# Tag Archives: WIMPs

## Hexaquark Dark Matter: Bosons, but not WIMPy at all

Dibaryons

Imagine you smash a proton and neutron together. What do you get? Typically you get a deuteron which is the nucleus of deuterium, heavy hydrogen. Deuterium has one electron in its neutral atomic state. And it has two baryons, the proton and neutron, so it is known as a dibaryon.

Now as you have heard, protons and neutrons are really quark triplets, held together by gluons in bound configurations. A proton has two up quarks (electric charge +2/3) and a down quark (charge -1/3) for a net charge of +1 and a neutron has two down quarks and an up quark for a net charge of 0.

These are the two lightest quarks and protons and neutrons are by far the dominant components in the ordinary matter in the universe, mostly as hydrogen and helium.

Quarks, protons, and neutrons are all fermions, particles with half-integer spins (1/2, 3/2, -1/2, etc.).

The other main class of particles is called bosons, and that class includes photons, gluons, the W and Z of the weak interaction, and the never directly observed graviton. They all have integer spins (typically 1, but 0 for the Higgs boson, and 2 for the graviton).

Figure 1: The Standard Model major particles: quarks (purple), leptons (green), force carrier bosons (orange), Higgs boson (yellow) with mass, charge, spin indicated.

Six quarks in a Bag

Suppose you collided a proton and neutron together, each with three quarks, and you ended up with a single six quark particle that was stable. It would be a more exotic type of dibaryon. It would have three up quarks, three down quarks, and it would not be a fermion. It would be a boson, with integer spin, spin 0 or 1, in this case. It would be six quarks in a bag, a bound state held together by gluons.

Figure 2. Six quarks in a bag, a hexaquark

Figure 3. The d* resonance at 2.38 GeV, observed at the Cooler Synchrotron in Julich, Germany

Such a particle has been discovered in the past decade, and is named the d* hexaquark. It is seen as the resonance in Figure 3 above, found in proton-neutron collisions, and has a mass of 2.38 GeV (for reference the proton mass is 0.935 GeV and the neutron mass is 0.938 GeV). It decays to a deuteron and two pions, either neutral as shown in the figure, or charged pions.

It is also possible to produce a d* by irradiating a deuteron with a gamma ray.

The d* was already predicted by the famed mathematician and physicist Freeman Dyson in 1964, working with his collaborator Xuong. Their mass estimate was quite close at 2.35 GeV, using a simple quark model.

Dyson just passed away recently; you may have heard of his Dyson sphere concept. The idea is that an advanced civilization would build a sphere of solid material surrounding its star in order to hold an extremely large population and absorb virtually all of the star’s energy. Larry Niven modified this to a ring in his 1970 sci-fi novel Ringworld.

Hexaquark dark matter

Azizi, Ageav, and Sundu have recently suggested a hexaquark of the form uuddss, that is, two up, two down, and two strange quarks. Their mass estimate is around 1.2 GeV, half that of the d* composed of only up and down quarks. It is expected to be stable with long lifetime.

And also recently, Bashkanov and Watts at the University of York have made a nice proposal that d* could be the dark matter particle. The d* particle is itself unstable, but they propose that stable condensates with many d* particles could form. Their paper,  “A New Possibility for Light-Quark Dark Matter” is here:

https://iopscience.iop.org/article/10.1088/1361-6471/ab67e8/pdf

The d* has one great advantage over the other proposed particles, it has actually been discovered! The d* has a good sized mass for a dark matter candidate, at about 2.5 times the mass of the proton.

The authors find that the d* could form lengthy chains or spherical condensates with thousands to millions of d* particles. Unlike individual d* particles, the condensates could be stable ‘super atoms’ lasting for billions of years.

However to make this work the binding energy would have to exceed the difference between the 2.38 GeV d* mass and the deuteron mass of 2.014mGeV, thus would have to be greater than about 0.4 GeV.

The d* would be produced thermally when the universe was at temperatures in the range from 1 to 3 trillion Kelvins. The condensates would need to form quickly before individual d* particles of short lifetimes decayed away.

The favored candidates for dark matter have been WIMPs, supersymmetric particles. But no supersymmetric particle has ever been detected at the Large Hadron Collider or elsewhere, which is incredibly disappointing for many particle physicists. The other main candidates have been the axion and sterile neutrino, both quite low in mass. These have never been directly detected either; they remain hypothetical.

