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.

Image

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:

http://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”


More Dark Matter: First Planck Results

Image

Credit: European Space Agency and Planck Collaboration -

Map of CMB temperature fluctuations with slightly colder areas in blue, and hotter areas in red.

 

The first results from the European Space Agency’s Planck satellite have provided excellent confirmation for the Lambda-CDM (Dark Energy and Cold Dark Matter) model. The results also indicate somewhat more dark matter, and somewhat less dark energy, than previously thought. These are the most sensitive and accurate measurements of fluctuations in the cosmic microwave background (CMB) radiation to date.

Results from Planck’s first 1 year and 3 months of observations were released in March, 2013. The new proportions for mass-energy density in the current universe are:

  • Ordinary matter 5%
  • Dark matter 27%
  • Dark energy 68%

Planck_cosmic_recipe_node_full_image

Credit: European Space Agency and Planck Collaboration

The prior best estimate for dark matter primarily from the NASA WMAP satellite observations, was 23%. So the dark matter fraction is higher, and the dark energy fraction correspondingly lower, than WMAP measurements had indicated.

Dark energy still dominates by a very considerable degree, although somewhat less than had been thought prior to the Planck results. This dark energy – Lambda – drives the universe’s expansion to speed up, which is known as the runaway universe. At one time dark matter dominated, but for the last 5 billion years, dark energy has been dominant, and it grows in importance as the universe continues to expand.

The Planck results also added a little bit to the age of the universe, which is measured to be about 13.8 billion years, about 3 times the age of the earth. The CMB radiation itself, was emitted when the universe was only 380,000 years old. It was originally in the infrared and optical portions of the spectrum, but has been massively red-shifted, by around 1500 times, due to the expansion of the universe.

There are many other science results from the Planck Science team in cosmology and astrophysics. These include initial support indicated for relatively simple models of “slow roll” inflation in the extremely early universe. You can find details at the ESA web sites referenced below, and in the large collection of papers from the 47th ESlab Conference link.

References:

http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe – news article at ESA site

http://darkmatterdarkenergy.com/2011/07/04/dark-energy-drives-a-runaway-universe/ – runaway universe blog

http://www.rssd.esa.int/index.php?project=planck – Planck Science Team site

http://www.sciops.esa.int/index.php?project=PLANCK&page=47_eslab – 47th ESlab Conference presentations on Planck science results


SuperCDMS Collaboration Possible Detection of Dark Matter

Hard on the heels of the Alpha Magnetic Spectrometer (AMS) positron excess and possible dark matter report, we now have a hint of direct dark matter detection from the SuperCDMS Collaboration this month. A recent blog here on darkmatterdarkenergy.com discusses the detection of excess positron flux seen in the AMS-02 experiment on board the Space Shuttle. The two main hypotheses for the source of excess positrons are either a nearby pulsar or dark matter in our Milky Way galaxy and halo.

Image

Photo: CDMS-II silicon detector, Credit: SuperCMDS Collaboration

CDMS-II (CDMS stands for Cryogenic Dark Matter Search) is a direct dark matter detection experiment based in the Soudan mine in Minnesota. The deep underground location shields the experiment from most of the cosmic rays impinging on the Earth’s surface. Previously they had reported a null result based on their germanium detector and ruled out a detection. Now they have more completely analyzed data from their silicon detector, which has higher sensitivity for lower possible dark matter masses, and they have detected 3 events which might be due to dark matter and report as follows.

“Monte Carlo simulations have shown that the probability that a statistical fluctuation of our known backgrounds could produce three or more events anywhere in our signal region is 5.4%. However, they would rarely produce a similar energy distribution. A likelihood analysis that includes the measured recoil energies of the three events gives a 0.19% probability for a model including only known background when tested against a model that also includes a WIMP contribution.”

So essentially they are reporting a possible detection with something ranging from 95% to 99.8% likelihood. This is a hint, but cannot be considered a firm detection as it rises to the level of perhaps 3 standard deviations (3 sigma) of statistical significance. Normally one looks to see a 5 sigma significance for a detection to be well confirmed. If the 3 events are real they suggest a relatively low dark matter particle mass of around 8 or 9 GeV/c² (the proton mass is a little under 1 GeV/c², and the Higgs boson around 126 GeV/c²).

