DARK MATTER - Introduction
From time immemorial the enigmatic Universe fascinates the human
imagination and intellect. Humans wondered at themotion of the heavenly
bodies in the vault of the sky and found resemblence between
constellations of stars and earthly living beings. In the absence of any
sophisticated instruments, the thinkers of those distant times used their
diligent observations of the displacements of the heavenly bodies in the
sky, their ascents and descents, to make various astronomical calulations.
The advent of the telescope by Galileo Galilei heralded a new
dawn in astronomical observations and calculations. Mathematician
Johannes Kepler put forward the laws of planetary motion. The revolutionary
discovery and mathematical formulation of gravitation – one
of the fundamental forces of nature – by Sir Issac Newton paved the
way for a more formidable understanding of the motion of the heavenly
bodies.
Any digression of the observed motion of the known astrophysical
objects from the theory appears to indicate the presence of
unknown objects.
This is indeed initially the study of galactic dynamics, the dynamics
of galaxy clusters and the consequent application of cosmic virial theorem
that led to the prediction of not only the existence of dark matter,
but also its very substantial amount that appeared to far outweigh the
visible Universe. The first indication to this effect in the past century
came from the famous Dutch astronomer Jan Hendrik Oort in 1932
who, while measuring the velocities of the stars along the direction
vertical to the plane of the galactic disk of our Milky Way galaxy,
noticed that the vertical velocities of the stars are too high to have escaped
the galactic influence. The Milky Way galaxy is a spiral galaxy
having a disk-like structure with a central bulge of more concentrated
matter. The extent of the disk is around 10 kpc (1 kpc = 3.12×1016
Km) from the galactic center and the disk itself has a thickness of ∼ 4
kpc. The fact that the stars are confined within the galaxy, even thoughtheir vertical velocities are measured to be high enough, necessitates
the presence of unseen mass in the galaxy. Oort reported his observations
in the Bulletin of the Astronomical Institutes of the Netherlands
in 1932 where he reported “Integrating over a column perpendicular
to the galactic plane I find that an average unit of photographic light
corresponds to a mass of 1.8 (if both are expressed in the sun as unit),
...”
Galaxies as noted by Herschell way back in 1780, are not distributed
randomly in the Universe but rather they exist in separate groups or
clusters. Galaxies in each such cluster form a gravitationally bound
group. The famous astronomer Zwicky made his investigations in the
galaxy cluster at Coma constellation 90 Megaparsecs away and also at
the cluster in Virgo constellation and calculated its gravitational mass
using the “virial theorem.” He then used the mass-luminosity relation
of the stars of the individual galaxies and estimated the mass of the
luminous matter in each of the clusters. He came up with a huge discrepancy
between these twomasses and predicted the existence of dark
invisible matter.
The galaxies of the clusters that are x-ray bright are contained within
the x-ray emitting gas. These x-rays are produced when the gas that
embeds the galaxies of the cluster is excited to a temperature (virial
temperature ∼ keV) by the potential of the matter present inside the
cluster. Observations of such x-ray bright clusters and the subsequent
analysis of the observed data give a clear indication that only the galactic
mass and the gas surrounding it is not sufficient to explain them –
one would require the presence of unseen mass or dark matter in the
cluster.
The study of the rotation curve of spiral galaxies shows more profound
evidence of the overwhelming presence of dark matter in the
galaxy. For the rotation curve analysis of a spiral galaxy, one measures
the rotational velocity v(r) of a star or gas in the galaxy as a function of
their distance r from the galactic center. These velocities will depend
upon the mass enclosed by the sphere of radius r. Since for a spiral
galaxy, one has a dense central region and the density of the visible
mass is reduced as one goes away from the central region, one would
expect a Keplerian decline of the rotation curve as one goes away from
the dense central region of the galaxy. But instead, the observationalmeasurements show not a Keplerian decline for v(r) but rather a constant
behavior with r. This is only possible if there is enormous unseen
mass or rather a halo of unseen dark matter present at the galaxy.
The existence of huge unseen mass is also evident from the observed
phenomenon of gravitational lensing. Gravitational lensing is a consequence
of Einstein’s theory of general relativity whereby the gravity
of massive objects induces a curvature of the space-time in its vicinity.