The d* particle is a boson, and the authors’ theoretical approach is that in the early universe as it cooled, both baryons and dibaryonic matter froze out. The baryons ended up, after the cosmic nucleosynthesis phase as protons, deuterium dibaryons, and helium nuclei (alpha particles, that are composed essentially of two deuterons), the main constituents of ordinary matter.

What would happen to d* under the early conditions of the Big Bang? Bosons like to clump together, into something called Bose-Einstein condensates. Yes, that Einstein. And that Boson. Bose-Einstein statistics were developed in the 1920s and govern the statistics of bosons (integer spin particles), and differ from that of fermions.

To confirm this model would require astronomical observations or cosmic ray observations. Decays of d* particles could result in gamma ray production with energies up to 0.5 GeV. Their decay products might also be seen as upward moving cosmic rays, in Earth-bound cosmic ray experiments. These would be seen coming up through the Earth, unlike normal cosmic rays that cannot penetrate so much ordinary matter, and the decay events would result in gamma rays, nucleons and deuterons, as well as pions as the decay products.

## WIMPZillas: The Biggest WIMPs

In the search for direct detection of dark matter, the experimental focus has been on WIMPS – weakly interacting massive particles. Large crystal detectors are placed deep underground to avoid contamination from cosmic rays and other stray particles.

WIMPs are often hypothesized to arise as supersymmetric partners of Standard Model particles. However, there are also WIMP candidates that arise due to non-supersymmetric extensions to the Standard Model.

The idea is that the least massive supersymmetric particle would be stable, and neutral. The (hypothetical) neutralino is the most often cited candidate.

The search technique is essentially to look for direct recoil of dark matter particles onto ordinary atomic nuclei.

The only problem is that we keep not seeing WIMPs. Not in the dark matter searches, not at the Large Hadron Collider whose main achievement has been the detection of the Higgs boson at mass 125 GeV. The mass of the Higgs is somewhat on the heavy side, and constrains the likelihood of supersymmetry being a correct Standard Model extension.

The figure below shows WIMP interaction with ordinary nuclear matter cross-section limits from a range of experiments spanning from 1 to 1000 GeV masses for WIMP candidates. Typical supersymmetric (SUSY) models are disfavored by these results at higher masses above 40 GeV or so as the observational limits are well down into the yellow shaded regions.

Perhaps the problem is that the WIMPs are much heavier than where the experiments have been searching. Most of the direction detection experiments are sensitive to candidate masses in the range from around 1 GeV to 1000 GeV (1 GeV or giga-electronVolt is about 6% greater than the rest mass energy of a proton). The 10 to 100 GeV range has been the most thoroughly searched region and multiple experiments place very strong constraints on interaction cross-sections with normal matter.

WIMPzillas is the moniker given to the most massive WIMPs, with masses from a billion GeV up to  potentially as large as the GUT (grand Unified Theory) scale of $10^{16} GeV$.

The more general term is Superheavy Dark Matter, and this is proposed as a possibility for unexplained ultra high energy cosmic rays (UHECR). The WIMPzillas may decay to highly energetic gamma rays, or other particles, and these would be detected as the UHECR.

UHECR have energies greater than a billion GeV ($10^9 GeV$) and the most massive event ever seen (the so-called Oh My God Particle) was detected at $3 \cdot 10^{11} GeV$. It had energy equivalent to a baseball with velocity of 94 kilometers per hour. Or 40 million times the energy of particles in the Large Hadron Collider.

It has taken decades of searching at multiple cosmic ray arrays to detect particles at or near that energy.

Most UHECR appear to be spatially correlated with external galaxy sources, in particular with nearby Active Galactic Nuclei that are powered by supermassive black holes accelerating material near, but outside of, their event horizons.

However, they are not expected to be able to produce cosmic rays with energies above around $10^{11} GeV$, thus the WIMPzilla possibility. Again WIMPzillas could span the range from $10^9 GeV$ up to $10^{16} GeV$.

In a paper published last year, Kolb and Long calculated the production of WIMPzillas from Higgs boson pairs in the early universe. These Higgs pairs would have very high kinetic energies, much beyond their rest mass.

