hubble’s law ast 112. spectra if a light source is moving toward or away from an observer, its...

Hubble’s Law

AST 112

Spectra

• If a light source is moving toward or away from an observer, its spectral lines shift

• We can use this to measure approaching / receding velocity

Lab

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If the light source is moving away from us,the spectral lines will move toward the red.

The amount that they move toward the redis called redshift.

Motion of Galaxies

Say you take spectra of a bunch of galaxies.Near, far, in every part of the sky.

Do you expect to see a pattern in their approaching / receding velocities?

Redshift of Galaxies

• In 1912, Vesto Slipher obtained spectra of galaxies

• Distant galaxies all show redshift!

Edwin Hubble

• Hubble was invited to new 100 inch telescope on Mount Wilson

• “Regret cannot accept your invitation. Am off to the war.”

Edwin Hubble

• Measured Cepheid variables

• Measured galactic redshifts

Back to the Spectra

• Here are spectra from several galaxies. Note their distances.

Not only do distant galaxies all show redshift – there’s a pattern.

The farther away it is, the more redshift it shows.

Hubble’s Law

For distant galaxies:

The farther away a galaxy is, the faster it ismoving away from us.

This relation is linear. If a galaxy is twice asfar away as another one, it is flying away

from us twice as fast.

Velocity versus Distance

Hubble’s Law

v = H0d

H0 = 22 km/s per MLY

Hubble’s Law

For every 1 million LY of distance, a galaxy recedes an extra 12-14 miles

per second from us.

(That’s 22 km/s.)

Random Velocities vs. Hubble Expansion

• Some nearby galaxies are moving toward us– Andromeda is on a collision course

• Galaxies move around– This motion dominates over Hubble motion at

smaller distances

Random Velocities vs. Hubble Expansion

• Consider Andromeda (2.1 million LY away)

– How fast is the expansion carrying it away?

– Average velocity of group members is 61 km/s

– Will we notice the expansion velocity or the group velocity?

Random Velocities vs. Hubble Expansion

• Consider a galaxy in the Virgo Cluster (50 million LY away)

– How fast is the expansion carrying it away?

– Assume a cluster member moves at 50 km/s

– Will we notice the expansion velocity or the random velocity?

Random Velocities vs. Hubble Expansion

• Consider a galaxy in the cluster Abell 2151 (570 million LY away)

– How fast is the expansion carrying it away?

– Assume average cluster member velocity is 1 km/s

– Will we notice the expansion velocity or the random velocity?

Cosmic Distances

• Hubble’s Law is what we use to calculate distances across the Universe

– Requires large distances: • Expansion effect more measurable at large distances• Expansion overwhelms random motion at large distances

• Redshifts of spectral lines relate directly to a galaxy’s distance

Verifying Hubble’s Law

• We can compare Type 1a supernovae distances with Hubble’s Law

• Matches up well

Distances

• When we say that Andromeda is 2.1 million LY away, that’s fine. Why is there more ambiguity in dealing with galaxies that are much farther away?

NO NO NO!

• Does the stars and planets revolve around Earth?– No! We see parallax and retrograde motion.

• Astronomers thought the Sun was at the center of the Milky Way– No! All because of dust clouds.

• Is the Milky Way at the center of the Universe since everything is expanding away from it?

Expansion of the Universe

• Everything is flying away from everything else

What’s going on?

Cosmological Redshift

• Galaxies are not Doppler shifted.

• The shift does not happen because they are “flying away from us”.

• The shift happens because as the light travels toward us, space expands and stretches the light.

Cosmological Redshift

• This is in complete agreement with Einstein’s Theory of General Relativity.

• If it’s just a ball of galaxies flying apart:– We’d have to be right at the center, otherwise

there’d be asymmetry in the redshifts on different sides of the sky

– Redshifts might also decrease with distance

Cosmological Redshift: Step by Step

• Consider two galaxies, far apart. Each one emits light.

• Assume they are not moving “through space”.

• Look at the left one. Consider the light that leaves it at a given instant.

– Is it Doppler shifted?

• The galaxies were not moving through space. But the space between them expands as time goes on.

– What happens to the distance between the galaxies?

– What happens to the wavelength of the light?

Cosmological Redshift

• From the book:

– “It is better to think of space itself as expanding, carrying the galaxies along for the ride, than to think of the galaxies as projectiles flying through a static universe. The cosmological redshift of a galaxy therefore tells us how much space has expanded during the time since light from the galaxy left on its journey to us.”

The Cosmological Constant

• Einstein’s General Theory of Relativity predicts expanding or contracting space

• Einstein added a “cosmological constant” to create a static universe– Assumed that gravity might cause the Universe to contract

• He ended up thanking Hubble and deeming the cosmological constant his “greatest blunder”– It’s back!

The Observable Universe

• Two objects cannot move through space at or greater than the speed of light

• If the space between two objects expands such that the distance between them increases at greater than the speed of light…

– That’s ok!

The Observable Universe

• If the distance between us and an object is increasing at greater than the speed of light:

– Does light from that object ever reach us?

The Observable Universe

• There may be a radius beyond which all objects are receding at greater than the speed of light– Everything within this radius is known as the

observable universe

• We have no hope of observing objects outside of the observable universe