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Edwin Hubble’s next project. Having established in 1925 that galaxies were not in the Milky Way, Hubble used the Mt Wilson telescope to obtain spectra of galaxies. When he analyzed the spectra he found that, with the exception of the galaxies in our local group, all other galaxies where moving away from us. He found this using the Doppler shift of absorption lines in the galaxy spectra. Not only were all the galaxies found to be moving away, the farther away a galaxy was, the faster it was moving away.

In order to establish the relation between distance and recessional velocity, Hubble needed to determine the distance to the galaxies. He did this by assuming all the galaxies he observed were of similar size, and figured out their relative distance from their apparent size. He had already calculated the actual distance to several nearby galaxies, so this allowed him to find the true distance to the galaxies that were farther away. Here is a plot from his 1929 publication.

Recessional velocity verses Distance.

Modern Day Hubble plots

What is the equation for a straight line? 1.y = ax 2 2.y = 1/x + b 3.y = mx + b

So a straight line has the equation of y = mx + b In the Hubble plot the y-axis is velocity (v) and the x-axis is distance (d) So we can write the equation as v = md + b What are m and b?

1.The slope and y- intercept 2.The slope and the rise over run 3.The x-intercept and the y-intercept

Modern Day Hubble plots

The Hubble Constant – The slope of the line The Hubble constant is a very fundamental quantity, which tells us the age of the universe. Today we see that the universe is expanding, and it is growing larger every day. This means that the distance between galaxies are growing in size. What would happen if we could run the clock in reverse? Move backward in time. The galaxies would get closer together, with the most distant galaxies moving toward us at the greatest speed. The result is that all galaxies would arrive at the same point, at the same time.

The equation of a straight line for the Hubble plot looks like this, with b = 0 v = H o d velocity = H o times distance What does our normal velocity equation say? v = d/t velocity = distance divided by time Or v = (1/t)d compared to v = (H o )d

So H o tells us the time it takes for all the galaxies in the universe to collapse to the same point. This is the age of the universe. H o = 1/t age Notice: H o has units of km/s/Mpc Or t age = 1/H o Today the best value is H o = 71 km/s/Mpc We can use this value to compute the age of the universe. We first need consistent distance units. 1 Mpc = 3.1 x km

So H o = (71km/s/Mpc)(1 Mpc/3.1 x km) H o = 2.3 x (1/seconds) t age = 1/Ho = 1/2.3 x (1/seconds) t age = 4.37 x seconds There are 3.14 x 10 7 seconds in a year. So dividing we get: t age = 13.7 x 10 9 years t age = 13.7 billion years

The age of 13.7 billion years is consistent with the age of the oldest known stars, which are found to be between 12 and 14 billion years old. Note that star age is based off of stellar physics and has nothing to do, whatsoever with the calculation of the age of the universe using the Hubble constant.

Modern Day Hubble plots

For our local portion of the universe the Hubble relation is linear. That doesn’t have to be the case for the entire universe. Space-time for the universe can appear very flat over small distances but actually be very curved over extremely large distances. Let’s think carefully about different possible Hubble plots.

Here is Case #1 velocity distance

What would this Hubble plot tell you? 1.The universe is contracting 2.The universe is expanding 3.The universe is static

Universe is static, not expanding or contracting velocity distance #1#2

The rate of expansion is the slope of the line. What would a linear slope, all the way back to the greatest distances tell us. velocity distance 13.7 Glyrs today Early universe

What would a linear relation back to the Big Bang tell us about the universe 1.The expansion rate is zero 2.The expansion rate is constant 3.The expansion rate is increasing

The universe (Space-time) is expanding, but the mass in the universe is still going to be attracted from the gravity of all the mass acting on each other.

Think carefully here. Which line would represent a universe that has mass in it? velocity distance 13.7 Glyrs a b c

Which universe has mass in it? 1.a 2.b 3.c

Think carefully here. Which line would represent a universe that has mass in it? velocity distance 13.7 Glyrs a b c

For a universe with mass only effected by gravity we expect a curve like “a” “a” shows a universe that was expanding quickly and has slowed as time goes by due to the presence of gravity from massive objects. The more mass that was present in the early universe, the more deceleration we expect. And the curve “a” becomes steeper. Something like this.

We know that there is mass in the universe, so if gravity is the only thing affecting the expansion… velocity distance 13.7 Glyrs High density Low density Nothing should be found below the solid black line

The straight line represents a mass-less universe with no gravity. In other words, the expansion began and now the universe is coasting. Growing in size but at a constant rate. When the data falls below the sloping straight line it means that the universe was moving more slowly in the past and the expansion is speeding up. How can this be?

What is required for the expansion to speed up as time goes by? 1.Dark matter 2.A universal repulsive force 3.Less than zero matter in the universe

Gravity is only attractive. It can only work to help slow the expansion of the universe. If the expansion is speeding up, then there has to be a repulsive force that is acting to force the expansion to grow more rapidly Gravity can’t do this. This repulsive force has been named “Dark Energy” It fits into Einstein’s equations just like his old cosmological constant. But this isn’t keeping the universe static. It is forcing it to grow more rapidly.

Using relativity we can model what will happen in the future as well.

Past Future

Our location in the Universe A distant galaxy or quasar Today

Quiz 11 Explain why we see many high luminosity quasars at extremely large distances but none in our local area of the universe. Consider these points. What is a quasar? Where does the luminosity come from? When is the quasar? What is happening at this time?