This production would occur during the “Reheating” period after inflation, as the inflaton (scalar energy field) dumped its energy into particles and radiation of the plasma.

There is another production mechanism, a gravitational mechanism, as the universe transitions from the accelerated expansion phase during cosmological inflation into the matter dominated (and then radiation-dominated) phases.

Thermal production from the Higgs portal, according to their results, is the dominant source of WIMPzillas for masses above $10^{14} GeV$. It may also be the dominant source for masses less than about $10^{11} GeV$.

They based their assumptions on chaotic inflation with quadratic inflation potential, followed by a typical model for reheating, but do not expect that their conclusions would be changed strongly with different inflation models.

It will take decades to discriminate between Big Bang-produced WIMPzilla style cosmic rays and those from extragalactic sources, since many more $10^{11} GeV$ and above UHECRs should be detected to build statistics on these rare events.

But it is possible that WIMPzillas have already been seen.

The density is tiny. The current dark matter density in the Solar neighborhood is measured at 0.4 Gev per cc. Thus in a cubic meter there would be the equivalent of 400,000 proton masses.

But if the WIMPzillas are at energies $10^{11} Gev$ and above (100 billion GeV), a cubic kilometer would only contain 4000 particles at a given time. Not easy to catch.

References

http://cdms.berkeley.edu/publications.html – SuperCDMS experiment led by UC Berkeley

http://pdg.lbl.gov/2017/reviews/rpp2017-rev-dark-matter.pdf – Dark matter review chapter from Lawrence Berkeley Lab (Figure above is from this review article).

http://home.physics.ucla.edu/~arisaka/home3/Particle/Cosmic_Rays/ – Ultra high energy cosmic rays

https://arxiv.org/pdf/1708.04293.pdf – E. Kolb and A. Long, 2017 “Superheavy Dark Matter through Higgs Portal Operators”

## Primordial Black Holes and Dark Matter

Based on observed gravitational interactions in galactic halos (galaxy rotation curves) and in group and clusters, there appears to be 5 times as much dark matter as ordinary matter in the universe. The alternative is no dark matter, but more gravity than expected at low accelerations, as discussed in this post on emergent gravity.

The main candidates for dark matter are exotic, undiscovered particles such as WIMPs (weakly interacting massive particles) and axions. Experiments attempting direct detection for these have repeatedly come up short.

The non-particle alternative category is MACHOs (massive compact halo objects) composed of ordinary matter.  Planets, dwarf stars and neutron stars have been ruled out by various observational signatures. The one ordinary matter possibility that has remained viable is that of black holes, and in particular black holes with much less than the mass of the Sun.

The only known possibility for such low mass black holes is that of primordial black holes (PBHs) formed in the earliest moments of the Big Bang.

Gravitational microlensing, or microlensing for short, seeks to detect PBHs by their general relativistic gravitational effect on starlight. MACHO and EROS were experiments to monitor stars in the Large Magellanic Cloud. These were able to place limits on the abundance of PBHs with masses from about one hundred millionth of a the Sun’s mass up to 10 solar masses. PBHs from that mass range are not able to explain the total amount of dark matter determined from gravitational interactions.

LIGO has recently detected several merging black holes in the tens of solar mass range. However the frequency of LIGO detections appears too low by two orders of magnitude to explain the amount of gravitationally detected dark matter. PBHs in this mass range are also constrained by cosmic microwave background observations.

Extremely low mass PBHs, below 10 billion tons, cannot survive until the present epoch of the universe. This is due to Hawking radiation. Black holes evaporate due to their quantum nature. Solar mass black holes have an extremely long lifetime against evaporation. But very low mass black holes will evaporate in billions of years or much sooner, depending on mass.

The remaining mass window for possible PBH, in sufficient amount to explain dark matter, is from about 10 trillion ton objects up to those with ten millionths of the Sun’s mass.

Figure 5 from H. Niikura et al. “Microlensing constraints on primordial black holes with the Subaru/HSC Andromeda observation”, https://arxiv.org/abs/1701.02151

Here f is the fraction of dark matter which can be explained by PBHs. The red shaded area is excluded by the authors observations and analysis of Andromeda Galaxy data. This rules out masses above 100 trillion tons and below a hundred thousandth of the Sun’s mass. (Solar mass units used above and grams are used below).

