Earth's Dark Matter Halo - "Dark Earth" Hypothesis
Recent computations suggest that the dark matter density in the Solar System and around the Earth [1, 2] exceeds the galactic halo density significantly. This aggregation of dark matter particles around the Earth forms effectively a halo of dark matter particles. It has also been proposed that dark matter may be composed of plasmas of exotic particles [3]. It therefore logically follows that a dark matter halo exists around the visible component of Earth composed largely of plasmas of exotic particles.
DARK MATTER DENSITY AROUND EARTH
The background galactic halo dark matter density is about 5.35 x 10-28 kg cm-3 [4]. The mass of dark matter within the Solar System, between 0.2 AU and 100 AU, as a result of gravitational capture, was estimated to be 1.07 x 1020 kg (or 1.78 x 10-5 the Earth mass) [1]. The mass of dark matter was estimated to be 7.69 x 1019 kg within the orbit of Neptune and 3.23 x 1017 kg within the orbit of Earth (i.e. approximately within 1 AU). The dark matter density within the orbit of the Earth (or approximately 1 AU) would therefore be approximately 9.65 x 10-23 kg cm-3. This is greater than the background galactic halo dark matter density by five orders of magnitude.
Xu and Sigel’s [1] estimate that the dark matter density around Earth exceeds the galactic halo density significantly has been correlated by Adler [2]. Anomalies relating to accelerations, observed during fly-bys of spacecraft orbiting the Earth, suggest that the dark matter density around Earth had been significantly understated. According to Adler [2] the magnitude of the observed anomalies requires dark matter densities many orders of magnitude greater than the galactic halo density.
Adler has suggested that by comparing the total mass (in gravitational units) of the Earth-Moon system (determined by lunar laser ranging) with the sum of the lunar mass (determined by its gravitational action on satellites or asteroids) and the Earth mass (determined by the LAGEOS geodetic survey satellite), a direct measure of the mass of Earth-bound dark matter lying between the radius of the Moon’s orbit and the geodetic satellite orbit can be obtained. Based on this, the mass of Earth-bound dark matter must be less than 4×10-9 of the Earth’s mass, giving an upper dark matter mass limit of 2.32 x 1016 kg. To explain the flyby anomalies, Earth-bound dark matter would have to be concentrated within a radius of about 70,000 km around Earth, within a volume of approximately 1.44 × 1030 cm3. For the dark matter mass within this volume not to exceed 4 × 10-9 of the Earth’s mass, the mean dark matter density would have to be about 10-14 kg cm-3. This is greater than the background galactic halo dark matter density by fourteen orders of magnitude.
Frere, Ling, and Vertongen [5] have proposed that dark matter concentrations within our galactic neighborhood became bound to the Solar System during its formation. Adler [2] suggests that a large density within the Solar System could result from an accumulation cascade. In this scenario dark matter that accumulates within the Solar System (including the initial contribution during its formation) over its lifetime leads to further accumulation through gravitational capture. This cascade of Earth bound dark matter results in a dark matter density within the Solar System far exceeding the average density in the galaxy.
Adler [2] contends that dark matter particle density peaks at about 70,000 km, then reduces until it is much lower on the Earth’s surface (although still higher than the background galactic halo density) and the interior of the Earth. Various methods were used to arrive at this conclusion. At 12,600 km, the LAGEOS satellite experienced smaller residual accelerations, due to drag effects, of 3 x 10-12 ms-2 compared to 10-6 ms-2 at higher altitudes.
The mean dark matter density on the surface of the Earth, assuming a steady-state situation and similar dark matter velocities at Earth’s radius (at the surface) of 6,400 km and 70,000 km was estimated to be much lower at 10-23 kg cm-3. This is still four orders higher than the galactic halo density. Furthermore, the mean dark matter density in the interior of the Earth was estimated to be even lower, being not more than 1.07 x 10-28 kg cm-3 (this is slightly lower than the background galactic halo density). The latter estimate was determined by analyzing the Earth’s heat flow budget and luminosity, assuming a steady-state situation. Adler concludes that dark matter density is therefore much smaller near the Moon’s orbit (which exceeds 70,000 km) and near the Earth’s surface using a variety of analyses and assumptions.
