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Dark matter
Topics
Galactic detections
Cluster detections
X-ray gas
Results from gravitational lenses
Dark matter interactions with visible matter
Proposed forms of dark matter?
Motivation
Learning about the occurrence and extent of visible matter
flies in the face of what we can infer.
What might it be?
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Dark matter
Most of astronomy is dedicated to studying the visible contents of the Universe.
Indeed, this occupies about 90% of a typical astronomy course. But we have learned, in
the last 50 years, that something is afoot—much of the Universe’s matter eludes us.
We refer to this mystery, this terra incognita, as Dark Matter.
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Evidence for dark matter in galaxies
In 1970, Vera Rubin and Kent Ford developed the
technology to obtain spectra of separate portions of
galaxies.
They published their measurements of the rotation rate
of the Andromeda Galaxy, as a function of distance.
Note that the orbital velocities, as a function of distance
from the center of the galaxy, are more or less constant.
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Using rotation curves
Consider our solar system, where 99% of the mass is concentrated in the central object
(the Sun).
Using Newton’s laws, equate the centripetal force to gravity:
Fc = mvc2/R
Fgrav = GMm/R2
vc2 = GM/R
G=6.67×10-11m3/kg-s2
M = 2×1030 kg
R(1 a.u.) =1.5×1011 m
vEarth = 29.8 km/s
Note how velocity drops rapidly
with increasing distance.
Clearly this is not the case with the
rotation curve of our galaxy.
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Using rotation curves
What can we infer from a rotation curve where velocities do not change with
distance, i.e., when the circular velocity vc = constant?
First, we note (without proof beyond handwaving) the interesting
result that in a symmetric distribution of matter, only the matter
interior to the orbit contributes to the orbital speed.
Since: Fc = mvc2/R
and
Fgrav = GMgalaxym/R2
mvc2/R = GMgalaxym/R2
→
vc2 = GMgalaxy/R
→ Mgalaxy = Rvc2/G
Mgalaxy = R(vc2/G)
Results
1) We can easily weigh galaxies by measuring their rotation speeds and sizes.
2) Since vc is constant, we discover that the “interior mass” (or “enclosed mass”) in
a galaxy is directly proportional to the radius that is being surveyed.
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Sample calculation: weighing the Milky Way
Modern studies of gas clouds in the Milky Way Galaxy at 21 cm
radiation (atomic hydrogen) maintain this experimental result.
Rotational velocity = 215 km/s at 10 kpc.
Mgalaxy = Rvc2/G
G=6.67×10-11m3/kg-s2
M = 2×1030 kg
vc= 215 km/s × (1000 m/km)
= 2.15×105 m/s
R = 10 kpc × (1000 pc/kpc) × (3.26 LY/pc) × (9.46×1015 m/LY)
= 3.08×1020 m
Mgalaxy = Rvc2/G = 3.08×1020 m × (2.15×105 m/s)2/(6.67×10-11m3/kg-s2)
= 2.1×1041 kg
= 1×1011 M
A distance twice as far encompasses twice the mass.
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Evidence for dark matter in galaxies
Meanwhile, surveys of our galaxy detect only about 1×1010 M of
material interior to the Sun’s orbit.
Mass (visible)/ Mass (gravitational)
= 1×1010 M / 1×1011 M = 0.1, or 10%
90% of the galaxy is dark to our detectors.
Hence, the name “Dark Matter.”
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Dark matter in elliptical galaxies
Elliptical galaxies can be studied in much the same way.
However
Elliptical galaxies do not have much interstellar material, so we
cannot use the 21-cm atomic hydrogen as a probe.
Also, the stars in ellipticals do not orbit in a disk; they buzz
around the core like angry bees.
Still…in the spirit of the Faber-Jackson relation, we can examine
the spectra of elliptical galaxies and learn about the distribution of
mass by looking at the Doppler broadening of absorption lines.
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Dark matter in elliptical galaxies
The elliptical galaxy on the right has more overall mass.
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Dark matter in elliptical galaxies
Results
Interestingly, the stars in the outskirts of ellipticals do not move very fast. This
has been interpreted as evidence that ellipticals do not contain much dark matter.
The question raged: how was dark matter stripped from ellipticals?
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Dark matter in elliptical galaxies
Results
More recently (2005), this was explained as being due to the fact that the outer
stars are travelling in highly elliptical orbits, and so are going slower than would
be expected for a circular orbit.
So, the outer stars are moving, not because of a low amount of gravity (hence
little dark matter), but rather because they are in highly elliptical orbits, and slow
down as a consequence of Kepler’s laws.
Taking this into account, we find that ellipticals are also beset with dark matter.
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Dark matter in galaxy clusters
Galaxies in a cluster orbit in response to the gravitational field created by the pull of
all the galaxies within the cluster.
They orbit in response to the gravity created by the cumulative masses of all the
galaxies in the cluster.
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Dark matter in galaxy clusters
In 1934, Fritz Zwicky used redshifts (i.e., the
Doppler effect) to measure orbital speeds of
the galaxies in the Coma Cluster. From this,
he determined the mass of the cluster.