The more the influence of gravitation, the more distorted is the
space-time geometry, suggesting the presence of larger mass. Light
from a distant object (such as galaxy cluster) if it moves along such
a curved space-time follows this local curvature of space-time giving
rise to the lensing effect which is manifested as the appearence of multiple
images of that object around the gravitationalmass that causes the
lensing. Astronomers found such a phenomenon (of multiple imaging)
while observing certain galaxy clusters, when these kind of images appear
surrounding such clusters. Needless to say, the light from the
astronomical object that undergoes such lensing is behind the galaxy
cluster that is being observed by the astronomers and the cluster is on
the line of sight. The estimated mass that can produce a lensing effect
is found to outweigh themass of the target galaxy cluster around which
such multiple images are observed. Thus there is certainly enormous
mass in and around the galaxy cluster that remains invisible or “dark.”
Gravitational lensing is very useful for the search of dark matter even
at the distant reaches of the Universe.
In discussions of evidence of dark matter, the observed phenomenon
of bullet cluster needs mention. It was created in one of the most energetic
events since the Big Bang when two gigantic galaxy clusters
collided with each other some 4 billion light years away from the Earth
at the constellation Carina. These two clusters collided with a speed
of several million kilometers per hour. The x-ray images from these
clusters reveal the shape of normal matter in the clusters after collision
and the dark matter halos around them are known from the method
of gravitational lensing. These observations suggest that due to collision,
the smaller of the two clusters passes through the bigger cluster
and the normal matter in the smaller cluster takes the shape of a bullet
caused by the impact. But the dark matter halos of the two clusters
pass through each other undistorted. It is also revealed that the normalmatter in each of the clusters is dislocated away from their respective
dark matter halos due to the impact of the collision. The event of
“bullet cluster” is not only prolific evidence of the existence of dark
matter but it also points to the fact that they have almost no interaction
between them, as also with normal known matter.
Now the immediate question that arises is how much dark matter
the Universe contains or in what ratio the dark matter exists with
the known (luminous) visible matter such as the galaxies, clusters of
galaxies, superclusters, innumerable stars, planets, and other objects.
In other words, what fraction of the energy budget of the Universe is
in fact dark matter. This is also important to understand: what role
the dark matter plays in the formation of galaxies and galaxy clusters
(structure formation), and how the dark matter influences the destiny
of the Universe. The general wisdom supported by the experimental
evidence suggests that the Universe (and hence the space-time) begins
from a “singularity” with the so-called “Big Bang” and it is everexpanding
thereafter (with an initial rapidly accelerated inflationary
phase). If the mass content of the Universe is very low, it would expand
forever but on the other hand, if the mass content is very large,
this would eventually collapse due to the gravitational pull of the matter.
But the Universe appears to strike a very fine balance of maintaining
a critical mass-energy density such that it will expand with a
constant rate but the expansion is not infinite in time. ∗
The estimation of the energy budget of the Universe is made by measuring
the anisotropies in the cosmic microwave background radiation
(CMBR). The CMBR is the primordial radiation that last scatters
from the Universe soup when the available free electrons were combined
with the ions and atoms started appearing in the Universe. Thus
no free electrons were available for the primordial photons by which
the latter could undergo scattering, and therefore those photons started
free-streaming and remained as background. The wavelengths of these
photons suffer elongation with the expansion of the Universe (the scalefactor of the Universe also obviously changes with the expansion of
the Universe) and in the present epoch, the wavelengths of these background
photons are of microwave order (and hence the name CMBR).
In principle the CMBR should be uniform from any direction in the
sky but any non-uniformity (anisotropy) in CMBR, however small,
is in fact indicative of the imprint of different concentration of mass
of the last scattering surface from where the photons free-streamed.
Thus anisotropies in CMBR contain enormous information regarding
the mass-energy budget of the Universe. The analysis of observational
data of the satellite-borne experiment, Wilkinson Microwave
Anisotropy Probe or WMAP that look for such very tiny anisotropies
in CMBR and more recently the data from another satellite-borne experiment,
namely PLANCK, suggest that around 27% of the massenergy
content of the Universe is made of dark matter while a meager
4% accounts for the rest of the mass, which includes all the stars
and galaxies, galaxy clusters, superclusters and all other known matters.
This known matter is also called the “baryonic matter” and the
above estimate follows from the requirement that the abundances of
observed light elements such as H, D, 3He, 4He, and 7Li agree with
the prediction of Big Bang nucleosynthesis that gives a theoretical understanding
of the synthesis of light elements after the first minute of
the Big Bang. The remaining 69% is a mysterious unknown energy
called dark energy that is thought to be the cause of recently discovered
late time accelerated expansion of the Universe. Therefore a huge
96% of the constituents of the Universe is totally unknown or “dark,”
and the visible or “luminous” Universe accounts for only 4% of the
total mass-energy content. The “luminous” matter signifies, in the microscopic
domain, the fundamental particles or fundamental building
blocks of matter such as quarks, leptons, the vector gauge bosons (the
carrier of fundamental forces), and the scalar Higgs boson that follow
the theory of the Standard Model of particle physics and in the macroscopic
domain, the heavenly bodies like galaxies and galaxy clusters,
superclusters and innumerable stars, novae and supernovae, pulsars
and neutron stars, white dwarfs, planets, intersteller dust, etc.