Image

Figure: Error ellipses for CDMS-II and CoGeNT, assuming a dark matter WIMP explanation. Blue ellipses are the 68% (dark blue) and 90% (cyan) confidence levels for the CDMS-II experiment. The purple ellipse is the 90% confidence level for CoGeNT.

The figure shows the plane of dark matter (WIMP, or weakly interacting massive particle) cross-section on the y-axis vs. the WIMP mass on the x-axis. Note this is a log-log plot, so the uncertainties are large. The dark blue region is the 1 sigma error ellipse for the CDMS experiment and the light blue region is the 90% confidence error ellipse. The best fit is marked by an asterisk located at mass of 8.6 GeV/c² and with a cross-section a bit under 2 x 10^-41 cm². But the mass could range from less than 6 to as much as 20 or more GeV/c². And the cross-section uncertainty is over two orders of magnitude.

However, this is quite interesting as the error ellipse for the mass and interaction cross-section from this CDMS-II putative result overlaps well with the (smaller) error ellipse of the CoGeNT results. The CoGeNT experiment is a germanium detector run by a different consortium, but based in the same Soudan Underground Laboratory as the CDMS-II experiment! COGENT sees a possible signal with around 2.8 sigma significance as an annual modulated WIMP wind, with the modulation in the signal due to the Earth’s motion around the Sun and thus relative to the galactic center. The purple colored region in the figure is the CoGeNT 90% confidence error ellipse, and it includes the CDMS-II best fit point and suggests also a mass of roughly 10 GeV/c².

The DAMA/LIBRA experiment in Italy has for years been claiming a highly significant 9 sigma detection of a WIMP (dark matter) wind, but with very large uncertainties in the particle mass and cross-section. However both the COGENT results and this CDMS-II possible result are quite consistent with the centroid of the DAMA/LIBRA error regions.

And both the CoGeNT and DAMA experiments are consistent with an annual modulation peak occurring sometime between late April and the end of May, as is expected based on the Earth’s orbit combined with the Sun’s movement relative to the galactic center.

What we can say at this point is the hottest region to hunt in is around 6 to 10 GeV/c² and with a cross section roughly 10^-41 cm². Physicists may be closing in on the target area for a confirmed weakly interacting dark matter particle detection. We await further results, but the pace of progress seems to be increasing.

References:

http://darkmatterdarkenergy.com/2013/04/07/ams-positron-excess-due-to-dark-matter-or-not/ – Recent first results from AMS for positron excess

http://cdms.berkeley.edu/ – SuperCDMS Collaboration web site

http://arxiv.org/abs/1304.4279 – “Dark Matter Search Results Using the Silicon Detectors of CDMS II”

http://cdms.berkeley.edu/APS_CDMS_Si_2013_McCarthy.pdf – Kevin McCarthy’s presentation at the American Physical Society, April 15, 2013

http://cogent.pnnl.gov/ – CoGeNT website

http://darkmatterdarkenergy.com/2011/06/16/do-we-have-a-cogent-direct-detection-of-dark-matter/ - Discussion of CoGeNT 2011 results

http://arxiv.org/pdf/1301.6243v1.pdf  – DAMA/LIBRA results summary, 2013


AMS Positron Excess: Due to Dark Matter or not?

The first results from the Alpha Magnetic Spectrometer (AMS), which is an experiment operating in orbit on the International Space Station (ISS), have been released.

ImageIt’s been two years since the delivery via Space Shuttle to the ISS (in May, 2011) of the AMS-02 instrument, which was especially designed to explore the properties of antimatter. And it’s been a long time coming to get to this point, since the experiment was first proposed in 1995 by the Nobel Prize-winning M.I.T. physicist, professor Samuel Ting. A prototype instrument, the AMS-01, flew in a short-duration Space Shuttle mission in 1998, and had much lower sensitivity.

Over 16 countries across the globe participate in the AMS mission, and the instrument underwent testing at the CERN particle physics research center near Geneva and also in the Netherlands before being launched from Cape Canaveral, Florida.

The lifetime of the mission is expected to extend for over 10 years. In this first data release, with over 30 billion cosmic rays detected, the AMS has detected among these over 400,000 positrons, the positively charged antiparticles to electrons. This is the most antimatter that has ever been directly measured in space.

