Download Clusters of Galaxies

Clusters of Galaxies
Galaxies are not randomly strewn throughout space. Instead the
majority belong to groups and clusters of galaxies. In these structures,
galaxies are bound gravitationally and orbit a common center of mass.
Groups: have less than ~50 members with a size of ~2 Mpc. They have
velocity dispersions ~150 km/s and total mass 2-3 x 1013 M⊙. They have
mass-to-light ratios of ~300-400 M⊙/L⊙.
Clusters: have ~50 members (a poor cluster) to as many as 1000
members (a rich cluster). They have sizes of 6-8 Mpc, velocity
dispersions of ~800-2000 km/s and total mass of 1-3 x 1015 M⊙. They
have mass-to-light ratios of >500 M⊙/L⊙.
Superclusters: clusters of clusters of galaxies, and so on.
The Local Group
There are about 35 galaxies within roughly 1 Mpc of the Milky Way and these have velocities implying they
are all bound to a common center of mass (about 460 kpc in the direction of Andromeda). The most
prominent members are the Milky Way (us), and the Andromeda (M31) and Triangulum (M33) galaxies.
The Local Group
There are about 35 galaxies within roughly 1 Mpc of the Milky Way and these have velocities implying they
are all bound to a common center of mass (about 460 kpc in the direction of Andromeda). The most
prominent members are the Milky Way (us), and the Andromeda (M31) and Triangulum (M33) galaxies.
The Local Group - Map
from
Grebel 2001
The Local Group
Andromeda has a “blueshift”. It has a negative recessional velocity of roughly -300
km/s. Given the current distance of 770 kpc, they should collide in 2-3 Gyr.
What would this look like ? The Local Group
Using the orbital speeds and distances of galaxies in the local
group, you can estimate how much mass their is in the local
group. The answer is at least 4 x 1012 M⊙. Using all the light
we see, this gives a mass to light ratio of ~60 M⊙/L⊙.
The mass-to-light ratio of “luminous matter”) in the the Milky
Way (~ 3 M⊙/L⊙ in the Solar circle) is much, much smaller.
Luminous matter accounts for ~5-10% in the Local Group. The Virgo Cluster
First recognized by William Herschel where the constellations
Virgo and Coma meet. The cluster covers 10 x 10 degrees on
the sky (the Full Moon cover 0.5 x 0.5 degrees). The center of
the cluster is ~18 Mpc from Earth.
The Virgo Cluster contains >250 large galaxies and more than
2000 smaller ones contained within an area 3 Mpc across.
The largest galaxies are all ellipticals (M87, M86, M84) and
these have sizes equal to the distance between the Milky Way
and Andromeda. These are “giant” Ellipticals (gE). Central Part of Virgo Cluster
M91
M88
M90
M86
M84
M87
M58
M89
Virgo Cluster of Galaxies sky.google.com
The Coma Cluster
The Virgo Cluster is small compared to the Coma Cluster.
The Virgo Cluster contains >250 large galaxies and more than
2000 smaller ones contained within an area 3 Mpc across.
Most of the large galaxies are spirals in Virgo.
The Coma Cluster is 15o of Virgo, in the constellation Coma
Berenices, and is ~90 Mpc away. It has an angular diameter of
~4o which at 90 Mpc away is a linear diameter of 6 Mpc.
Coma contains possibly more than 10,000 galaxies. Of the
>1000 large galaxies, only 15% are spirals. The majority are
ellipticals (and some S0’s).
The Coma Cluster
The Coma Cluster
In 1933 Fritz Zwicky measured the doppler shift
velocities of galaxies in the Coma Cluster. He measured the velocity dispersion (average velocity)
of cluster galaxies to be σ=977 km/s.
This gives a Virial Mass of M = 5σ2 R /G = 3.3 x 1015 M⊙.
Fritz Zwicky
1898-1974
Comparing this to all the luminosity from the galaxies in the cluster, Ltot
= 5 x 1012 L⊙ gives a mass-to-light ratio of M/L ≈ 660 M⊙/L⊙.
The Luminous matter in Coma accounts for 1/660 = 0.1% of the mass !
Zwicky argued in 1933 that Dark Matter must dominate clusters.
Turns out it does, but at the time no one believed Zwicky..... The Coma Cluster
A portion of Zwicky’s “Missing Mass” was discovered in the X-rays. In 1977 the High
Energy Astronomical Observatory (HEAO) satellites indicated that clusters contain an
intracluster medium (ICM). This includes a hot intracluster gas that is so hot it
emits in the X-rays (by thermal Bremsstrahlung radiation).