In all probabilities, the total dark matter content or at least the major
part of it is not made up of the known fundamental particles as otherwise
they would have undergone the Standard Model interactions andtherefore they could have been already probed by now. Therefore its
constituents or at least a majority of its constituents do not supposedly
follow the theory of the StandardModel of particle physics. For example,
the invisibility of dark matter signifies that they do not emit any
electromagnetic radiation and are incapable of undergoing any electromagnetic
interaction, suggesting that they must be made up of neutral
particles. Thus theories beyond Standard Model (BSM) may need to
be invoked in order to predict a suitable particle candidate for dark
matter. Such theories lead to the domain of new physics in the unchartered
energy scale where new symmetries of nature may have to be
envisaged.
The other important issue for understanding the dark matter in the
Universe is its distribution in space, such as galaxies and galaxy clusters.
The question is whether it is uniformly distributed throughout
or its density varies in different regions in a galaxy. Rigorous astrophysical
calculations indicate that the dark matter density is different
in different regions. For example, the local (in the region of our solar
system) dark matter density may be different from a more dense region
such as the galactic center. Not only that their densities may vary
at different locations in the galaxy, but their density profiles may also
vary at different locations.
This is also a matter of concern of how massive the particles are that
make up this huge quantity of dark matter. Experimental endeavors so
far are suggestive of the dark matter candidate particles being massive
(∼GeV or tens of GeV). These particles were in chemical and thermal
equilibrium in a very early epoch of the Universe. With the expansion
of the Universe, when their interaction rate lagged behind the expansion
rate of the Universe, they failed to interact with each other and as
a result they decoupled from the content of the Universe and remained
“frozen” thereafter with a relic density. The temperature at which this
“freeze-out” occurs for the particle of a particular species is called the
“freeze-out” temperature (Tf ). If the dark matter candidate particle is
massive enough so as to exceed the Universe temperature at the time
of decoupling (both quantities are expressed in energy units), then that
particle moves nonrelativistically and such a candidate for dark matter
is called cold dark matter or CDM. A light particle (relativistic at the
time of decoupling) candidate for dark matter is termed hot dark matter (HDM). This is not to suggest that there is no HDMin the Universe
but it is perhaps the CDMthat dominates the dark matter component of
the Universe. The theoretical calculation of relic density requires the
annihilation cross-section of the dark matter particles and comparing
such calculations with the observed relic density (e.g., extracted from
the observed CMBR anisotropy) reveals that the value of such crosssections
(multiplied by the relative velocity) should be around ∼10−26
cm3 sec−1. This is clearly of weak interaction order and hence the
CDM is often termed WIMP, or weakly interacting massive particles.
From the above discussions for the evidence of dark matter, a scenario
of the dark matter properties seems to emerge. They can be
naively summarized as follows:
• Dark matter is a nonluminous object. It has no interaction with
photons and is incapable of emitting any electromagnetic radiation.
• The dark matter should consist of chargeless neutral particles, as
it does not undergo any electromagnetic interaction.
• The dark matter is all pervading in the Universe and helps the
formation of large-scale structure such as galaxy clusters by
helping in accumulating gravitating mass.
• The dark matter particle is stable; otherwise it would perhaps
decay to known fundamental particles and would have been detected
in laboratory experiments.
• The interaction of dark matter with other Standard Model particles
must be very weak.
• The known fundamental particles (Standard Model particles)
like leptons and quarks cannot be dark matter candidates as they
are mostly charged particles. The only exceptions are neutrinos,
which are neutral particles but the relic density of neutrinos falls
far too short of the observed relic density of dark matter. Although
neutrinos cannot have mass within the framework of the
Standard Model, various neutrino oscillation experiments have
established that the neutrinos are indeed massive, however small(∼eV) its mass may be. Neutrinos (active neutrinos) fall into the
category of hot dark matter while a sterile neutrino, if exists, is
thought to be in the “warm dark matter” (in between HDM and
CDM) category and can contribute (however negligible) to the
total dark matter content of the Universe.