Estimates of dark matter around Earth can be confirmed by further analysis of spacecraft acceleration anomalies and sensitive underground detection facilities. An enhanced Solar System density of dark matter particles would show up as a daily sidereal time modulation of dark matter particle counting rates in DAMA/LIBRA type of experiments, in addition to any annual modulation in the counting rate [2]. More accurate assessments of a larger sample of spacecraft acceleration anomalies and dark matter particle detections in the future, coupled with a more consistent measurement model, may alter the density profile of dark matter within the Earth system as proposed by Adler [2].
EARTH’S DARK MATTER HALO
Based on the analyses above [1, 2], we conclude that there exists a halo of dark matter particles around the visible component of the Earth within a radius of approximately 70,000 km. Considering that dark matter density varies significantly over different Earth radii, it is possible to model the dark matter density as being distributed in concentric shells of different particle densities around Earth.
A sphere of dark plasma with a radius of 70,000 km [2] has a volume of 1.44 x 1030 cm3. The volume of the visible Earth at a radius of 6,378km is about 1.09 x 1027 cm3. This means that the dark matter halo would be three orders of magnitude or about 1.32 x 103 or 1,320 times larger in volume than the visible rocky Earth. This approximates with the dimensional relationship between the volume of Jupiter’s huge gas envelope and its tiny rocky core (the latter approximates the volume of the visible rocky Earth). In other words, we would expect an envelope of dark matter particles the size of Jupiter around the visible component of the Earth with a mean density of 10-14 kg cm-3 [2].
Xu and Siegel [1] have also computed dark matter densities for other planets in the Solar System. It is predicted that there should be dark matter halos around planets; and purely dark matter halos and blobs (occupying volumes comparable to planets but with low densities of dark matter particles) within the Solar System that would cause anomalies in spacecraft accelerations that will be measured in the future.
EARTH’S DARK PLASMA HALO
It has been proposed that dark matter may be composed of plasmas of exotic particles [3, 11, 12, 13]. Ackerman et al [3] propose a new long-range dark abelian gauge field (“dark electromagnetism") that couples only to dark matter, not to the Standard Model (SM), with gauge coupling constant and dark fine structure constant . (The “D” subscripts refer to the dark sector.) The field, which is taken to be initially a singlet under SU(3)C X SU(2)L X U(1)Y, is anomaly free and provides the right relic abundance at thermal freeze-out. The correct relic abundance can be obtained if the dark matter couples to the conventional weak interactions. Under an extended model, DM particles are charged under both and .
The dark matter consists of an equal mixture of positive and negative charges under the new force which is mediated by “dark photons” that are the source of “dark radiation”. In the most basic scenario, they [3] propose a dark sector which consists of a single particle with charge of +1 along with its antiparticle with a charge of -1. In other words, it is a plasma of positively and negatively charged particles and anti-particles or an “ambiplasma”. Since the galactic DM halo is overall neutral under there are no net long-range electromagnetic interactions in the dark sector. Quasi-neutrality is of course a general feature of plasma. Plasma effects in dark matter dynamics are therefore expected. However, these effects are only very briefly explored in Ackerman et al’s paper [3].
Annihilations between particle and anti-particles are suppressed and dark matter will be effectively collisionless if the dark matter mass is sufficiently high, in the TeV range, and the dark fine structure constant outside the galactic cores. Inside galactic cores, however, annihilations are expected to occur when the density of dark matter reaches high values. If this is the case, then annihilation radiation in the form of gamma rays from the center of our galaxy may be detectable to distances of tens to hundreds of Mpc and would provide evidence of the existence of dark matter in the center of the Milky Way.
Results from the INTEGRAL satellite [8], however, do not support dark matter as the major source of the gamma rays from the center of our galaxy. This is because it shows an asymmetry of emission (by a factor of two) with respect to the central axis of the galaxy, which is correlated more with the distribution of low mass X-ray binaries than with the predicted distribution of dark matter in the galactic core. The question of whether anti-dark matter actually exists is an empirical matter for further investigation. The fact that there are no significant sources of gamma (annihilation) radiation within a radius of 70,000 km from the center of the Earth (i.e. within Earth’s dark plasma halo), despite the estimated high density of dark matter around this region, rules out large amounts of anti-dark matter in the vicinity of the Earth.