For Bremsstrahlung radiation, the Luminosity density
(energy per second per unit volume) is For Coma, consider that the radius of the gas is R=1.5 Mpc (one-half the actual radius), the Xray spectrum is best-fit with a gas of temperature T=8.8 x 107 K.
The total Luminosity is = 5 x 1037 W from observations.
The value of the number density of free electrons, ne, is Recall that giant molecular clouds have nH ~ 108 to 109 m-3. The Coma Cluster
A portion of Zwicky’s “Missing Mass” was discovered in the X-rays. In 1977 the High
Energy Astronomical Observatory (HEAO) satellites indicated that clusters contain an
intracluster medium (ICM). This includes a hot intracluster gas that is so hot it
emits in the X-rays (by thermal Bremsstrahlung radiation).
Using ne = 300 m-3 and R=1.5 Mpc, the total mass for ionized hydrogen (there is one free
proton for every free electron in the gas) we get the total mass of the X-ray emitting gas:
This is 10x higher than the Mass of the galaxies in the cluster (Mgalaxies ~ 1013 M⊙,
for L=5 x 1012 L⊙ and M/L ~ 3 M⊙/L⊙).
And, this is still much, much less than the mass from the dynamical measurement,
Mtotal = Mgas + Mgalaxies + M??? = 3.3 x 1015 M⊙.
>90% of the mass of the cluster is in the form of some kind of dark matter.
Superclusters
As the name suggests, superclusters are seen in the distribution of clustering of galaxies
and clustering of clusters. These are structures on scales of ~100 Mpc.
The Milky Way sits at one end of the Local Supercluster, which is ~50 Mpc long.
Distribution of 2175 galaxies out
to roughly 50 Mpc from Tully,
1982, ApJ, 257, 389. The Milky Way is at the center
of the circle and runs in the
triangular regions with no
galaxies (can’t see them in the
plane of the galaxy)
Superclusters
The whole Local Group, the Virgo Cluster, and thousands of other galaxies are
apparently headed toward some large concentration of mass on the other side of our
galaxy - The Great Attractor.
Distribution of 2175 galaxies out
to roughly 50 Mpc from Tully,
1982, ApJ, 257, 389. The Milky Way is at the center
of the circle and runs in the
triangular regions with no
galaxies (can’t see them in the
plane of the galaxy)
Dressler & Faber, 1990, 354, L45
Redshift Surveys
Many galaxy surveys measuring the angular position (RA and Decl) and redshift (the
distance) have been carried out. These show strong clustering in all dimensions. The
galaxy distribution is far from random.
Angular coordinate on sky (in
hours, there are 24 hrs in a
complete circle)
This “slice” is 6 degrees
thick (in the page), from
26.50 < δ < 32.50.
v = c z ( = H0 d)
Earth
d = 70 Mpc for v=5000 km/s
Redshift Surveys
Modern survey:
Sloan Digital Sky
Survey, probes
out to nearly
1000 Mpc.
800 Mpc
400 Mpc
Earth
This spans almost the
“whole sky”, except for
where the Galaxy blocks
our view.... Courtesy of Michael Blanton.
Summary: Evidence for Dark Matter
1.  Rotation Curves in Galaxies: The rotation velocities of galaxies at
large radii are constant. This is not what one would expect if the
luminous matter (stars and gas) were all the matter. One can work
out what the Dark Matter “Halo” looks like from this.
2. Velocities in Clusters of Galaxies: Average velocities of cluster
galaxies is ~1000 km/s, which implies very large masses, ~1015 solar
masses, which comes from the Virial Theorem. The gas and stars
add up to only 10% of this, so 90% of matter is “Dark” in clusters.
3.  Cluster and galaxy masses from gravitational lensing. This is
from General Relativity, which predicts that as the light from
distant objects passes near massive objects, it will get bent. The
observed phenomenon is exactly as General Relativity predicts, but
it implies that galaxies and clusters have dark matter that accounts
for ~90% of the mass.
The Extragalactic Distance Scale
One of the important relations in Astronomy. It lets us Measure the distance to
distance objects. Each rung on the ladder is calibrated using lower-rung calibrations.