Although dark matter is still by and large an enigma, attempts are
being made to detect them directly or indirectly through various terrestrial
and satellite-borne experiments. The direct detection of dark
matter is attempted following the principle that, if a dark matter particle
hits a nucleus of a detecting material, it suffers elastic scattering,
as a result of which the target nucleus undergoes a recoil. As the interaction
of dark matter with other particles is supposedly very feeble,
the recoil energy of the target nucleus is very tiny (∼ a few keV).
In dark matter direct detection experiments, this tiny recoil energy is
measured. In the absence of any convincing signature of detection of
dark matter (there are however a very few claims from certain experiments),
these experiments generally give an upper bound of the elastic
scattring cross-section of the dark matter particle for different masses
of the dark matter particle. The direct detection of dark matter should
also exhibit a periodic annual variation of the detection due to the periodic
revolution of Earth around the sun. The solar system, along
with the sun, revolves about the galactic center (time for one revolution
is ∼ 225 million Earth years). Since it is moving through the halo
of dark matter (static halo), the sun (and the Earth as well) will encounter
an apparent wind of dark matter impinging from a direction
opposite to the direction of motion of the solar system. The ecliptic
or the sun-Earth plane makes an angle of 60o with the galactic plane.
As the Earth revolves around the sun in a periodic motion, the parallel
component vp of its velocity of revolution also changes its direction
periodically over the year. Thus in the course of Earth’s revolutionary
motion around the sun, vp will be just oppositely aligned to the apparent
dark matter wind at a certain time of the year while direction
of vp will be aligned to the apparent dark matter wind direction at the
other time around 6 months later, when the Earth is at a diametrically
opposite location on its orbit of revolution. In the former event, Earth
will encounter maximum dark matter flux while in the latter case, the
Earth will embrace minimum dark matter flux. Thus there will be anexpected modulation of detection of dark matter at an earthbound dark
matter detection laboratory over the year. This phenomenon is known
as annual modulation of dark matter signal and is a very powerful signature
in dark matter direct detection experiments.
The dark matter can also trapped by the gravity of heavenly bodies.
This happens when the dark matter passes through a body with high
gravity such as the solar core or near the galactic center. In case the
dark matter particles inside those bodies lose their velocities to values
less than the velocities required to escape from these bodies, they are
trapped inside them. When, by this process they accumulate inside
such bodies in large numbers, and they can undergo pair annihilation
among themselves to produce fermion-antifermion pairs and also photons
by primary or secondary processes. The target objects for such
annihilation products include galactic center, solar core, dwarf galaxies
and galaxy clusters, galactic halo, and also extra-galactic sources.
There are several earthbound experiments that are making attempts to
detect such annhilation products, such as neutrinos from dark matter
annihilations in heavenly bodies. Neutrino experiments such as ICECUBE
(a 1 km3 detector at the South Pole that uses Antarctic ice as
detecting material and primarily meant for detecting high-enrgy neutrinos
from heavenly sources like Gamma Ray Bursts or GRBs, Active
Galactic Nuclei or AGN, etc.) also look for such neutrinos from sun or
galactic center. The undersea neutrino detector such as ANTARES at
the Mediterranian sea bed also can look at the galactic center for such
neutrinos. Attempts are being made to detect photons from dark matter
annihilations at the possible sites mentioned above through earthbound
experiments like H.E.S.S., VERITUS, etc., and also the satellite-borne
experiments like Fermi-LAT. There are extensive searches for excess
positrons at cosmos that cannot be explained by cosmic ray sources.
Satellite-borne experiments like PAMELA andmore recently AMS experiment
on-board the International Space Station or ISS have found
an increasing trend of positron excess beyond 10 GeV energy, a phenomenon
that cannot be explained by cosmic ray origins or other astrophysical
processes. They may have originated from dark matter
annihilation, and researchers are vigorously pursuing it.
Thus, understanding dark matter may perhaps unfold several unknown
mysteries of the Universe. This will throw more insight intohow the Universe evolved after the Big Bang and how the structure
of the present Universe with all these galaxy clusters and superclusters
came into being. Dark matter physics also has the potential to
probe new unknown fundamental physics and perhaps new unknown
symmetries of Nature that might predict new particles in Nature as yet
unknown to us with which the dark matter may perhaps be constituted.
Thus, the study of dark matter adresses three very important areas of
fundamental physics, namely cosmology, particle physics, and astrophysics.