It is hoped that the AMS can shed light on dark matter, since one of the possible signatures of dark matter is the production of positrons and electrons when dark matter particles annihilate. This assumes that some type of WIMP is the explanation for dark matter, WIMP meaning a “weakly interacting massive particle”. Weakly interacting signifies that dark matter particles (in this scenario highly favored by many physicists) would interact through the weak nuclear force, but not the electromagnetic force. Which basically explains why we can’t easily detect them except through their gravitational effects. Massive particle refers to a particle substantially more massive than a proton or neutron, which have rest masses of just under 1 GeV (1 giga volt) in energy terms. A WIMP dark matter particle mass could be 10 to 1000 times or more higher. The lightest member of the neutralino family is the most-favored hypothesized WIMP dark matter candidate.

The figure below shows the positron relative abundance versus energy, based on 18 months of AMS operational data. The energy of detected positrons ranges from 1/2 GeV to over 300 GeV. The abundance, shown on the y-axis, is the fraction of positrons relative to total electrons and positrons detected at a given energy. The spectrum shows a clear trend to relatively fewer positrons as the energy grows to 10 GeV and then a substantially increasing relative number of positrons at higher energies. This general shape for the spectrum was seen with previous experiments including Fermi, Caprice94 and Pamela, but is much clearer with the AMS due to the higher resolution and significantly greater number of positrons detected. It is particularly this increase in positrons seen above 10 GeV that is suggestive of sources other than the general cosmic ray background.

PositronspectrumFigure: Positron relative fraction (y-axis) versus energy (x-axis)

So what is the source of the energetic positrons detected by the AMS? Some or all of these could be produced when two dark matter WIMP particles meet one another. In the WIMP scenario the dark matter particle such as the neutralino is neutrally charged (no electromagnetic interaction, remember) and also its own antiparticle. And when a particle meets its antiparticle what happens is that they mutually annihilate. The energy of the pair of colliding dark matter particles is transformed into lighter particles, including electron-positron pairs and energetic photons including gamma rays.

Another likely source is pulsars, which are rotating neutron stars with magnetic fields. Since neutron stars are compact and rotate quickly, and their magnetic field strengths are high, electrons and positrons can be accelerated to very high energy. In particular, the Geminga pulsar is the closest energetic pulsar and has been suggested as a major source of these extra positrons.

More data is needed, especially at higher energies above 100 GeV. Over the next few years as AMS continues to operate and the number of positrons detected climbs to 1 million and above, this spectral shape will be better determined. And as the shape of the high-energy portion of the spectrum becomes clearer, it will help elucidate whether dark matter or pulsars or something else are the primary source of the positrons.

You can follow AMS-02 on Facebook here.

References:

http://www.ams02.org/2013/04/first-results-from-the-alpha-magnetic-spectrometer-ams-experiment/

http://www.nytimes.com/2013/04/04/science/space/new-clues-to-the-mystery-of-dark-matter.html

http://press.web.cern.ch/backgrounders/first-result-ams-experiment

http://physicsworld.com/cws/article/news/2009/aug/10/excess-positrons-are-linked-to-geminga-pulsar

http://darkmatterdarkenergy.com/2012/06/05/antimatter-is-not-dark-matter-antimatter-being-uncovered-with-nuclear-reactors/


Caught in the Cosmic Web – Dark Matter Structure Revealed

NASA/ESA Hubblecast 58

This video reports on a very impressive research effort resulting in the first 3-D mapping of dark matter for a galaxy cluster. A massive galaxy cluster over 5 billion light-years from Earth is the first to have such a full 3-dimensional map of its dark matter distribution. The dark matter is the dominant component of the cluster’s mass. The cluster, known as MACS J0717, is still in the formation stage. The Hubble Space Telescope and a number of ground-based telescopes on Mauna Kea in Hawaii were used to determine the spatial distribution. The longest filament of dark matter discovered by the international team of astronomers stretches across 60 million light-years. Gravitational lensing of galaxy images (as Einstein predicted) and redshift measurements for a large number of galaxies were required in order to uncover the 3-D shape and characteristics of the filament.


2012 in review

The WordPress.com stats helper monkeys prepared a 2012 annual report for this blog.