Distance
Objects
Technique
1-100 AU = 5-500 x 10-6 pc
Sun, Solar System
Radar, timing orbits, geometry
1-100 pc
Nearby stars
Earth-based Parallax
1000 pc
Galactic stars
Space-based Parallax
(Hipparcos Satellite)
10,000 pc
Cepheid and other Variable
stars
Luminosity-Period relation
10 -100 kpc
Globular clusters
Stellar Main sequence and
post-main sequence fitting
0.1 - 1 Mpc
Cepheids (Earth
Measurements)
Luminosity-Period relation
10-50 Mpc
Cepheids (HST Measurements)
Luminosity-Period relation
>50 Mpc
Spiral Galaxies
Tully-Fisher relation, Faber
Jackson relation
1 - 1000 Mpc
Supernovae Type Ia
Light Curve Measurements
The Extragalactic Distance Scale
The Extragalactic Distance Scale
In 1925 Edwin Hubble discovered
Cepheid Variables in M31
(Andromeda “Nebula”). Hubble
continued his search for
Cepheids, and determined the
distances to 18 galaxies. At the same time, V. M. Slipher at
Lowell Observatory looked at
velocity shifts of extragalactic
“nebulae” using the Calcium “HK”
lines (Ca II, like in the Sun). Distance
(Mpc)
24.3
v=1210 km s-1
17.1
v=15,000 km s-1
214
v=21,600 km s-1
557
v=39,300 km s-1
Vesto Slipher
(1875-1969)
871
v=61,200 km s-1
The Extragalactic Distance Scale
Radial velocities of nebulae measured by Slipher:
NGC
221
224
598
1023
1068
3031
3115
3627
4565
4594
4736
4826
5194
5866
7331
Vesto Slipher
(1875-1969)
velocity (km/sec)
-300
-300
~zero
+200 roughly
+1100
+ small
+400 roughly
+500
+1000
+1100
+200 roughly
+ small
+ small
+600
+300 roughly
The Extragalactic Distance Scale
We can compare these velocities with a three other velocities:
orbital speed of the Earth around the Sun ~ 30 km/sec
orbital speed of Sun around center of Galaxy ~ 220 km/sec
Escape speed from our Galaxy is
(Vesc)2 = 2 G MGal / rGal
With a mass of the Galaxy of 2.5 x 1012 solar masses and a radius of
25 kpc, the escape speed is about 930 km/sec.
Vesto Slipher
(1875-1969)
The Extragalactic Distance Scale
In 1929, Hubble showed that the velocities and distances are linearly correlated,
and satisfy
v = H0 d
where v is the recessional velocity (km/s) and d is the distance (Mpc). H0 is a
constant, “Hubble’s Constant” and has units of km s-1 Mpc-1.
The Extragalactic Distance Scale
In 1929, Hubble showed that the velocities and distances are linearly correlated,
and satisfy
v = H0 d
where v is the recessional velocity (km/s) and d is the distance (Mpc). H0 is a
constant, “Hubble’s Constant” and has units of km s-1 Mpc-1.
The Extragalactic Distance Scale
The Extragalactic Distance Scale
Size of Grid x 1.01
The Extragalactic Distance Scale
Size of Grid x 1.02
The Extragalactic Distance Scale
Size of Grid x 1.03
The Extragalactic Distance Scale
Points the farthest away, also
have moved the furthest.
Size of Grid x 1.04
The Extragalactic Distance Scale
The Extragalactic Distance Scale
Size of Grid x 1.01
The Extragalactic Distance Scale
Size of Grid x 1.02
The Extragalactic Distance Scale
Size of Grid x 1.03
The Extragalactic Distance Scale
Size of Grid x 1.05
The Extragalactic Distance Scale
Size of Grid x 1.07
The Extragalactic Distance Scale
Size of Grid x 1.10
The Extragalactic Distance Scale
Hubble initially derived a value of H0 = 500 km/s/Mpc. He could only see Cepheids out to a few Mpc. For more distant galaxies, we
assumed that the brightest star he could see was the same luminosity for each
galaxy. In most cases the brightest star he could see was instead a Globular
Cluster (containing lots and lots of stars). He perceived stars being ~100x more luminous intrinsically, thus he thought
their distances must be (100)0.5 ~ 10x nearer than they are.
Hubble relation (also called “Hubble Flow”) gives us a way to measure the
distance of an object knowing only its redshift:
v = H0 d
or
d = cz / H0 for z << 1.
For z < 2, the approximate relation holds:
The Extragalactic Distance Scale
Note that H0 has units of inverse time ! (km/s/Mpc).
Rewriting H0 = 500 km/s/Mpc = 1.6 x 10-17 s-1.
To estimate how long all galaxies were in the same place in space and time,
calculate the time it would take for a galaxy with a velocity v to have traveled a
distance d: t = d / v = d / (H0 d) = H0-1 = (1.6 x 10-17)-1 s = 1.96 Gyr.