ΑΠΟΣΠΑΣΜΑ ΑΠΟ ΤΟ ΒΙΒΛΊΟ "DARK MATTER AN INTRODUCTION" TOY
D e b a s i s h M a j u m d a r
Saha Institute of Nuclear Physics
Calcutta, India
11/9/2016
From time immemorial the enigmatic Universe fascinates the human
imagination and intellect. Humans wondered at themotion of the heavenly
bodies in the vault of the sky and found resemblence between
constellations of stars and earthly living beings. In the absence of any
sophisticated instruments, the thinkers of those distant times used their
diligent observations of the displacements of the heavenly bodies in the
sky, their ascents and descents, to make various astronomical calulations.
The advent of the telescope by Galileo Galilei heralded a new
dawn in astronomical observations and calculations. Mathematician
Johannes Kepler put forward the laws of planetary motion. The revolutionary
discovery and mathematical formulation of gravitation – one
of the fundamental forces of nature – by Sir Issac Newton paved the
way for a more formidable understanding of the motion of the heavenly
bodies.
Any digression of the observed motion of the known astrophysical
objects from the theory appears to indicate the presence of
unknown objects.
This is indeed initially the study of galactic dynamics, the dynamics
of galaxy clusters and the consequent application of cosmic virial theorem
that led to the prediction of not only the existence of dark matter,
but also its very substantial amount that appeared to far outweigh the
visible Universe. The first indication to this effect in the past century
came from the famous Dutch astronomer Jan Hendrik Oort in 1932
who, while measuring the velocities of the stars along the direction
vertical to the plane of the galactic disk of our Milky Way galaxy,
noticed that the vertical velocities of the stars are too high to have escaped
the galactic influence. The Milky Way galaxy is a spiral galaxy
having a disk-like structure with a central bulge of more concentrated
matter. The extent of the disk is around 10 kpc (1 kpc = 3.12×1016
Km) from the galactic center and the disk itself has a thickness of ∼ 4
kpc. The fact that the stars are confined within the galaxy, even thoughtheir vertical velocities are measured to be high enough, necessitates
the presence of unseen mass in the galaxy. Oort reported his observations
in the Bulletin of the Astronomical Institutes of the Netherlands
in 1932 where he reported “Integrating over a column perpendicular
to the galactic plane I find that an average unit of photographic light
corresponds to a mass of 1.8 (if both are expressed in the sun as unit),
...”
Galaxies as noted by Herschell way back in 1780, are not distributed
randomly in the Universe but rather they exist in separate groups or
clusters. Galaxies in each such cluster form a gravitationally bound
group. The famous astronomer Zwicky made his investigations in the
galaxy cluster at Coma constellation 90 Megaparsecs away and also at
the cluster in Virgo constellation and calculated its gravitational mass
using the “virial theorem.” He then used the mass-luminosity relation
of the stars of the individual galaxies and estimated the mass of the
luminous matter in each of the clusters. He came up with a huge discrepancy
between these twomasses and predicted the existence of dark
invisible matter.
The galaxies of the clusters that are x-ray bright are contained within
the x-ray emitting gas. These x-rays are produced when the gas that
embeds the galaxies of the cluster is excited to a temperature (virial
temperature ∼ keV) by the potential of the matter present inside the
cluster. Observations of such x-ray bright clusters and the subsequent
analysis of the observed data give a clear indication that only the galactic
mass and the gas surrounding it is not sufficient to explain them –
one would require the presence of unseen mass or dark matter in the
cluster.
The study of the rotation curve of spiral galaxies shows more profound
evidence of the overwhelming presence of dark matter in the
galaxy. For the rotation curve analysis of a spiral galaxy, one measures
the rotational velocity v(r) of a star or gas in the galaxy as a function of
their distance r from the galactic center. These velocities will depend
upon the mass enclosed by the sphere of radius r. Since for a spiral
galaxy, one has a dense central region and the density of the visible
mass is reduced as one goes away from the central region, one would
expect a Keplerian decline of the rotation curve as one goes away from
the dense central region of the galaxy. But instead, the observationalmeasurements show not a Keplerian decline for v(r) but rather a constant
behavior with r. This is only possible if there is enormous unseen
mass or rather a halo of unseen dark matter present at the galaxy.
The existence of huge unseen mass is also evident from the observed
phenomenon of gravitational lensing. Gravitational lensing is a consequence
of Einstein’s theory of general relativity whereby the gravity
of massive objects induces a curvature of the space-time in its vicinity.