The dark plasma envisaged in this paper would therefore consist of positively and negatively charged particles with varying mass, similar to the attributes of the heavy and light charginos under the MSSM (Minimal Supersymmetric Standard Model), together with neutrals (such as MSSM’s neutralinos). The cold dark tenuous plasma in the Earth system would therefore be composed of complex plasmas of heavy and light DM particles with opposite charge, together with neutral DM particles.
It is envisaged that the difference between the masses of the charged DM particles are not as great as between the proton and the electron and more in line with the MSSM’s heavy and light charginos. This would make it more likely to remain in the plasma state due to lower ionization potentials. Furthermore, due to the large inter-particle distance in tenuous plasma and the weaker dark electromagnetic interactions (approximately one hundred times weaker than ordinary electromagnetism) [3], recombination is less likely to occur. Plasma bodies in the dark sector would therefore be long-lived.
From the findings in II and III, above, it follows that a tenuous (i.e. low density) cold dark plasma halo exists around the visible component of the Earth composed largely of plasmas of dark matter particles which weakly interact with SM particles.
It is proposed that the shape and volume of this halo is dynamic. This is due primarily to 3-body interactions between the Earth, Moon and the Sun. According to Adler [2], the Sun-bound dark matter density near the Sun may be higher than near the Earth. Dark matter particles blasted out in the solar wind of the Sun will therefore flatten the face of Earth’s dark plasma halo facing the Sun and generate a tail at the opposite end, parallel to the direction of the dark matter wind. In other words, it will have a tear-dropped shape similar to Earth’s magnetosphere. During “full moons” i.e. when the Moon is directly opposite the Sun, relative to the Earth, the combined effects of the solar wind and the gravitational attraction of the Moon would allow the tail of the halo to extend to the Moon’s orbit. Dark matter winds from other parts of the galaxy would also affect the shape and size of the halo. Since particle density can also change due to these influences, the size of the dark plasma halo also undergoes changes (just like Earth’s visible atmosphere). The shape and size of this dark plasma Earth is therefore dynamical and would be constantly size and shape-shifting much like Earth’s magnetosphere.
The dark halo, with a total mass much lower than the visible Earth (it does not exceed 4 × 10-9 of the Earth’s mass [2]), would be gravitationally coupled to the Earth and corotate with it. Furthermore, just like the Sun (which is a near-sphere composed of plasma) and Jupiter, it would be expected to experience differential rotation; with the maximum rate of rotation in the equatorial region slowing down towards the direction of the poles. A day in the dark halo (as measured by one full rotation) would therefore vary from location to location although the year would be the same as the visible Earth (as the halo is gravitationally coupled to the visible Earth).
It is worth reflecting that the density of dark matter is almost 5 times that of baryonic matter in the universe. The average baryon density in the universe currently is about 10-33 kg cm-3. The average mass density in the interstellar medium (ISM) is 10-27 kg cm-3. This is many orders less than the computed densities of dark matter around Earth, within a radius of 70,000km, of about 10-14 kg cm-3 (as discussed above). This, however, does not stop stars, composed of baryonic matter, to form with vast amounts of almost empty space in between. Similarly we expect dark plasma blobs to form and drift around the Earth even if the average density is low - just as dark matter clouds are believed to drift through the galaxy [14]. Adler [2] claims that we have detected these clumps or blobs in the form of anomalous accelerations of spacecraft during fly-bys and orbits of Earth.
We now know that galaxies have gigantic halos composed of dark matter. Does Earth also possess such a halo? If so, we would be living inside this halo. Based on research so far, it is highly probable that Earth does possess a low density halo of dark matter because there are numerous sources for Earth to receive and attract dark matter into its gravitational influence. We also know that there is a mutual affinity between dark and ordinary matter throughout the universe.
