Distances to Galaxies and Expansion of Universe

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Distances to Galaxies and Expansion of Universe
Galactic Distances Main sequence
fitting Extragalactic Distance Ladder Hubble
Law Peculiar velocities Expansion of the
Universe No center, no edge Scale factor R(t) and
redshift z Spectra give redshifts and
distances Age of universe from Hubble constant
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Distances to Nearby Galaxies
This called the distance ladder. We use different
methods as we move out. The near by methods
calibrate the farther ones. If the near ones are
wrong, so are the farther ones. If AU is wrong,
so are all other larger distances which depend on
the AU.
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Main Sequence Fitting gives distance to Star
Clusters
All stars in a cluster of stars are at about the
same distance, d. Plot HR diagram, using
brightness vertically. We find d by trial and
error. We slide the graph up and down to find d.
The correct d will convert the b into L which
agree with the L of stars in another cluster of
known D and L.
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Distances to Intermediate Distance Galaxies
We use Cepheids (notes 18) to find distances to
near by Galaxies, and these galaxies to calibrate
distance methods that can give distances to
farther galaxies, including brightest star
(hypergiants), then H II regions (star
formation) largest spiral in cluster
brightest galaxy in cluster. In each case we
assume that the brightest or largest in a near by
galaxy or cluster is intrinsically similar that
in a far galaxy or cluster. The Tully-Fisher
relation is a different type of distance method.
We have found that the luminosity of a spiral
galaxy in red or infrared correlates with the
width of its 21-cm emission line. The line width
depends on the rotation rate, hence velocity,
mass and luminosity, assuming that the M/L is
constant. We can then use the correlation to
convert a measurement of a 21cm line width (in
km/s) to Luminosity. We then compare with
brightness to get distance.
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Edwin Hubble 1924 Universe is expanding
Plot velocity of several galaxies (from spectra)
against their distances the resulting Hubble
Diagram shows a strong correlation. The only
reasonable interpretation universe is expanding,
at rate given by the Hubble Law vHd where
HHubbles Constant.
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Local structure complicates the Hubble flow
Galaxies pull each other. All galaxies have some
motion relative to their local space peculiar
motions and peculiar velocities. Clusters pull
strongly on their neighbors.
This figure shows the density of matter in
the local Supercluster. The peaks show the
locations of massive galaxies.
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Galaxy Peculiar Motions
The small arrows in the figure show the peculiar
motions of near by galaxies. The are moving into
the regions with the highest density of galaxies.
This figures shows a computation of the motions
that we expect to see measurements are not this
accurate.
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Can Ignore Peculiar Velocity over large Distances
Galaxies have two types of velocities 1.The
Hubble flow from the expansion of space vHd 2.
Peculiar velocities, which are typically few
hundred km/s. For nearby galaxies, d is a few
Mpc, and the Hubble flow is similar in size to
the peculiar velocities. Hence a few local
galaxies, such as M31 (Andromeda) are
approaching us. Over large distances, the Hubble
flow velocities keep increasing and dominate.
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Cepheids are the key link
One primary justification for the Hubble Space
Telescope was to
resolve Cepheids in galaxies far enough away to
measure the Hubble flow properly, and thus obtain
the Hubble constant and age of the Universe.
Along with other methods, this gives about 14
billion years.
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Hubble Diagram to Larger Distances
Modern measurements, using many methods,
especially supernovae out to huge distances, show
that the Hubble law is accurate.
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Hubble Constant
Various ways of measuring galaxy distances all
show that Ho 72 (km/s)/Mpc
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Hubble Expansion not a conventional Explosion
In an explosion, the stuff that is moving faster
will have gotten further, so you would see what
Hubble saw. Despite the term Big Bang to
describe the expanding Universe, that is NOT what
is going on! However, it is an ok analogy to help
understand Hubble Law.
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Space is expanding in all 4 dimensions
The apparent increase of velocity with distance
is due to the increase in the amount of space.
The raisin bread shows how each galaxy (raisin)
sees all others moving away from it. All the
distances between the galaxies are twice as large
on the right.
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There is no spatial center of expansion
The view is the same from all galaxies. They all
see the others moving away form them, at speeds
given by the Hubble law.
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The Universe has no center or edges
The loaf model misleads you to think that the
universe must have a center and edge. The loaf
clearly has both a center and an edge, but the
universe has no center and no edge!
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Finite and without edges
The universe has no edge, even if it is finite
(which it appears not to be)! A finite universe
is one in which you could go to every place in a
finite amount of time.
A sheet if paper is finite, with edges. But there
are other 2 dimensional surfaces that do not have
edges, like the 2 dimensional surface of the loaf
(not its 3 dimensional volume pretend that the
volume does not exist just consider the
surface). It has a finite area, and it has no
edge, again in 2 dimensions. You can travel all
over the surface, and continue as long as you
like in any direction. Eventually you will cover
the whole surface. There is no edge, just like
the surface of the Earth has no edge. The surface
of a donut is another example finite and
without edges. The universe is a 4 (or more)
dimensional extension of this no center and no
edge, even if finite!
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Age of the Universe from the Hubble Constant
We can get the approximate age of the universe by
assuming that the expansion rate (H) has remained
constant. We can then draw straight lines on the
graph below. They meet when universe began.
