Dark Matter


So how do we weigh the universe?

5) There is still a big dark mystery out there

There is only a single God, Mixcoatl, whose image they posess, but they beleive in another, invisible, god, not represented by any image, called Yoalli Ehecatl, That is to say, God Invisible, Impalpable, Benificent, Protector, Omnipotent by whose streght alone...rules all things

Nahuatlan Myth


First Guess: What you see is what you get!

Count number of galaxies in a region of space, assume they consist of stars much like the sun, so \color{red}{\upsilon = \frac{M}{L} \approx \frac{{M_ \odot }}{{L_ \odot }}}


1st order estimate:

based on loose estimates of dark nebulae, obscuration of light and dust seen in other galaxies
\color{red}{ \frac{{\rho _{DM} }}{{\rho _{lum} }} \approx 1 \Rightarrow \frac{M}{L} \approx \frac{{2M_o }}{{L_o }}}

Local Dynamics:

Can get estimate of local density by motion of stars
\color{red}{ \frac{{\rho _{DM} }}{{\rho _{lum} }} \approx 2 \Rightarrow \frac{M}{L} \approx \frac{{3M_o }}{{L_o }}}

(first direct evidence for D.M.)


Masses of Spiral galaxies

direct observation i.e. measurement of velocities of individual stars in nearby => rotation curves or measurement of hydrogen via 21cm line or estimates of no. of stars
Luminosity of galaxy should reflect mass

Typical Spiral (NGC3198) R ≈ 20 kpc but outer parts are just seen as H gas

Should be able to calculate rotational speed

In core of galaxy,

\color{red}{ \frac{{mv^2 }}{{r_1 }} = \frac{{GM\left( {r_1 } \right)m}}{{r_1 ^2 }}}
M(r1) is mass inside orbit: total mass of core M0 Hence inside core
\color{red}{ v = \sqrt {\frac{{GMr^2 }}{{R^3 }}} }

Outside core:

\color{red}{ v = \sqrt {\frac{{GM}}{r}} }

Most of the light is fairly concentrated, so this should be good approx to the mass.
These show rotation curves

i.e. velocity curve doesn't drop as expected


Not perfect: by fitting we can get a better result

Halo + core add together to give correct curve

Note this is not unique to NGC 3198: all measured spirals show same. (Have to have spiral that is not "flat on", since no Doppler, or "side on" since cannot separate different parts)

For spirals
\color{red}{ \frac{{10M_o }}{{L_o }} < \frac{M}{L} < \frac{{40M_o }}{{L_o }}}

Large clusters of galaxies:

By measuring vel. cpt. in line of sight (via Doppler) can get estimate of M from virial theorem
\color{red}{ \left\langle {K.E.} \right\rangle = - \frac{1}{2}\left\langle {P.E.} \right\rangle }
for a cluster, this becomes
Hence
\color{red}{ M = \frac{{r_h \left\langle {v^2 } \right\rangle }}{{\alpha G}}}

A check: Large clusters contain a lot of hot gas, which is strong X-ray source

X-ray pictures measure density and temp:


Can use Hydrostatic Equilibrium equation and Eqn. of State to estimate mass (just as we did with stellar modelling
\color{red}{ \frac{{dP}}{{dr}} = - \frac{{Gm\left( r \right)\rho \left( r \right)}}{{r^2 }},P = \frac{{k\rho T}}{{\mu m}}}
hence can measure
\color{red}{ m\left( r \right) = 4\pi \int {\rho \left( r \right)} r^2 dr}
which is the mass attracting the more distant gas
\color{red}{ M \sim 10^{15} M_ \odot \Rightarrow \upsilon \approx 300\upsilon _ \odot }
for Coma

This gives much higher masses than individual spirals.


