Dark matterTopics

Galactic detectionsCluster detectionsX-ray gasResults from gravitational lensesDark matter interactions with visible matterProposed forms of dark matter?

MotivationLearning 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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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.

Dark matter

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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.

Evidence for dark matter in galaxies

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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 = GMm/R2

vc2 = GM/R

G=6.67×10-11m3/kg-s2

M = 2×1030 kg R(1 a.u.) =1.5×1011 mvEarth = 29.8 km/s Note how velocity drops rapidly with increasing distance.

Clearly this is not the case with therotation curve of our galaxy.

Using rotation curves

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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 → vc

2 = GMgalaxy/R

→ Mgalaxy = Rvc2/G Mgalaxy = R(vc

2/G)

Results1) 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.

Using rotation curves

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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.

Sample calculation: weighing the Milky Way

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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.”

Evidence for dark matter in galaxies

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Elliptical galaxies can be studied in much the same way.

HoweverElliptical 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.

Dark matter in elliptical galaxies

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Dark matter in elliptical galaxies

9The elliptical galaxy on the right has more overall mass.

Dark matter in elliptical galaxies

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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?

Dark matter in elliptical galaxies

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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.

Dark matter in galaxy clusters

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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.

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, whichare 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 = Rvc

2/G) is slightly modified:

Mcluster = 5Rv2average/G

Dark matter in galaxy clusters

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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!

Sample calculation: weighing the Coma Cluster

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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.

X-ray gas in galaxy clusters

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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 → vH

2 ≈ 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)vH

2 ≈ (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!

X-ray gas in galaxy clusters

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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?

Is dark matter baryonic?

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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 starMO = 60 M LO = 106 L → (M/L)O = 6×10-5

MG = 1 M LG = 1 L → (M/L)G = 1MM = 0.2 M LM = 0.01 L → (M/L)M = 20

Inner parts of the Milky WayM/L ≈ 1/3, meaning that the mass can be accounted for by stars.

Edge of the Milky Way diskM/L ≈ 20, possibly accountable by low mass stars.

Halo regionsM/L ≈ 100!

Mass to light ratio of baryonic stars

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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!

What is the identity of the dark matter?

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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.

Is dark matter baryonic?

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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.

Is dark matter baryonic?

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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.

Microlensing and baryonic matter

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There are two more types of gravitational lensing. In these cases, the background objects being lensed are galaxies.

Strong gravitational lensingThe 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.

More info from gravitational lenses

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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.

By a careful analysis of the many small distortions, the mass of the lensing object, and its spatial extent, can be calculated!

More info from gravitational lenses

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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.

Mapping dark matter

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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.

The Bullet Cluster hints at something strange

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The dark matter around CL0024+17 has a strange, ring-shaped distribution.

More dark matter activity

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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 atpoints 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.

But are we are missing something?

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We know more about what dark matter isn’t, than what it is!

– It is not luminousSo 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 gravityDark → 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

What is dark matter?

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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.

WIMPs vs. MACHOs

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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.

A roundup of dark matter hypotheses

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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.

Modified gravity theories

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