The more the influence of gravitation, the more distorted is the
space-time geometry, suggesting the presence of larger mass. Light
from a distant object (such as galaxy cluster) if it moves along such
a curved space-time follows this local curvature of space-time giving
rise to the lensing effect which is manifested as the appearence of multiple
images of that object around the gravitationalmass that causes the
lensing. Astronomers found such a phenomenon (of multiple imaging)
while observing certain galaxy clusters, when these kind of images appear
surrounding such clusters. Needless to say, the light from the
astronomical object that undergoes such lensing is behind the galaxy
cluster that is being observed by the astronomers and the cluster is on
the line of sight. The estimated mass that can produce a lensing effect
is found to outweigh themass of the target galaxy cluster around which
such multiple images are observed. Thus there is certainly enormous
mass in and around the galaxy cluster that remains invisible or “dark.”
Gravitational lensing is very useful for the search of dark matter even
at the distant reaches of the Universe.
In discussions of evidence of dark matter, the observed phenomenon
of bullet cluster needs mention. It was created in one of the most energetic
events since the Big Bang when two gigantic galaxy clusters
collided with each other some 4 billion light years away from the Earth
at the constellation Carina. These two clusters collided with a speed
of several million kilometers per hour. The x-ray images from these
clusters reveal the shape of normal matter in the clusters after collision
and the dark matter halos around them are known from the method
of gravitational lensing. These observations suggest that due to collision,
the smaller of the two clusters passes through the bigger cluster
and the normal matter in the smaller cluster takes the shape of a bullet
caused by the impact. But the dark matter halos of the two clusters
pass through each other undistorted. It is also revealed that the normalmatter in each of the clusters is dislocated away from their respective
dark matter halos due to the impact of the collision. The event of
“bullet cluster” is not only prolific evidence of the existence of dark
matter but it also points to the fact that they have almost no interaction
between them, as also with normal known matter.
Now the immediate question that arises is how much dark matter
the Universe contains or in what ratio the dark matter exists with
the known (luminous) visible matter such as the galaxies, clusters of
galaxies, superclusters, innumerable stars, planets, and other objects.
In other words, what fraction of the energy budget of the Universe is
in fact dark matter. This is also important to understand: what role
the dark matter plays in the formation of galaxies and galaxy clusters
(structure formation), and how the dark matter influences the destiny
of the Universe. The general wisdom supported by the experimental
evidence suggests that the Universe (and hence the space-time) begins
from a “singularity” with the so-called “Big Bang” and it is everexpanding
thereafter (with an initial rapidly accelerated inflationary
phase). If the mass content of the Universe is very low, it would expand
forever but on the other hand, if the mass content is very large,
this would eventually collapse due to the gravitational pull of the matter.
But the Universe appears to strike a very fine balance of maintaining
a critical mass-energy density such that it will expand with a
constant rate but the expansion is not infinite in time. ∗
The estimation of the energy budget of the Universe is made by measuring
the anisotropies in the cosmic microwave background radiation
(CMBR). The CMBR is the primordial radiation that last scatters
from the Universe soup when the available free electrons were combined
with the ions and atoms started appearing in the Universe. Thus
no free electrons were available for the primordial photons by which
the latter could undergo scattering, and therefore those photons started
free-streaming and remained as background. The wavelengths of these
photons suffer elongation with the expansion of the Universe (the scalefactor of the Universe also obviously changes with the expansion of
the Universe) and in the present epoch, the wavelengths of these background
photons are of microwave order (and hence the name CMBR).
In principle the CMBR should be uniform from any direction in the
sky but any non-uniformity (anisotropy) in CMBR, however small,
is in fact indicative of the imprint of different concentration of mass
of the last scattering surface from where the photons free-streamed.
Thus anisotropies in CMBR contain enormous information regarding
the mass-energy budget of the Universe. The analysis of observational
data of the satellite-borne experiment, Wilkinson Microwave
Anisotropy Probe or WMAP that look for such very tiny anisotropies
in CMBR and more recently the data from another satellite-borne experiment,
namely PLANCK, suggest that around 27% of the massenergy
content of the Universe is made of dark matter while a meager
4% accounts for the rest of the mass, which includes all the stars
and galaxies, galaxy clusters, superclusters and all other known matters.
This known matter is also called the “baryonic matter” and the
above estimate follows from the requirement that the abundances of
observed light elements such as H, D, 3He, 4He, and 7Li agree with
the prediction of Big Bang nucleosynthesis that gives a theoretical understanding
of the synthesis of light elements after the first minute of
the Big Bang. The remaining 69% is a mysterious unknown energy
called dark energy that is thought to be the cause of recently discovered
late time accelerated expansion of the Universe. Therefore a huge
96% of the constituents of the Universe is totally unknown or “dark,”
and the visible or “luminous” Universe accounts for only 4% of the
total mass-energy content. The “luminous” matter signifies, in the microscopic
domain, the fundamental particles or fundamental building
blocks of matter such as quarks, leptons, the vector gauge bosons (the
carrier of fundamental forces), and the scalar Higgs boson that follow
the theory of the Standard Model of particle physics and in the macroscopic
domain, the heavenly bodies like galaxies and galaxy clusters,
superclusters and innumerable stars, novae and supernovae, pulsars
and neutron stars, white dwarfs, planets, intersteller dust, etc.