The velocities he measured were only
line-of-sight velocities of the galaxies, which
are moving in three dimensions.
Also, Zwicky’s method assumed the galaxy
cluster had time to reach a state of reasonable
equilibrium (i.e., that the Virial Theorem
holds)—this is a safe assumption in this case.
In this case, the equation for determining
mass (M = Rvc2/G) is slightly modified:
Mcluster = 5Rv2average/G
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Sample calculation: weighing the Coma Cluster
Typical velocities for galaxies in the Coma Cluster are about 860 km/s.
The Coma Cluster’s radius is 6.1 Mpc.
Mcluster = 5Rv2average/G
G=6.67×10-11m3/kg-s2
M = 2×1030 kg
R = 6.1 Mpc × (106pc/Mpc) × (3.26 LY/pc) × (9.46×1015 m/LY)
= 1.9×1023 m
vaverage = 860 km/s × (1000 m/km)
= 8.6×105 m/s
Mcluster = 5Rv2average/G
= 5×(1.9×1023 m) × (8.6×105 m/s)2/(6.67×10-11m3/kg-s2)
= 1.1×1046 kg
= 5×1015 M
But… the M/L ratio, i.e., mass (gravitational)/ mass (visible) ≈ 10 – 50!
Dark matter again!
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X-ray gas in galaxy clusters
Recall that the average speed of atoms in a cloud is one and the same
as the cloud’s temperature. The atoms in hotter gases travel faster.
In galaxy clusters, the combined gravity of all the galaxies tends to
hold the intergalactic gas within the cluster.
Consider: galactic clusters will retain gas, as long as the gas is not too
hot. (The atoms in overly-hot gas would travel fast enough to escape.)
This means that the temperature of intergalactic gas is a measure of
the galaxy cluster’s gravitational strength, and therefore mass.
Galaxy clusters are filled with gas that emits X-rays at about 108K!
That is very energetic; the atoms are moving extremely rapidly!
Therefore, the galaxy clusters must be very massive in order to retain
these ultra-speedy gas atoms in the galactic cluster.
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X-ray gas in galaxy clusters
How fast do the atoms move? The amount of kinetic energy in a single
atom can be estimated as:
EKE ≈ kT
k = 1.38×10-23J/K (Boltzmann constant)
So, for a hydrogen atom:
½mHvH2 ≈ kTH →
vH2 ≈ 2kTH/mH
Treating these atoms as if they were orbiting in the galaxy cluster’s
gravitational field, recall the equation for an orbiting object in a galaxy:
Mgalaxy = Rvc2/G →
Mcluster = RvH2/G =(R/G)vH2 ≈ (R/G)(2kTH/mH) ≈ 2RkTH/mHG
The high-temperature X-ray gas atoms move at about 106 m/s. The masses
determined for their clusters provide more evidence for dark matter!
It also tells us that fully ⅔rds of the cluster mass is in the X-ray gas, and
not the galaxies!
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Is dark matter baryonic?
Objects made of protons and neutrons (baryons) are baryonic.
Examples of baryonic matter include planets, brown dwarfs, black
dwarfs, faint red stars, black holes, and you!
Is dark matter baryonic?
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Mass to light ratio of baryonic stars
We often express the Sun’s mass and luminosity in “solar units”
Luminosity = 1 L
Mass = 1 M
The mass/light ratio of an object is its M/L ratio, expressed in solar units.
Consider an O star, a G star (our sun), and an M star
MO = 60 M
LO = 106 L
→
(M/L)O = 6×10-5
MG = 1 M
LG = 1 L
→
(M/L)G = 1
MM = 0.2 M
LM = 0.01 L
→
(M/L)M = 20
Inner parts of the Milky Way
M/L ≈ 1/3, meaning that the mass can be accounted for by stars.
Edge of the Milky Way disk
M/L ≈ 20, possibly accountable by low mass stars.
Halo regions
M/L ≈ 100!
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What is the identity of the dark matter?
O, B, A, F, G Stars?
No. We would easily detect them. Also, the M/L ratio observed for dark matter
prohibits this, except for perhaps near the galactic center.
Faint stars?
No. For K and M stars to account for the mass, they would have to be more
common than we have seen with the HST. Brown dwarfs would have to be
even more common.
Interstellar dust and gas?
No and no. While often difficult to detect in visible wavelengths, these are not
hidden from resourceful astronomers. We can detect gas and dust at whatever
temperature you might devise.
Black dwarfs (cooled white dwarfs), black holes?
No and no. Black dwarf wannabes have not had enough time to cool to black.
Exotic stellar remnants like black holes, if so common, would be observable
interacting with the interstellar medium.
Dark matter remains a mystery!
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Is dark matter baryonic?
The Big Bang theory predicts the concentrations of hydrogen, helium, and other
elements. These predictions are strongly affected by the densities of the universe.
To match the observed elemental abundances, the Big Bang requires that baryonic
densities should be around 4% critical density (ρcrit = 10-29 g/cm3).
4% ρcrit is more or less the
same density as the
NON-dark matter that we
CAN see.
