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Galaxy Clusters, Large Scale Structure and Hubbles Law


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Title: Galaxy Clusters, Large Scale Structure and Hubbles Law

Galaxy Clusters, Large Scale Structure and
Hubbles Law
  • Chapter 18

Galaxy Clusters
  • Half of all galaxies are in clusters or groups
  • Clusters contain 100s to 1000s of gravitationally
    bound galaxies
  • Typically few Mpc across
  • Central Mpc contains 50 to 100 luminous galaxies
  • Contain many Ellipticals and SOs
  • Nearest rich clusters are Virgo and Fornax (15-20
    Mpc away)
  • Next is Coma cluster at 70 Mpc away

Coma Cluster
  • Groups of galaxies are smaller than clusters
  • Contain less than 100 galaxies
  • Loosely (but still gravitationally) bound
  • Contain more spirals and irregular galaxies than

The Local Group
Compare relative sizes of groups and clusters
  • Distribution of galaxies in a cluster falls as
    r1/4 (like surface brightness of elliptical
  • May be dynamically relaxed systems
  • Crossing time in a typical cluster (galaxy moving
    at 1000 km/s, cluster size 1 Mpc) ? 109 years
  • Thus, clusters must be gravitationally bound
    systems and have possibly had enough time to
  • If clusters are relaxed systems, we can use the
    virial theorem to estimate their masses
  • M (5/3)(ltv2gtR/G) eq. 13.47
  • Using radial velocity component only (Doppler
  • M 5ltvr2gtR/G eq. 13.52
  • For Coma cluster, vrms 860 km/s and cluster
    size 6.1 Mpc, what is mass?

M 5 x 1015 Msun
Clusters have a Dark Matter problem too
Luminous matter does not make up this mass Adding
up mass in DM halos of spiral galaxies still not
enough Look for mass in hot, intracluster gas -
T107K Estimate gas mass from diffuse X-ray
Some significant mass in gas, but still not
enough to account for viral mass estimates
Mass may be contained in individual galaxy halos
that extend further than we can measure Clusters
may have their own Dark Matter halos M/L ratios
for clusters is 2001
  • Many clusters have a central dominant or cD
    galaxy at their center (e.g. M87 in Virgo)
  • contain multiple nuclei
  • could come from merger of central galaxies
  • galactic cannibalism

Numerical simulations reveal what happens to the
stars and gas when two galaxies collide and merge
Note most mergers are actually thought to occur
in groups rather than clusters. Why? The
relative velocities of galaxies in groups are
slower (v 100 to 500 km/s) allowing them to
have greater interactions.
Are there structures larger than clusters?
YES Local Supercluster - 106 galaxies in 1023
  • Cant get mass via VT
  • Crossing times are too large, systems are not
  • In addition to superclusters, large scale
    structure of galaxies reveals equally large voids

Redshift surveys of distant galaxies reveal the
3-d large-scale structure in the Universe
  • CfA redshift survey
  • 3 slices 6 degrees in declination thick
  • Galaxies appear to sit on 3-d surfaces (e.g.
    bubbles, sponges)
  • Galaxy motions (wrt each other) are sometime
    organized ? attraction by some matter
  • Our own MW and local group are moving towards the
    Virgo cluster at 300 km/s. Virgo is also moving
    towards the great attractor.

Where does the structure come from?
Top-down First largest scale structures form
(superclusters, voids) and then smaller
structures form out of the matter Bottom-up
Smaller scale structures (i.e. galaxies) form
first and then come together to form larger scale
Which is it?
Compare large galaxy surveys with simulations
designed to model the data. The largest
simulation recently completed is the Millenium
  • Assumes cold dark matter dominates Universe
    (alternative is hot dark matter - particles like
    neutrinos rather than protons, electrons,
    neutrons -regular old atoms)
  • N-body simulation with particles interacting
  • 1010 particles mapped from early times in the
    Universe to the present in cube 500 h-1 Mpc on a

Dark Matter
The simulation shows that structure forms more
along the lines of the bottom-up model (i.e.
galaxies form first), but that these form in the
already over-dense regions of the dark matter
Redshift z1.4 (t 4.7 Gyr)
Redshift z18.3 (t 0.21 Gyr)
Redshift z0 (t 13.6 Gyr)
Redshift z5.7 (t 1.0 Gyr)
Hubbles Law
In 1912, Vesto Slipher discovered that with few
exceptions, every galaxy is receding from us,
i.e. has redshifted spectral lines. Redshift
is defined by

z Dl/l
  • In the 1920s, Edwin Hubble discovered that more
    distant galaxies (using distances determined from
    Cepheids) are receding faster (have larger
  • The relationship, well fit by a straight line, is
    called Hubbles Law.

Hubbles Law is written Recessional Velocity
(in km/sec) Ho ? distance (in Mpc) V Ho
D where Ho is Hubbles constant (slope of the
Universal Expansion
You can think of space as the surface of a
balloon. As the balloon expands, the space
between galaxies stretches. This means that
the wavelength of light photons emitted by
galaxies are also stretched as space expands.
That is to say, the wavelengths are expanded,
i.e. redshifted.
If the rate of expansions stays constant over
time, and all objects are together at t0,
current distance between two objects is d v
to where to is current age of Universe Then, v
(1/to)d Same as Hubbles law with
identification Ho 1/to Where 1/Ho is called
the Hubble Time (age of the Universe if expansion
is constant, which is probably not the case) Ho
has units of km/s/Mpc to express velocity and
distance in convenient units (btw, Hubbles
first estimate of Ho was 500 km/s/Mpc, pretty far
from the current value of around 70!)
How to determine the Hubble Constant We need to
get accurate distances to the most distant
galaxies we can see to measure the expansion rate
of the Universe. Galaxy velocities must be
dominated by the Hubble flow, not the random
motions caused by gravitational attractions to
nearby galaxies in groups, clusters, etc.
With their high luminosities (10,000 Lsun),
Cepheid variables extend the distance scale to
nearby galaxies, out 25 Mpc (80 million light
Type 1a SN
Type-I supernova result from the detonation of
white dwarf stars when their mass (slightly)
exceeds 1.4 Msun. The brightness of the
explosion should be (roughly) the same for every
Type-1 supernova.
Type-I Supernovae are standard candles. Knowing
their luminosity, and comparing to their measured
flux, yields the distance via the inverse-square
Useful for determining distances out to (3
billion light years - 1 Gpc).
Tully-Fisher Relation
(a broadened line)
  • Galaxy rotation is often measured via the 21cm
    atomic hydrogen line.
  • Rotation speed (line width) is proportional to
    the galaxys mass.
  • Galaxy luminosity is also proportional to galaxy
    mass (number of stars).
  • The correlation between luminosity and rotation
    speed is referred to as the Tully-Fisher relation.

Extending the distance scale allows us to put
more galaxies on the Hubble Diagram and determine
Hubbles constant with greater accuracy.
Type 1a SN
Each distance technique has uncertainties which
then add to the error in determining the Hubble
Constant Current values hover around 70 km/s/Mpc
with an error of /- 8 km/s/Mpc
The Cosmic Distance Ladder
Hubbles law allows us to measure distances to
the ends of the visible universe, (12
billion light years).
It is less accurate for distances lt 100 Mpc
because of the peculiar velocities of galaxies
(i.e. motions affected by local gravitational