Now, a team of Japanese astronomers have used the Subaru telescope on the Big Island of Hawaii (operated by Japan’s national observatory) to determine constraints on PBHs by observing millions of stars in the Andromeda Galaxy.

The idea is that a candidate PBH would pass in front of the line of sight to the star, acting as a lens, and magnifying the light from the star in question for a relatively brief period of time. The astronomers looked for stars exhibiting variability in their light intensity.

With only a single nights’ data they made repeated short exposures and were able to pick out over 15,000 stars in Andromeda exhibiting such variable light intensity. However, among these possible candidates, only a single one turned out to fit the characteristics expected for a PBH detection.

If PBHs in this mass range were sufficiently abundant to explain dark matter, then one would have expected of order one thousand events, and they saw nothing like this number. In summary, with 95% confidence, they are able to rule out PBHs as the main source of dark matter for the mass range from 100 trillion tons up to one hundred thousandth of the Sun’s mass.

The window for primordial black holes as the explanation for dark matter appears to be closing.

## 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

## 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)

## 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)

## Black Holes Destroy Dark Matter (and Emit Gamma Rays)

Black holes can cause dark matter to annihilate in their vicinity by concentrating the dark matter and enhancing the collision rate between dark matter particles. The best observational candidates are supermassive black holes, such as the 4 million solar mass black hole found at the center of our Milky Way galaxy. Some galaxies have much larger supermassive black holes, reaching as high as several billion or even tens of billions of solar masses. Most massive galaxies appear to have supermassive black holes in their centers.

Artist’s conception of a supermassive black hole (public domain; courtesy NASA JPL)

We infer the existence of supermassive black holes through their effect on nearby stellar or molecular cloud orbits. And we more directly detect supermassive black holes (SMBHs) by the radiation emitted from ordinary matter that is near the black hole (BH), but has not yet fallen into the BH’s event horizon (from which nothing, not even light, can escape). Such matter will often form a hot accretion disk around the SMBH. The disk or other infalling matter can be heated to millions of degrees by the strong gravitational potential of the BH as the kinetic energy of infall is converted to thermal energy by frictional processes. Ordinary matter (OM) heated to such high temperatures will give off X-rays.

Now if OM is being pulled into a SMBH, so is dark matter, which pervades every galaxy. Dark matter (DM) responds to the same gravitational potential from the SMBH. The difference is that OM is collisional since it easily interacts with other OM via the electromagnetic force, whereas DM is generally collisionless, since it does not interact via electromagnetism.

Nevertheless DM – DM collisions can occur, rarely, via a ‘direct hit’ (as if two bullets hit each other in mid-air) and this leads to annihilation. Two DM particles meet directly and their entire energy content, from their rest mass as well as their kinetic energy of motion, is converted into other particles. The cross-section strength is not known, but it must be small due to observational limits, yet is expected to be non-zero. The most likely candidates for decay products are expected to be photons, neutrinos, and electrons.

The leading candidate for DM is some sort of weakly interacting massive particle with a mass of perhaps 5 to 300 GeV; this is the range where DM searches from satellites and on Earth are focused. (The proton mass is a little less than 1 GeV = billion electron Volts.) So if two DM particles mutually annihilate, there is of order 10 GeV to 600 GeV of available rest mass energy to produce highly energetic gamma rays.

The likelihood of a direct hit is proportional to the square of the density of the DM. A SMBH’s gravitational potential acts as a concentrator for DM, allowing the density to be high enough that there could be a significant number of annihilation events, resulting in a detectable flux of escaping photons reaching Earth. Relativistic effects work to further increase the annihilation rate. And it is possible that the annihilation signal could scale as M³ (mass of the SMBH cubed), and thus the most massive SMBHs would be very strong gamma ray emitters. These would be highly energetic gamma rays with well over 1 GeV of energy.

Movie from NASA Goddard showing Dr. Jeremy Schnittman’s simulation

Dr. Jeremy Schnittman of the NASA Goddard Space Flight Center has investigated possible annihilation rates and the nature of the observable gamma ray spectrum for some simple dark matter models. He used a compute cluster to simulate hundreds of millions of DM particles moving in the general direction of a SMBH. One of his remarkable findings is that much higher gamma ray energies can be produced than previously believed, in the case of SMBHs which are rapidly spinning.