So it seems very unlikely
that low luminosity baryonic
objects—called MAssive
Compact Halo Objects
(MACHOs)—can be used
to explain dark matter.
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Is dark matter baryonic?
The Big Bang theory seems to rule out baryonic matter as an
explanation for dark matter. Even so, some scientists persist in
using MACHOs to explain dark matter.
Gravitational Microlensing
Gravitational lensing is the well-documented bending of light by
gravity. Conventional lensing is when foreground galaxies lens the
images of background cosmic objects.
A less-well known form of lensing is called gravitational
microlensing.
This results in a short term change in brightness of the lensed
(background) object, usually a star.
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Microlensing and baryonic matter
Looking for the frequency of microlensing events can tell us about the number of
MACHOs in the galaxy.
Microlensing events have been observed (Optical Gravitational Lensing
Experiment; groundbased and HST), but are relatively rare.
Since microlensing is so infrequent, MACHOs cannot be common enough to
account for the dark matter.
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More info from gravitational lenses
There are two more types of gravitational lensing. In these cases, the
background objects being lensed are galaxies.
Strong gravitational lensing
The image of the background object can be twisted, bent,
elongated, or split into multiple components.
Large lensed arcs are called Einstein Rings.
Multiple images of quasars can be identified by their having the
exact same redshift, spectral features, and variability in their
energy fluctuations.
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More info from gravitational lenses
Weak gravitational lensing
The images of background object are weakly distorted. Instead of
dramatic effects on a few objects, what is more important is that
many background objects are distorted.
Weak lensing
By a careful analysis of the many small distortions, the mass of
the lensing object, and its spatial extent, can be calculated!
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Mapping dark matter
With lensing, we can even map the distribution of dark matter in space.
The distribution of dark matter is both similar, and dissimilar, with that of
visible matter.
We can even observe how it fragmented in time—its fragmentation
history mirrors the fragmentation of normal matter.
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The Bullet Cluster hints at something strange
Combined datasets for the Bullet Cluster and MACS J0025.4-1222
1. Visible HST images of pairs of colliding galaxy clusters;
2. X-ray gas as viewed by the Chandra satellite, displayed as a
red glow;
3. Weak gravitational lensing analyzed to determine the
distribution of overall matter (shown as a blue glow).
Apparently, during the collision process, the X-ray gas was stripped
from the galaxy clusters. Yet, the majority of the matter (as traced
by lensing) is still centered on the galaxies.
The dark matter is not something like an extended baryonic gas. It
is something more exotic.
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More dark matter activity
The dark matter around CL0024+17 has a strange, ring-shaped distribution.
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But are we are missing something?
Similar maps of Abell 520 (The Train Wreck Cluster) shows
something inexplicable.
– X-ray gas was stripped from the galaxies, as expected, and is
concentrated around point 3;
– The galaxies are mostly concentrated at points 1, 2, 4, and 5.
But the dark matter distribution does not
mirror the galaxy distribution.
– Dark matter does follow the galaxies at
points 1, 2, and 4;
– Meanwhile, much dark matter is
centered around point 3 (which lacks
galaxies);
– Finally, there is no dark matter
associated with the galaxies at point 5.
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What is dark matter?
We know more about what dark matter isn’t, than what it is!
– It is not luminous
So says every large-scale M/L measurement
– It is not baryonic
So says Big Bang nucleosynthesis
– It does not interact strongly with regular matter, except by gravity
Dark → no electromagnetism interaction.
No effect on nuclear processes → no nuclear force interaction
– It does not even interact strongly with itself
So says cluster-cluster stripping
– It does not appear to consist of MACHOs
So says HST/groundbased measures of microlensing
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WIMPs vs. MACHOs
The leading alternate hypothesis is of WIMPs (Weakly Interacting Massive Particles)
– Some kind of atomic particle that does not interact via the electromagnetic or
strong force;
– Unable to interact, it cannot cool by collisions, and so stays in the halo;
– Unable to interact, it is unaffected by collisions with other WIMPs;
– The Higgs particle is the current favorite.
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A roundup of dark matter hypotheses
Cold dark matter (currently the favorite with most researchers)
– Material with particles that move at conventional speeds (v<0.1c);
– MACHOs;
– WIMPs (esp. the Higgs);
– Axions (a theoretical particle proposed by some quantum theories).
Warm dark matter
– Material with particles that move at relativistic speeds;
– Gravitinos and photinos (particles from supersymmetry theories; to be
discussed).
Hot dark matter
– Material with particles that move at ultrarelativistics speeds (v>0.95c);
– Neutrinos;
– A problem with HDM is that it would not stay grouped with clusters; this is
argued against by gravitational lens maps.
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Modified gravity theories
Some theorists, starved for publications and happy to work in a theoretical
realm unconstrained by data, thrill at the prospect of proposing half-baked,
unsubstantiated hypotheses suggesting that our understanding of gravity is
incorrect in some mad way.
Such a result would require modifications to gravity at very large scales.
These modifications produce effects that manifest themselves nowhere else,
but which would explain dark matter.
Most efforts at modified gravity require some new equivalent of dark matter to
get them to work, so what’s the point?
But don’t let me prejudice you against such ideas.
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