In all probabilities, the total dark matter content or at least the major
part of it is not made up of the known fundamental particles as otherwise
they would have undergone the Standard Model interactions andtherefore they could have been already probed by now. Therefore its
constituents or at least a majority of its constituents do not supposedly
follow the theory of the StandardModel of particle physics. For example,
the invisibility of dark matter signifies that they do not emit any
electromagnetic radiation and are incapable of undergoing any electromagnetic
interaction, suggesting that they must be made up of neutral
particles. Thus theories beyond Standard Model (BSM) may need to
be invoked in order to predict a suitable particle candidate for dark
matter. Such theories lead to the domain of new physics in the unchartered
energy scale where new symmetries of nature may have to be
envisaged.
The other important issue for understanding the dark matter in the
Universe is its distribution in space, such as galaxies and galaxy clusters.
The question is whether it is uniformly distributed throughout
or its density varies in different regions in a galaxy. Rigorous astrophysical
calculations indicate that the dark matter density is different
in different regions. For example, the local (in the region of our solar
system) dark matter density may be different from a more dense region
such as the galactic center. Not only that their densities may vary
at different locations in the galaxy, but their density profiles may also
vary at different locations.
This is also a matter of concern of how massive the particles are that
make up this huge quantity of dark matter. Experimental endeavors so
far are suggestive of the dark matter candidate particles being massive
(∼GeV or tens of GeV). These particles were in chemical and thermal
equilibrium in a very early epoch of the Universe. With the expansion
of the Universe, when their interaction rate lagged behind the expansion
rate of the Universe, they failed to interact with each other and as
a result they decoupled from the content of the Universe and remained
“frozen” thereafter with a relic density. The temperature at which this
“freeze-out” occurs for the particle of a particular species is called the
“freeze-out” temperature (Tf ). If the dark matter candidate particle is
massive enough so as to exceed the Universe temperature at the time
of decoupling (both quantities are expressed in energy units), then that
particle moves nonrelativistically and such a candidate for dark matter
is called cold dark matter or CDM. A light particle (relativistic at the
time of decoupling) candidate for dark matter is termed hot dark matter (HDM). This is not to suggest that there is no HDMin the Universe
but it is perhaps the CDMthat dominates the dark matter component of
the Universe. The theoretical calculation of relic density requires the
annihilation cross-section of the dark matter particles and comparing
such calculations with the observed relic density (e.g., extracted from
the observed CMBR anisotropy) reveals that the value of such crosssections
(multiplied by the relative velocity) should be around ∼10−26
cm3 sec−1. This is clearly of weak interaction order and hence the
CDM is often termed WIMP, or weakly interacting massive particles.
From the above discussions for the evidence of dark matter, a scenario
of the dark matter properties seems to emerge. They can be
naively summarized as follows:
• Dark matter is a nonluminous object. It has no interaction with
photons and is incapable of emitting any electromagnetic radiation.
• The dark matter should consist of chargeless neutral particles, as
it does not undergo any electromagnetic interaction.
• The dark matter is all pervading in the Universe and helps the
formation of large-scale structure such as galaxy clusters by
helping in accumulating gravitating mass.
• The dark matter particle is stable; otherwise it would perhaps
decay to known fundamental particles and would have been detected
in laboratory experiments.
• The interaction of dark matter with other Standard Model particles
must be very weak.
• The known fundamental particles (Standard Model particles)
like leptons and quarks cannot be dark matter candidates as they
are mostly charged particles. The only exceptions are neutrinos,
which are neutral particles but the relic density of neutrinos falls
far too short of the observed relic density of dark matter. Although
neutrinos cannot have mass within the framework of the
Standard Model, various neutrino oscillation experiments have
established that the neutrinos are indeed massive, however small(∼eV) its mass may be. Neutrinos (active neutrinos) fall into the
category of hot dark matter while a sterile neutrino, if exists, is
thought to be in the “warm dark matter” (in between HDM and
CDM) category and can contribute (however negligible) to the
total dark matter content of the Universe.