This is a result of something known as the Penrose process, which allows energy to be extracted from a rotating BH. There is a region called the ergosphere outside of the event horizon and when two DM particles annihilate in this region and produce two gamma rays, one gamma ray photon would fall into the event horizon (into the BH), and the other photon would escape to infinity, possibly in the direction of Earth. Dr. Schnittman’s simulation indicates that the energy boost can be as high as 6 times or more. The faster the SMBH is spinning, the greater the potential energy boost.

He also has looked at DM particles on bound orbits, which are likely to form into a (donut-shaped) corotating torus around the SMBH, aligned with its spin vector. The bound DM particle annihilations lead to lower energy gamma ray production, as compared to the unbound particles.

One of the important considerations is that the influence radius of the BH is very large. The size of the BH itself (event horizon or Schwarzschild radius) is small, even for SMBHs. The radius is proportional to the mass, via the relation 2GM/R = c² (G is the gravitational constant, c the speed of light and M and R are the BH mass and radius, respectively). A SMBH with a mass of 10 million solar  masses will have a radius of only around 30 million kilometers, or about 1/5 of the Earth-Sun distance (an AU, or astronomical unit).

But the gravitational influence is much greater, since DM particles are typically expected to be moving at around only a couple of hundred kilometers per second far away from the SMBH. Thus DM particles that are 1 million times further away than the SMBH will have their orbits in their galaxy perturbed by the SMBH. And the scale of influence is thus parsecs (1 parsec = 3.26 light-years) or tens of parsecs or even hundreds of parsecs, depending on the SMBH mass.

The most energetic gamma rays can be produced by unbound DM particles. These are on orbits which can approach near to the SMBH after falling from far away (a “swan dive” toward the SMBH) and these DM particles would then typically head out away from the SMBH in the opposite direction. But before they are able to, they have a direct hit with another DM particle and annihilate into gamma rays or some other decay products.

The search for gamma rays from annihilating DM around SMBHs is already underway. There is in fact a possible detection by the Fermi telescope at 130 GeV in our Milky Way galaxy, from the direction of the Sagittarius A* SMBH. Future more sensitive gamma ray surveys may lead to many detections, helping us to better understand both dark matter and black holes.

References

J.D. Schnittman, 2015. “The Distribution and Annihilattion of Dark Matter around Black Holes”, http://arxiv.org/abs/1506.06728

J.D. Schnittman, 2014. Phys. Rev. Letters 113, 261102,  “Revised Upper Limit to Energy Extraction from a Kerr Black Hole”

## Dark Matter Eludes LUX

The LUX (Large Underground Xenon) experiment has just announced results from their first run, which gathered data for 85 days between April and August of this year. LUX is located a mile underground (to shield from cosmic rays and other interference) in an old mine in South Dakota, and employs a liquid Xenon detector with total mass of 370 kg. LUX is searching for WIMP dark matter particles which recoil directly off the nucleus of Xenon atoms in the detector.

Large Underground Xenon detector, Photo by Carlos Faham, CC Attribution 3.0 license

They have two important findings from this first swath of data. First, to within the sensitivity of their experiment, they detected no weakly interacting massive dark particles (WIMPs). And second, their experiment has much greater sensitivity than other experiments in the low mass range from about 5 GeV to 100 GeV (the proton rest mass is a bit less than 1 GeV). Thus it is placing much tighter constrains on the cross-section for dark matter to interact with a nucleus, and the density of dark matter at the Earth’s orbit. The previous largest Xenon-based experiment was XENON100 (for 100 kg total detector mass). With LUX, the sensitivity has improved over the results of that earlier experiment by around a factor of 20 for a possible 10 GeV WIMP mass, due to the larger target and better rejection of background events.

This chart is the most interesting portion of Fig. 5 from the LUX first results paper (reference below). The blue line shows the upper limit on the cross section dropping from 10^-40 cm² to less than 10-44 cm² as a function of WIMP mass, as the mass increases from about 5 to 12 GeV (X-axis above the chart). Note the Y-axis is logarithmic, so the new limit is orders of magnitude below other limits (various colored curves) and claimed possible detections (shaded areas).