This gave an age to the Universe. How does this compare to other ages in this class ? At the same time, physicists were solving Einstein’s theory of General Relativity
and coming up with an expanding Universe theory.
In 1917, Willem de Sitter (1872-1935) concluded the Universe is expanded (or
contracting).
Einstein himself solved his equations and introduced a “Cosmological Constant”
to keep the Universe static. In 1930, when presented with Hubble’s data we
recanted. He called this the “biggest blunder of his career”.
Supernovae as Distance Indicators
Supernovae (or all types) can be used as distance indicators. One measures the
angular velocity of the expanding photosphere (explosion) at two different
times: ω = Δθ/Δt. Then one measures the velocity from the doppler shift of the “explosion”, v.
Combining them, you use the angular distance of the expanding photosphere to
get the physical distance to the supernova.
d = v / ω
This only works for nearby supernovae. Alternatively, you can assume the
expanding photosphere is a blackbody, and measure its Temperature. This gives:
L = 4πR(t)2 σT4 Thus, you can measure R = v t. So tracking the Temperature, T, and the doppler
shift of the ejecta and and t gives you R, which gives you L. Once you have L
you have d by: d2 = L / 4π F
where F is the flux.
The Extragalactic Distance Scale
One of the important relations in Astronomy. It lets us Measure the distance to
distance objects. Each rung on the ladder is calibrated using lower-rung calibrations.
Distance
Objects
Technique
1-100 AU = 5-500 x 10-6 pc
Sun, Solar System
Radar, timing orbits, geometry
1-100 pc
Nearby stars
Earth-based Parallax
1000 pc
Galactic stars
Space-based Parallax
(Hipparcos Satellite)
10,000 pc
Cepheid and other Variable
stars
Luminosity-Period relation
10 -100 kpc
Globular clusters
Stellar Main sequence and
post-main sequence fitting
0.1 - 1 Mpc
Cepheids (Earth
Measurements)
Luminosity-Period relation
10-50 Mpc
Cepheids (HST Measurements)
Luminosity-Period relation
>50 Mpc
Spiral Galaxies
Tully-Fisher relation, Faber
Jackson relation
1 - 1000 Mpc
Supernovae Type Ia
Light Curve Measurements
Supernovae as Distance Indicators
Supernovae Type Ia (SN Ia) are “special”. They are probably white dwarf stars
with a giant companion that is providing material to the white dwarf. Once the
WD accretes a mass of 1.4 M⊙, it explodes as it becomes a neutron star.
Because SN Ia all have a common progenitor, they likely have similar properties.
They are “standard candles”.
Empirically they all have a peak maximum light of MB=MV=-19.3 +/- 0.03. All
you do is measure the apparent magnitude and then you get the Distance
Modulus and thus the distance !
m - M = DM = 5 log (d / 10 pc)
In practice, there is a correlation between the maximum brightness (MB) and
the rate of decline of its light curve. This is an empirical relation, and has been
calibrated.
Astronomers watch the rate of decline at several wavelengths. This is the
multicolor light curve shape (MLCS) method. Supernovae as Distance Indicators
The correlation between luminosity
and decay time can be calibrated.
One quantifies this as the
time it for the flux to
drop by a factor of 2.
Riess et al. 1995, ApJL, 438, L17
Time since “peak”
Supernovae as Distance Indicators
Supernovae are seen in very distant galaxies, > 1000 Mpc distant
The Extragalactic Distance Scale
Many different distance indicators can be tested against each other. Gives averages.
For example, as of 1992 (Jacoby et al. 1992, PASP, 104, 599) had as the distance to the
Virgo Cluster of galaxies:
Method
Distance (Mpc)
Range (Mpc)
Cepheids
15-25
29
Tully Fisher
15.8 +/- 1.5
> 100
Faber-Jackson
16.8 +/- 2.4
> 100
Type Ia Supernovae
19.4 +/- 5.0
>1000
Distance Modulus
= 5 log( d / 10pc)
The fact that ΩΛ is
so much greater
than ΩM implies
expansion of the
Universe is
accelerating
Difference between
data and the best-fit
model
Riess et al. 1998
How do Galaxies Form ? Remember that galaxies with high redshifts are very far away:
cz ~ v = H0 d
(for z << 1)
z = (λobs - λrest) / λrest
Because it takes up to billions of years for the light from distant galaxies to
reach us. We see them not as they are, but as they billions of years ago.
We can study high-redshift galaxies to learn about galaxy evolution.
HST images of ... galaxies from 6-8 Gyr ago.
galaxies from 10-11 Gyr ago.
from Papovich et al. 2005, ApJ, 631, 101