Also large clusters show gravitational lensing, can get quantitative estimate Einstein ring (if lensing is perfect)
\color{red}{ \theta _E = \left( {\frac{{4GM}}{{c^2 d}}\frac{{1 - x}}{x}} \right)}
if distance is d and lensinig object is at xd (can get x and d from red shifts)
For Abell 2218 (z = .18) again
\color{red}{ M \sim 10^{15} M_ \odot \Rightarrow \upsilon \approx 300\upsilon _ \odot }

The Bullet Cluster
Combination of lensing (blue) and X-rays (red) in the bullet cluster:

Strong evidence for non-interacting dark matter:
  • X-ray emitting material is gas, so gets stopped in collision
  • dark matter gets carried along

astro-ph/0608407 (Clowe et al)


IR sky surveys suggest that the total mass may be much higher


What the hell:

  1. Brown dwarfs
  2. Hydrogen gas
  3. Jupiters
  4. Hydrogen rain
  5. Low surface brightness galaxies
  6. Maxi Black holes
  7. Mini Black holes
  8. Neutrinos
  9. He H +
  10. Modified 1/r² law
  11. Axions
  12. Weakly Interacting Massive Particles (WIMPS)
  13. Magnetic Monopoles
  14. Majorons
  15. Photinos
  16. E8 shadow matter
  17. Cosmic Strings
Which is it? We don't know! However, all of the above have problems.
face face face

The Generic Candidates for Dark Matter :
  1. Baryonic (BDM) ordinary matter, but maybe in some odd form e.g. rocks
  2. Hot (HDM) particles which were relativistic at time of BB e.g. ν's
  3. Cold (CDM): heavy (usually) particles e.g. WIMPs
  4. Mixed (MDM) e.g. 70% WIMPs, 30% ν's
  5. Decaying Dark Matter (DDM)
Why can't it be all BDM (wouldn't it be a lot easier?).

We'll see later that primordial concentrations gave ΩB ≈ .03--.1 (Much too low!!!)

i.e. the dark matter cannot be all "normal" baryonic matter.



Neutrinos

SNO showed us ν's must be "heavy". Since they were formed in the BB and are about as numerous as γ's, we'll come back to them later

We need to search for stars in IR (T ≈ 1000K)

None in our neighbourhood.

would need
Have now found several brown dwarfs.


Microlensing

If one star passes in front of another, we cannot see a double image (as with quasars), but we can see brightening as the BD passes across a star's image.

The predicted rates are reasonable:

MASS (M₀)Radius (m)Mean μ-lensing time# Events/Month
103 × 109>1 yr0.5
11093 mth1.0
10-21089 d5
10-41071 d50
10-61062 hr500
10-810512 min5000

Distinguishing them from variables: Must be symmetrical, achromatic, single, on-off events.


The Experiments

Eros, ≈ 106 stars.
Macho, 300 digitized plates + CCD

ExperimentCandidatesMAτ
Eros219.32.526 days
Macho1 good19.33.330 days
+3 poor
OGLE4 poor11->45 days

Macho 1 "Gold-plated" event
M = 19.55
A = 6.8
τ ≈ 33.8 days


This event was also seen (but not completely) by EROS: Consistent with M = .1M₀ and with Ω ≈ .01 but not with all of halo consisting of these.


Hydrogen gas:

Can't see 21cm Line, so would have to be very diffuse (<.1 atom m-3) which doesn't solve the problem

Hydrogen rain

(Boiling point of H2 is 22K)

Could exist in molecular clouds, but cannot explain clusters of galaxies.


Low surface brightness galaxies

Galaxies as big as (e.g. M31) but with only 107 stars would be invisible.

Number of these now known in local group

Not enough near us


No-Nameons: CDM candidates

Although these are similar cosmologically, they are very different from the point of view of detection.


Rates


A lot can be ruled out by "in vitro" experiments (e.g. OPAL (Richard Hemingway and others) at CERN puts limits on LSP's)

ATLAS (2008: Manuella Vinctner and 1500 others) will be able to rule out a lot more option (any reasonable super-sym. candidate with m < ∼ 1TeV)


Dark Matter

Generic WIMPS can be seen "in vivo" via a variety of low temp. expts.: e.g. Queens-U de Montreal Picasso expt. Nucleus will recoil and transfer energy to super-heated freon liquid and cause transition to gas.

Measures spin-dep X-sect

In solid, nucleus will recoil and transfer energy to lattice, flipping superconductor or sending off ballistic phonons. So far, no results!

Note coordinates: if X-sect is small, can't see them If mass is large, get a good recoil, but don't need very many

Only positve result is from DAMA (but no one understands it)

DEAP (see Kevin Graham): will use 1 tonne of liquid argon: can set useful limits


What the hell:


Collect your Nobel prize on the way out........

Now want to look at the next major ingredient: the microwave background