These new LUX results are in direct conflict with possible detections from CoGeNT (small red-shaded area on chart), CRESST (yellow-shaded), CDMS- II (green-shaded area), and DAMA/LIBRA (grey-shaded area), all of which were suggesting detections with a WIMP dark matter mass around 10 GeV. Now certain assumptions are made about the astrophysical parameters such as the density of dark matter at the Earth being the same as the average in our part of the galaxy. But other experimental results are based on similar assumptions, so this does not explain the discrepancy.

Both CoGeNT and CDMS-II sit in the same Soudan Laboratory in Minnesota, one state over from where the LUX experiment resides. However different experiments use different atoms as targets: CoGeNT uses germanium, CDMS uses silicon, CRESST uses calcium tungstate crystals and DAMA/LIBRA uses thallium doped sodium iodide. These latter two experiments are both located in Italy, in a mountain tunnel. All of these experiments are attempting to discern a very faint signal against significant backgrounds. And perhaps earn a Nobel Prize in Physics as well. So it’s natural for the researchers on the associated teams to lean toward optimism It remains quite possible, and now seems more and more probable, that the experiments other than LUX are observing some unexplained non-dark matter background effect, so this is a very significant result.

LUX is not finished, of course. It’s just getting going. So we await their further results, with either a possible WIMP detection in the future, or even tighter limits on the existence of lower mass WIMPs.

References:

http://t.co/1hyXRSiBsK – D.S. Akerib et. al., 2013,  “First results from the LUX dark matter experiment at the Sanford Underground Research Facility”

https://theconversation.com/dark-matter-experiment-finds-nothing-makes-news-19707 – LUX results are constraining WIMP parameter space

## Multi-component Dark Matter: Let there be Heavy and Let there be Light

Around 27% of the universe’s mass-energy is due to dark matter, according to the latest Planck satellite results; this finding is consistent with a number of other experiments as well. This is approximately 6 times more than the total mass due to ordinary matter (dominated by protons and neutrons) that makes up the visible parts of galaxies, stars, planets, and all of our familiar world.

The most likely explanation for dark matter is some kind of WIMP – Weakly Interacting Massive Particle. The amount of deuterium (heavy hydrogen) produced in the very early universe rules out ordinary matter as the primary explanation for the various “excess” gravitational effects we see in galaxies, groups and clusters of galaxies and at the largest distance scales in our observable universe.

WIMPs are thought to be a class of new, exotic particles, beyond the Standard Model. A favored candidate for dark matter is the lightest supersymmetric particle, although supersymmetry is as of yet unproven. The lightest such particle would be very stable, having nothing into which it could decay readily. A mass range of 5 to 300 GeV or so is the range in which most of the direct detection experiments looking for dark matter are focused (1 GeV = 1 giga-volt is a little more than the mass of a proton).

But there would certainly be more than one kind of such WIMP formed in the very early universe. These would be heavier particles, and most would quickly decay into lighter products, but there might still be some heavier WIMPs remaining, provided their lifetime was sufficiently long. Particle physicists are actively working on models with more than one component for dark matter, typically two-component models with a heavy particle above 100 GeV mass, and a lighter component with mass of order 10 GeV (more or less).

In fact there are observational hints of the possibility of both a light dark matter particle and a heavier one. The SuperCDMS team has announced a possible detection around 8 or 9 GeV. The COGENT experiment has a possible detection in the neighborhood of 10 GeV, and in general agreement with the SuperCDMS results.

Fermi satellite payload, photo credit: NASA/Kim Shiflett

At the heavier end, the Fermi LAT gamma-ray experiment has made a possible detection of an emission line at 130 GeV which might result from dark matter decay. A pair of such gamma rays could be decay products from annihilation of a heavier dark matter particle with mass around 260 GeV. Or a particle of that mass could decay into some other particle plus a photon with about half of the heavy dark matter mass, e.g. 130 GeV.

Kajiyama, Okada and Toda have built one such model with a light particle around 10 GeV and a heavier one in the 100 to 1000 GeV region. They claim their model is consistent with the observational limits on dark matter placed by the XENON 100 experiment.

Gu has developed a model with 2 dark matter components with magnetic moments. Representative values of the heavy dark matter particle mass at 262 GeV and the lighter particle mass at 20 GeV can reproduce the observed overall dark matter density. He also finds the decay lifetime for the heavier particle state to be very long, in excess of 10^20 years, or 10 billion times the age of the universe, thus in this model the heavy dark matter particle easily persists to the present day. In fact, he finds that the heavy particle dominates with over 99% of the total mass contribution to dark matter. And a heavy dark matter particle with the chosen mass can decay into the lighter dark matter particle plus an energetic 130 GeV gamma ray (photon). This might explain the Fermi LAT results.