Dark Matter within the Solar System
Our Solar System and the Earth sits inside the dark matter halo of our galaxy, the Milky Way. D Lin, a University of California astronomer, calculates that our galaxy’s halo of dark matter is equivalent to 600 to 800 billion solar masses, compared to the only 100 billion solar masses of visible matter. As our Solar System orbits the galaxy at a speed of almost 220km per second, it sweeps through the invisible sea of dark matter particles in the galaxy. Every kilogram of matter on Earth scatters as many as a thousand WIMPs (i.e. dark matter particles) per day.
The Solar System, itself, is sitting in an interstellar cloud of dark matter. The existence of the cloud and its geometry can be deduced from its effect on the spectra of nearby stars and cosmic rays. Priscilla Frisch of the University of Chicago calculates that our Solar System first encountered the cloud (moving at right angles to it) between 2,000 and 8,000 years ago.
Dark Matter Clouds Passing through Earth
Jürg Diemand, a physicist at the University of California in Santa Cruz, US, and colleagues say that computations suggest that small clouds of dark matter, which could be detected by future space missions, pass through Earth on a regular basis. He says that perhaps a million billion of them drift around our galaxy's dark matter halo. These clouds float through Earth every 10,000 years in an encounter lasting about 50 years, according to Diemand. However, they do not affect the (physical) Earth to any appreciable effect. Their relatively low densities mean they could only nudge our planet out of its normal orbit by less than a millionth of a meter per second.
Dark Matter Particles Blasted-Out from the Sun
According to researchers from the University of Oxford (as reported in the New Scientist journal), the Sun is harboring a vast reservoir of dark matter. Astrophysicists Ilidio Lopes and Joe Silk reasoned that passing dark matter particles would be captured by the gravity of heavy bodies like the Sun. In addition to heat and light, the Sun constantly emits low density plasma of charged electrons and protons called the ‘solar wind,’ which blasts out from the Sun in all directions at very high speeds to fill the entire Solar System and beyond. The solar wind and the much higher energy particles ejected by solar flares can have dramatic effects on the Earth ranging from power line surges and radio interference to the beautiful and mesmerizing aurora borealis. The composition of this solar wind has been largely analyzed by Science, up to now, to consist of only ordinary matter in the form of plasma. If there is a large dark matter reservoir in the Sun, as certain scientists are convinced, it is a logical next step to expect dark matter particles captured by the Sun from various sources to be also blown out of the Sun in its solar wind — just like ordinary matter particles. Trillions of dark matter particles from the Sun would be hitting Earth every minute.
Dark Matter Particles Raining Down from Dwarf Galaxy
Astrophysicist Heidi Newberg at Rensselaer Polytechnic Institute and her colleagues suggest that dark matter may be raining down on Earth from the dwarf galaxy "Sagittarius". For eons, the Milky Way has been absorbing and tearing apart Sagittarius, which is about one-tenth the size of the Milky Way. Newberg and other astronomers recently discovered two "tails" or streams of stars flowing-out from Sagittarius. The streams are believed to also contain dark matter particles. Our Solar System sits in one of these streams. We are therefore stuck in the middle of a fast-moving stream of dark matter particles, billions passing through every square meter of the Earth (and our bodies) each second at speeds of over a million kilometers per hour. Day-in and day-out, countless random dark matter particles rain down upon the Earth and through our bodies undetected.
Density of Earth's Dark Matter Halo
If trillions of dark matter particles are passing through ordinary matter - the Earth and our bodies every few seconds then it would not be difficult for Earth to capture these particles under its gravitational influence. Dark matter could also be already present during the formation of the Solar System – so that ordinary and dark matter worked together to form our Solar System. Perhaps the Pioneer anomaly was also caused by the presence of clumps of dark matter in the Solar System, as conjectured by Marcus Chown.
However, it appears (ignoring the effects of any dark energy) that whatever dark matter is present in the Solar System, it must be low in density. Firstly, this is because the planets comply with Newton's gravity laws – unlike the stars at the edge of galaxies. (Dark energy has a repulsive gravitational effect. To what extent this would neutralize the attractive gravitational force of dark matter within the Solar System is a matter of conjecture.)