Although dark matter is still by and large an enigma, attempts are
being made to detect them directly or indirectly through various terrestrial
and satellite-borne experiments. The direct detection of dark
matter is attempted following the principle that, if a dark matter particle
hits a nucleus of a detecting material, it suffers elastic scattering,
as a result of which the target nucleus undergoes a recoil. As the interaction
of dark matter with other particles is supposedly very feeble,
the recoil energy of the target nucleus is very tiny (∼ a few keV).
In dark matter direct detection experiments, this tiny recoil energy is
measured. In the absence of any convincing signature of detection of
dark matter (there are however a very few claims from certain experiments),
these experiments generally give an upper bound of the elastic
scattring cross-section of the dark matter particle for different masses
of the dark matter particle. The direct detection of dark matter should
also exhibit a periodic annual variation of the detection due to the periodic
revolution of Earth around the sun. The solar system, along
with the sun, revolves about the galactic center (time for one revolution
is ∼ 225 million Earth years). Since it is moving through the halo
of dark matter (static halo), the sun (and the Earth as well) will encounter
an apparent wind of dark matter impinging from a direction
opposite to the direction of motion of the solar system. The ecliptic
or the sun-Earth plane makes an angle of 60o with the galactic plane.
As the Earth revolves around the sun in a periodic motion, the parallel
component vp of its velocity of revolution also changes its direction
periodically over the year. Thus in the course of Earth’s revolutionary
motion around the sun, vp will be just oppositely aligned to the apparent
dark matter wind at a certain time of the year while direction
of vp will be aligned to the apparent dark matter wind direction at the
other time around 6 months later, when the Earth is at a diametrically
opposite location on its orbit of revolution. In the former event, Earth
will encounter maximum dark matter flux while in the latter case, the
Earth will embrace minimum dark matter flux. Thus there will be anexpected modulation of detection of dark matter at an earthbound dark
matter detection laboratory over the year. This phenomenon is known
as annual modulation of dark matter signal and is a very powerful signature
in dark matter direct detection experiments.
The dark matter can also trapped by the gravity of heavenly bodies.
This happens when the dark matter passes through a body with high
gravity such as the solar core or near the galactic center. In case the
dark matter particles inside those bodies lose their velocities to values
less than the velocities required to escape from these bodies, they are
trapped inside them. When, by this process they accumulate inside
such bodies in large numbers, and they can undergo pair annihilation
among themselves to produce fermion-antifermion pairs and also photons
by primary or secondary processes. The target objects for such
annihilation products include galactic center, solar core, dwarf galaxies
and galaxy clusters, galactic halo, and also extra-galactic sources.
There are several earthbound experiments that are making attempts to
detect such annhilation products, such as neutrinos from dark matter
annihilations in heavenly bodies. Neutrino experiments such as ICECUBE
(a 1 km3 detector at the South Pole that uses Antarctic ice as
detecting material and primarily meant for detecting high-enrgy neutrinos
from heavenly sources like Gamma Ray Bursts or GRBs, Active
Galactic Nuclei or AGN, etc.) also look for such neutrinos from sun or
galactic center. The undersea neutrino detector such as ANTARES at
the Mediterranian sea bed also can look at the galactic center for such
neutrinos. Attempts are being made to detect photons from dark matter
annihilations at the possible sites mentioned above through earthbound
experiments like H.E.S.S., VERITUS, etc., and also the satellite-borne
experiments like Fermi-LAT. There are extensive searches for excess
positrons at cosmos that cannot be explained by cosmic ray sources.
Satellite-borne experiments like PAMELA andmore recently AMS experiment
on-board the International Space Station or ISS have found
an increasing trend of positron excess beyond 10 GeV energy, a phenomenon
that cannot be explained by cosmic ray origins or other astrophysical
processes. They may have originated from dark matter
annihilation, and researchers are vigorously pursuing it.
Thus, understanding dark matter may perhaps unfold several unknown
mysteries of the Universe. This will throw more insight intohow the Universe evolved after the Big Bang and how the structure
of the present Universe with all these galaxy clusters and superclusters
came into being. Dark matter physics also has the potential to
probe new unknown fundamental physics and perhaps new unknown
symmetries of Nature that might predict new particles in Nature as yet
unknown to us with which the dark matter may perhaps be constituted.
Thus, the study of dark matter adresses three very important areas of
fundamental physics, namely cosmology, particle physics, and astrophysics.
ΑΠΟΣΠΑΣΜΑ ΑΠΟ ΤΟ ΒΙΒΛΊΟ "DARK MATTER AN INTRODUCTION" TOY
D e b a s i s h M a j u m d a r
Saha Institute of Nuclear Physics
Calcutta, India
11/9/2016
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