Furthermore, the existence of two highly stable dark matter particles of different masses would help explain some astrophysical issues related to the formation of galaxies and their observed density profiles. Mikhail Medvedev has numerically simulated galaxy formation using supercomputers, with a model incorporating two dark matter components. This model results in a better fit to the observed velocities of dwarf galaxies in the Local Group than does a model with a single dark matter component. (The Local Group includes our Milky Way, the Andromeda galaxy, the Magellanic Clouds and a number of dwarf galaxies.) His model also helps to explain the more flattened density profiles in galaxies and the smaller numbers of dwarf galaxies actually observed relative to what would be predicted by single dark matter component models.

Occam’s razor says one should adopt the simplest model that can explain observational results, suggesting one should add a second component to dark matter only if needed. It seems like a second dark matter component might be necessary to fully explain all the results, but we will require more observations to know if this is the case.

References:

http://prd.aps.org/abstract/PRD/v88/i1/e015029 Y. Kajiyama, H. Okada and T. Toda 2013, “Multicomponent dark matter particles in a two-loop neutrino model”

http://www.sciencedirect.com/science/article/pii/S2212686413000058
P. Gu 2013, “Multi-component dark matter with magnetic moments for Fermi-LAT gamma-ray line”

http://arxiv.org/pdf/1305.1307v1.pdf M. Medvedev 2013, “Cosmological Simulations of Multi-Component Cold Dark Matter”

## Dark Matter in the Solar System: Does it Matter?

Dark matter is the dominant form of matter in the universe. Measurements from supernovae, the cosmic microwave background, galaxy clusters, galaxy rotation and other techniques indicate that it is approximately 5 or 6 times as abundant by mass density as ordinary matter. By particle number, it is probably less abundant, as long as the dark matter particle has mass greater than 6 GeV (giga-electron Volts) as seems likely (actually mass is in units of GeV/c², but physicists like to use the shorthand of “GeV”). The ordinary matter mass component is dominated by protons and neutrons with approximately 1 GeV mass. So if the dark matter particle turns out to be 6 GeV, which is near the lower bound of expected mass, then just as many dark matter particles as protons and neutrons combined would explain the nearly 6 times as much dark matter mass density on average, as compared to ordinary matter density. Otherwise, if the dark matter particle mass is larger, fewer would suffice.

Dark matter clumps, under its own gravitational influence, into large scale structures including superclusters of galaxies, clusters and groups of galaxies, and individual galaxies and dwarf galaxies. Within our own Milky Way galaxy, the dark matter is more diffuse, more spread out, than ordinary matter. As one moves away from the center of the galaxy, and above the spiral disk that contains most of the ordinary, luminous matter, the dark matter to ordinary matter ratio increases. Ordinary matter clumps to a much greater degree since it feels electromagnetic forces, and these result in friction and shock waves that heat up the ordinary matter, but also cooling via radiative processes – emission of photons. Cold ordinary matter will clump due to mutual gravitational infall as it cools, and this is how we end up with molecular clouds (stellar nurseries), stars, and planets, moons, asteroids, and comets. In these structures, which are at much smaller distance scales, ordinary matter dominates over dark matter. Dark matter doesn’t feel electromagnetic forces, so it remains more spread out, influenced primarily by gravitational forces.

Nevertheless, one can ask the question, to what extent does dark matter influence our Solar System? For example, are the orbits of the Earth or other planets perturbed due to the gravitational effect of dark matter found in the Solar System? Surely there is some dark matter within the Solar System, assuming the most favored explanation, that it is some sort of new particle, a WIMP – weakly interacting massive particle, or perhaps an axion. This is why direct detection efforts looking for dark matter passing through Earth-bound laboratories are worthwhile.

