray Signal from the Central Milky Way: A Compelling Case for Annihilating Dark Matter”. They have reanalyzed observations from the Fermi Gamma Ray Space Telescope and confirmed that the distribution of gamma rays in the Galactic Center (GC) is largely spherically symmetric and extended. This spatial distribution likely rules out neutron stars as the source, since these are preferentially found in the galactic disk.

1-3 GeV residual gamma ray image. From Fig. 10 of T. Daylan et al., this is corrected for galactic diffuse emission and has point sources subtracted. The image extends over a 10◦ by 10◦ region.

Dark matter, on the other hand, would be expected to have a roughly spherical distribution around the GC. Interstellar gas is also largely confined to the galactic disk, so this explanation is disfavored. Their study also confirms that the emission extends beyond the GC to what is known as the Inner Galaxy, further ruling out the two alternatives other than dark matter annihilation. The emission falls off in intensity away from the GC, in a manner consistent with a spherically symmetric dark matter density distribution that is in accordance with a Navarro-Frenk-White profile often used successfully in modeling dark matter halos. No evidence is found for any significant deviation from spherical symmetry for the GC and Inner Galaxy components, the latter extending out to around 2 kiloparsecs.

There are various possible annihilation channels for dark matter and the authors’ analysis appears to favor a dominant channel to primarily b quarks (and b antiquarks). In this scenario the WIMP mass appears to lie in the range of 36 to 51 GeV (by comparison a proton or neutron mass is about .94 GeV). Recall that there are 6 types of quarks, and protons and neutrons are composed of u and d (up and down) quarks. The others are b, t, c, s (bottom, top, charm and strange). The quarks other than u and d are unstable and will decay to u and d.

The spectral (energy) distribution peaks at gamma ray energies of around 1 to 3 GeV and is a good fit to the predictions for annihilation to a b quark pair (b and anti-b). In addition, the cross-section for annihilation calculated from the gamma ray intensity is consistent with that expected from the required rate of thermal production of dark matter particles in the early universe, of order 10^-26 cm^3/sec (actually a value of the cross-section multiplied by the average velocity). The observed dark matter abundance freezes out from thermal equilibrium in the early universe as it expanded and cooled, and implies a cross section of that order.

There is also the possibility for other decay channels, including decays to u, d, c, s and t quarks and to tau lepton particles. The spectral shapes disfavor decays to tau leptons and u, d quarks in particular. After decays to b quarks, the c (charm) and s (strange) quark channels are the most likely.  Either a c or s quark channel implies somewhat lower WIMP masses, around the 20 to 40 GeV range. Annihilations to other fermions appear less likely.

In summary, quoting from their paper:

“This signal consists of a very large number of events, and has been detected with overwhelming statistical significance. The the excess consists of ∼ 10,000 gamma rays per square meter, per year above 1 GeV (from within 10◦ of the Galactic Center). Not only does this large number of events enable us to conclude with confidence that the signal is present, but it also allows us to determine its spectrum and morphology in some detail. And as shown, the measured spectrum, angular distribution, and normalization of this emission does indeed match well with that expected from annihilating dark matter particles.”

“There is no reason to expect that any diffuse astrophysical emission processes would exhibit either the spectrum or the morphology of the observed signal. In particular, the spherical symmetry of the observed emission with respect to the Galactic Center does not trace any combination of astrophysical components (i.e. radiation, gas, dust, star formation, etc.), but does follow the square of the anticipated dark matter density.”

There are also possible detections, marginally significant, of gamma ray emission due to dark matter in nearby dwarf galaxies, and in the direction of the Virgo cluster. We look forward to additional observations and theoretical work to confirm dark matter annihilation signals in our own galaxy and nearby galaxies.

NEW BOOK just released:

S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)

## Gravitational Waves and Dark Matter, Dark Energy

What does the discovery of gravitational waves imply about dark matter and dark energy?

The first detection of gravitational waves results from a pair of merging black holes, and is yet another magnificent confirmation of the theory of general relativity. Einstein’s theory of general relativity has passed every test thrown at it during the last 100 years.

While the existence of gravitational waves was fully expected to be confirmed, the discovery took several decades and represents a technological tour de force. Detected at the two LIGO sites, one in Louisiana and one in Washington State, the main event lasted only 0.2 seconds, and was seen as a change of length in the “arms” of the detector (laser interferometers) of only one part in a thousand billion billion.

The LIGO detection of gravitational waves. The blue curve is from the Louisiana site and the red curve from the Washington state site. The two curves are shifted by 7 milliseconds to account for the speed-of-light delay between the two sites. Note that most of the power in the signal occurs within less than 0.2 seconds. The strain is a measure of proportional change in length of the detector arm and is less than 1 part in 10²¹.

Nevertheless, this is the most energetic event ever seen by mankind. The merger of two large black holes totaling over 60 times the Sun’s mass resulted in the conversion of 3 solar masses of material into gravitational wave energy. Imagine, there were 3 Suns worth of matter obliterated in the blink of an eye. During this brief period, the generated power was greater than that from the light of all of the stars of all of the galaxies in our known universe.

What the discovery of gravitational waves has to say about dark matter and dark energy is essentially that it further confirms their existence.

Although there is as of now no direct detection of dark matter, we infer the existence of dark matter by using the equations of general relativity (GR), in a number of cases, including:

1. Gravitational lensing – Typically, a foreground cluster of galaxies distorts and magnifies the image of a background galaxy. GR is used to calculate the bending and magnification, primarily caused by the dark matter in the foreground cluster.
2. Cosmic microwave background radiation (CMBR) – The CMBR has spatial fluctuation peaks (harmonics) and the first peak tells us about ordinary matter and the third peak about the density of dark matter. A GR-based cosmological model is used to determine the dark matter average density.

Dark matter is also inferred from the way in which galaxies rotate and from the velocities of galaxies within galaxy clusters, but general relativity is not needed to calculate the dark matter densities in such cases. However, results from these methods are consistent with results from the methods listed above.

In the case of dark energy, it turns out to be a parameter in the equations of general relativity as first formulated by Einstein. The parameter, lambda, (Λ) is known as the cosmological constant, and represents the minimum energy of the vacuum. For many years astronomers and cosmologists thought it might take the value of zero. However in 1998 multiple teams confirmed that the value is positive and not zero, and it turns out that dark energy has more than twice the energy content of dark matter. Its non-zero value is actually another stunning success for general relativity.

Thus the detection of gravitational waves indirectly provides further support for the canonical cosmological model ΛCDM, with both dark matter and dark energy, and fully consistent with general relativity.

References

B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 – Published 11 February 2016 – http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102

NEW BOOK just released:

S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)