Size of Universe
Age of Universe Time from Big Bang
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Finite Universe is always Finite
The raisin bread makes you think universe began
at a point. This is only possible (not required)
if it is finite in volume. In a finite universe
you could visit every galaxy in a finite time.
But there is still no center, since the whole
universe began in that point. Reminiscent of
black holes and electrons also point objects.
Size of Universe
Age of Universe Time from Big Bang
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Infinite Universe is always Infinite
If the Universe is infinite, at any time, then it
is always infinite, including when it formed. We
do not know of any physical processes that turn
finite spaces into infinite ones, except in
infinite time. We can think of mathematical
structures that are infinite, such as lines,
spaces, series, etc.. The positive whole
numbers, 1,2,3,4are an infinite series.
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An Infinite Universe can change size
The expansion of an infinite universe happens
when each part, each cubic Mpc, expands.
Imagine a rubber band, with knots. If you stretch
it, it expands. This is possible even if it is
infinitely long stretch each part.
I can change the size of an infinite line of
numbers 1 2 3 4 5 6 7 . adding more
space between integers 1.1, 1.01, 1.001,
1.0001 2.1, 2.01, 3.1 4.1 5 6 7
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Scale Factor R(t) measures size of universe
Choose any two galaxies that are well separated,
so we can ignore peculiar velocities. Define
their separation as R(t), called the scale factor
of the universe. R(t) measures the expansion of
the universe.
Size of Universe, R(t)
t Age of Universe Time from Big Bang
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Scale Factor R(t) defines Redshift
We define redshift, z as the ratio of R(t) in the
past, to R(tnow) 1z R(now)/R(t)
Now
t1
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Redshift and Size of Universe
Light was emitted at time t1 when the universe
was smaller by a factor of R(t1)/R(now). That
light has a redshift 1z R(now)/R(t1)
R(t)
R(now)
R(t1)
Now
t1
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There is no spatial center of expansion
General Relativity tells us that the wavelength
of light expands as does the space. 1z
R(now)/R(t) wavelength(now)/wavelength(t).
When z ltlt1, z Dl/l v/c. Since vHd, z Hd/c
and z is proportional to distance. We think of z
as a distance scale that get stretched as large
distances. For each unit of distance, need more
and more z.
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Two ways of considering the motion
If peculiar velocities are zero, galaxies stay
fixed on the co-moving grid the boxes expand
along with the space, as below. Moving relative
to each other, but not to their local space.
co-moving grid expands with space
There is an error in the figures here!
A grid with constant proper size keeps the same
size as universe expands. Hence it shows a lower
density of gas and galaxies over time.
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Space expands Bound objects do not
The separation between galaxies increases because
the amount of space between them increases. The
separation or size of anything bound by gravity
or some other force, does not increase. eg
atoms, rocks, planets, planetary systems, stars,
galaxies. The gas between galaxies, the
intergalactic medium, is not bound and expands to
fit the new space. The density of this gas, atoms
per cm3, decreases with time, as (1z)3.
Galaxies stay same size and space between them
expands
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Spectra give Redshifts
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Galaxy spectra readily give redshifts
The Hubble law converts redshifts, from spectra,
into distances. Large z corresponds to large
distance.
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We can not get distances from images
This ultra long exposure shows thousands of
galaxies. Almost zero stars in such a small area
on the sky. From the image we can not tell which
are near and faint, and which distant and
luminous.
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Galaxy redshifts
We have obtained the spectra of each galaxy,
mostly with our Keck telescopes, to find the
redshifts show here.
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The Hubble Constant and the Age of the Universe
If you plot the scale of the Universe vs time,
the Hubble constant is the slope of the line now.
If it were precisely constant, then the age of
the Universe to 1/H since Hv/d(d/t)/dto,
and distance dvt or vd/t for constant v. If you
know how fast we are expanding, you can work out
how long you need to get to present
separations. Since expansion rate (H) was larger
in past, the age of universe is less.
to lt 1/H. Making this adjustment (red, not green
curve, ignore x axis numbers) we find Universe
is 13.7 0.2 Byr old where the means 68 chance
age is between 13.5 and 13.9 Byr The oldest
globular cluster have about the same ages.
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An example to Illustrate the Ho Age connection
Ignore peculiar velocities the Hubble law alone
then gives galaxy velocities vHd. Assume Ho70
(km/s)/Mpc Galaxy A is 100Mpc away. Its velocity
is v70x1007000 km/s. Galaxy B is 200Mpc away,
v200 Mpc x 70 (km/s)/Mpc 14,000 km/s. Assume
that all galaxies have had constant speeds since
the Universe began, to13.7Byr ago 4.3 x 1017
seconds. Galaxy A has traveled dvt 7000 kms/
x 4.3 x 1017s 3.0x1021 km 100 Mpc, where 1Mpc
3x1019 km. Galaxy B has traveled 14,000 km/s x
4.3x1017s 200 Mpc. The galaxies reached their
distances from us by traveling at nearly constant
speeds for to Galaxies that formed in regions
that were traveling at a high speed are now far
from us.
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Hubble Question 1
How can we measure the age of the universe?
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Hubble Answer 1
The age can be measured many ways including
older than oldest (population II) star the
Hubble constant. The age is lt 1/Ho The
correction depends on the amount of slowing.
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Hubble Question 2
How many measurement do you need to get the age
of the universe, assuming the expansion rate is
constant?
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Hubble Answer 2
Two. You need the distance and velocity of any
far away galaxy. H0v/d