Here’s an excerpt:

600 people reached the top of Mt. Everest in 2012. This blog got about 6,200 views in 2012. If every person who reached the top of Mt. Everest viewed this blog, it would have taken 10 years to get that many views.

Click here to see the complete report.


Looking for Dark Energy in the Lyman Alpha Forest

Baryon acoustic oscillations (BAO) are the acoustic (sound) waves that occur in the very early universe due to very small density inhomogeneities in the nearly uniform fluid. These primordial acoustic oscillations have left an imprint on the way in which galaxies are spatially distributed. The characteristic scale length for these oscillations is around 500 million light years (in the frame of the present-day universe). A spatial correlation function is used to measure the degree to which galaxies and clumps of matter in general, including dark matter, are separated from one another. The characteristic length scale serves as a standard ruler for very large-scale clustering, and is seen as a distinctive break (change in slope) in the power spectrum of the degree of spatial correlation vs. distance.

An international consortium of astronomers representing 29 institutions have submitted a paper last month to the journal Astronomy and Astrophysics; the current version can be found here (http://arxiv.org/abs/1211.2616). They used a clever technique of detecting clouds of neutral hydrogen along the line of sight to a large number of quasars with high redshifts. Thus the matter clumps in this case are neutral hydrogen clouds or neutral hydrogen within intervening galaxies or proto-galaxies. These absorb light from the quasar and produce absorption lines in the spectrum at discrete locations corresponding to various redshifts. The authors are detecting a characteristic transition known as the Lyman alpha line, which is found well into the ultraviolet at 121.6 nanometers (for zero redshift).

For this work over 48,000 high-redshift quasars, with a mean redshift of 2.3, were taken from the 3rd Sloan Digital Sky Survey. A quasar may have many hydrogen clouds intervening along the line of sight from the Earth to the quasar. These clouds will be seen at different redshifts (less than the quasar redshift) reflecting their position along the line of sight. This is referred to as the Lyman alpha “forest”. This study is the first application of Lyman alpha forest measurement to the detection of the BAO feature. At the average red shift of 2.3, the wavelength of Lyman alpha radiation is shifted to 401.3 nm [calculated as (1+2.3)*121.6 nm], in the violet portion of the visible spectrum. The study incorporated redshifts from the absorbing clouds in the range of 1.96 to 3.38; these are found in front of (at lower redshift than) quasars with redshifts ranging from 2.1 to 3.5.

Speedup or slowdown versus age of universe. The Big Bang is on the left, 13.7 billion years ago.

The authors’ measurement of the expansion rate of the universe is shown as the red dot in this figure. The white line through the various data points is the rate of expansion of the universe expected versus time for the standard Lambda-Cold Dark Matter cosmological model. The expansion rate at early times was lessening due to gravity from matter (ordinary and dark), but it is now increasing, since dark energy has come to dominate during the last 5 billion years or so. The red data point is clearly on the slowing down portion of the curve. Image credit: http://sdss3.wordpress.com/2012/11/13/boss-detects-baryon-acoustic-oscillations-in-the-lyman-alpha-forest-at-z-of-2-3/  

The BAO feature has been measured a number of times, using galaxy spatial distributions, but always at lower redshifts, that is at more recent times. This is not only the first Lyman alpha-based measurement, but the first measurement made at a high redshift for which the universe was still slowing down, i.e. the expansion was decelerating. At the redshift of 2.3, when the universe was only about 3 billion years old, the gravitational effect of dark plus ordinary matter was stronger than the repulsive effect of dark energy. It is only more recently, after the universe become about 9 billion years old (some 5 billion years ago), and corresponding to redshifts less than about z = 0.8, that dark energy began to dominate and cause an acceleration in the overall expansion of the universe.

Since this observation shows a significantly higher rate of expansion than occurred at the minimum around 5 billion years ago, it is further evidence that dark energy in some form is real. As the authors state in their paper: “Combined with CMB constraints, we deduce the expansion rate at z = 2.3 and demonstrate directly the sequence of deceleration and acceleration expected in dark-energy dominated cosmologies.” This is an exciting result, providing additional confirmation that dark energy represents around three-quarters of the present-day energy balance of the universe.


Follow

Get every new post delivered to your Inbox.

Join 338 other followers