Secondly, the density is low based on extrapolations of the density of dark matter in the local halo – which is roughly 0.3 GeV/cm3. The Earth-Sun distance is roughly 1.5 X 10^13 cm. So the amount of dark matter enclosed within Earth's orbit is approximately 10^40 GeV. For comparison, the Sun's mass is about 10^57 GeV. So the dark matter enclosed is 10^-17 of the mass of the Sun. It therefore has a negligible effect on the orbit of the Earth around the Sun. Based on these estimates, the average dark matter density is much lower (a trillion trillion times lower) than that of rocks, water and other substances typically found on Earth.
Is this Density Understated?
The numerous sources of dark matter particles suggest that there could be a local excess of dark matter in our Solar System over and above the galactic background. However, since the orbits of the planets comply with Newton's gravity laws very closely, the excess cannot be significant (barring the effects of any dark energy).
However, Newton's gravity laws require the mass of the Earth to be input. This mass is computed based on the gravitational acceleration measured at different places on Earth. This assumes from the start that the acceleration is due to only ordinary matter. The contribution of any dark matter on Earth has been ignored. A similar assumption is made when computing the mass of the Sun and the other planets.
Scientists have speculated that there could be a large reservoir of dark matter within Earth. David Peat says that the best calculations suggest that our Earth could contain as much as 10 per cent shadow matter. Shadow matter (consisting of supersymmetric particles and objects) is generally considered to be the same as dark matter (which also consists of supersymmetric particles and objects).
Halos of dark matter, as large as our Solar System and with the mass of the Earth, were the first structures to form in the universe, according to calculations from scientists at the University of Zurich. If we could allow 10 per cent of the Earth's mass to be in the form of dark matter, this would mean a halo one-tenth the size of the Solar System – this is really huge relative to the size of the visible Earth. The visible Earth would seem like a little stone sitting inside this gigantic halo.
Implications
Based on the above discussion, there is no doubt that there is dark matter in the Solar System and on Earth. What are the implications? If we are living within a dark matter halo and there is mutual affinity between dark and ordinary matter, do objects on Earth (including our physical bodies) possess low density halos of dark matter? Does dark matter also play a part in the formation of our visible bodies just as it probably did in the formation of the visible Solar System? Can these low density halos organize themselves into life-forms (just like physical matter), survive the death of the physical bodies and evolve independently of life-forms composed of ordinarily visible (or measurable) physical matter?
According to plasma metaphysics, a significant amount of dark matter is in the form of a (magnetic) plasma of super (i.e. supersymmetric) particles. See the author's article on
Dark Plasma.
A low density gas of dark matter particles (which has no electrical properties) probably would not have allowed the development of life-forms composed of dark matter. However, plasma consists of electrically conductive soups of charged particles that respond collectively to electromagnetic forces and are overall (quasi) neutral. Renowned plasma physicist David Bohm was surprised to find that once electrons were in a plasma, they stopped behaving like individuals and started behaving as if they were part of a larger and interconnected whole. He later remarked that he frequently had the impression that the sea of electrons in a plasma was in some sense alive. Unlike particles within atoms, particles in magnetic plasma have long-range effects and correlations; and each particle has an electric field. In other words, the effects of the field become dominant. The invisible spaces between the widely dispersed particles in a low density plasma are not empty – they contain electric fields and dynamic magnetic field lines which twist and turn – generating complex dynamics in plasma. There is a network of filamentary currents in plasma.
Hence, even a low density plasma of (supersymmetric, massive) dark matter particles in the Solar System and on Earth could have significant effects on the formation of the Earth and our physical bodies because of its electromagnetic field properties.
REFERENCES
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[12] J. J. Alfred, “Our Invisible Bodies”, Trafford Publishing, Canada, (2006).
[13] J. J. Alfred, “Between the Moon and Earth”, Trafford Publishing, Canada, (2007).
[14] J. J. Alfred, Articles (2007-2008) at http://www.ezinearticles.com
[15] J. Diemand, B. Moore, J. Stadel, (2005) arXiv: astro-ph/0501589v1 [astro-ph].
[16] British Ministry of Defense Report, “Unidentified Aerial Phenomena (UAP) in the UK Air Defence Region”, (2000: internal publication; 2006: declassified for public access).
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© Copyright Jay Alfred 2007, 2009