The amount of dark matter in the galactic plane in the vicinity of the Solar neighborhood is estimated by looking at the dynamics of stars nearby and above and below the Milky Way’s disk. By looking at their velocity distribution we can measure the total mass density and subtract out the ordinary matter component. The favored value in the Solar neighborhood for the galactic background is usually taken to be 0.3 GeV/cc and equates to the equivalent of 1 proton per every 3 cubic centimeters. Thus, with this value, if the dark matter particle has mass 10 GeV, there would need to be 1 of these particles for each 30 cc of space. This is not a significant amount; within Earth’s orbit it would amount to about 8 billion tons. Out to the orbit of Saturn, the total amount would be around 9 trillion tons. This is not much in Solar System terms.

However, there’s more to the story than just this quick estimate. Let’s look at the observational constraints first; one can look for perturbations in the orbits of the major Solar System bodies to place some constraints on the amount of dark matter. Then we will look at the possibility that the  Solar System’s complement of dark matter is significantly higher than the value inferred from stellar dynamics within the Milky Way, due to gravitational capture of some of the dark matter encountered over billions of years as the Sun (and the rest of the Solar System) orbits the center of our galaxy at over 200 kilometers per second. The idea is that the average in the Solar “suburban” neighborhood is close to the estimate above, but in the “urban” neighborhood closer to the Sun the dark matter is more concentrated, due to being gravitationally swept up by the Sun and larger planets.

Russian researchers Pitjev and Pitjeva have studied hundreds of thousands of observations – over a nearly 50 year period – of the planets, a number of their moons, and spacecraft in the Solar System, looking for orbital perturbations. They find no measurable deviations which could be ascribed to dark matter. They have found that the density is less than 1.1 x 10^-20 grams/cc at the orbit of Saturn, 1.4 x 10^-20 g/cc at Mars, and less than 1.4 x 10^-19 g/cc at Earth. We can convert this to GeV/cc by noting that the proton mass is .938 GeV, which is equivalent to 1.67 x 10^-24 grams. So their upper limit on density at Saturn is then equivalent to 6000 GeV/cc. This is a much looser constraint. In other words, even at several thousand GeV/cc for the dark matter density near to the Sun, no apparent orbital perturbations would be expected for the 8 planets and several moons and spacecraft studied.

Thus one can conclude that even if the dark matter density in the Solar neighborhood were 10 or even 100 times larger than expected from stellar dynamics observations, that its gravitational effects on the precisely measured orbits of the major planets and major moons in the Solar system would be of no consequence.

In fact the authors note that the aggregate dark matter within Saturn’s orbit should be less than 1/6th of 1 billionth of the Sun’s mass, which is 2 x 10^27 metric tons. We’re talking at most 3 x 10^17 metric tons, which is a lot, but not in Solar system terms. The mass of the Moon is 7 x 10^19 metric tons, so this is an amount over 200 times smaller than the Moon’s mass spread out over the volume within Saturn’s orbit.

Another research team, at the University of Arizona, used a different technique five years ago. They modeled how much dark matter would be swept up into and gravitationally captured, by the Solar System over its 4.5 billion year history as it moves around the galactic center. Drs. Xu and Siegel calculate that about 10^17 metric tons of dark matter have been captured, out to the outer reaches of the Solar system. This amount is just 0.14% of the Moon’s mass and 0.0018% the mass of the Earth. This is consistent with the less than 1/3 x 10^18 metric tons within Saturn’s orbit from the orbital study above.

One of the important consequences of the Xu and Siegel results is that direct searches for dark matter need to consider in their models for data analysis not only the flux of the high velocity component as the Earth and Solar System move around the galactic center at over 200 km/sec, but also the lower velocity component. This applies to the more abundant dark matter that is bound within the Solar System and through which the Earth moves at a rate of 30 km/sec. At the Earth’s location their model implies a density 2000 times higher, or 600 GeV/cc, for this low velocity, bound component so despite the lower velocity, it could well dominate in dark matter detection experiments.

References:

https://darkmatterdarkenergy.com/2012/08/14/dark-matter-on-mars/

http://arxiv.org/pdf/1306.5534v1.pdf – N. P. Pitjev and E. V. Pitjeva, 2013, “Constraints on Dark Matter in the Solar System”

http://www.universetoday.com/15266/dark-matter-is-denser-in-the-solar-system/ – describes Solar System dark matter capture model of Ethan Siegel and Xiaoying Xu of the University of Arizona

http://arxiv.org/abs/0806.3767 – E. Siegel and X. Xu, 2008, “Dark Matter in the Solar System”