Announcements

Announcements

• Third exam is Friday, October 29

• Review on Wednesday, October 27

• Please hand in or e-mail questions for the review

Cosmic Distances

• How to measure distances

• Primary distance indicators

• Secondary and tertiary distance indicators

• Recession of galaxies

• Expansion of the Universe

As the Earth moves from one side of the Sun to the other, a nearby star will seem to change its position relative to the distant background stars.

d = 1 / pd = distance to nearby star in parsecs

p = parallax angle of that star in arcseconds

Stellar Parallax

Stellar Parallax• Most accurate parallax measurements are from the European Space Agency’s Hipparcos mission.

• Hipparcos could measure parallax as small as 0.001 arcseconds or distances as large as 1000 pc.

• How to find distance to objects farther than 1000 pc?

Flux and Luminosity

• Flux decreases as we get farther from the star – like 1/distance2

• Mathematically, if we have two stars A and B

2

A

B

B

A

B

A

Distance

Distance

Luminosity

Luminosity

Flux

Flux

Standard Candles

2

A

B

B

A

B

A

Distance

Distance

Luminosity

Luminosity

Flux

Flux

BA LuminosityLuminosity

2

A

B

B

A

Distance

Distance

Flux

Flux

B

A

A

B

Flux

Flux

Distance

Distance

Standard Candles

B

A

A

B

Flux

Flux

Distance

Distance

1. Measure the distance to star A to be 200 pc.

2. Measure the flux of star A.

3. Measure the flux of star B with same spectral type and luminosity class to be lower by a factor of 1600

4. Find the distance to star B

1600pc 200

DistanceB

pc 8000DistanceB

Distances to galaxies

Standard candles, such as Cepheid variables, the most luminous supergiants, globular clusters, H II regions, and supernovae in a galaxy, are used in estimating intergalactic distances.

• Each stage in the ladder overlaps the previous and next• Cepheid distances are critical• Tully-Fisher, fundamental plane apply to whole galaxies• Supernova are now the best estimators at large distances

The Distance Ladder

Distances and velocities of galaxies

• If you measure the distances to a large set of galaxies and also measure the speed of the galaxies using the redshift, what do you find?

Hubble expansion v = H0d

Expansion of the Universe

Expansion of the Universe• Blow up the balloon to about a 3 inch diameter. Twist

the neck and hold it closed so that no air escapes, but do NOT make a knot because you will need to blow it up some more. Make SIX dots on its surface to represent galaxies and label them A-F.

• Measure and record the distances from cluster A to each of the other 5 clusters.

• Measure and record the distances from cluster D to each of the other 5 clusters.

• Blow up the balloon up more, to a diameter of about 6 inches. Measure the distances between the same clusters again and record them.

Expansion of the Universe

• Are all the other clusters moving away from cluster A?

• Are all the other clusters moving away from cluster D?

• Is there a cluster that could be considered to be at the center of the universe as represented by the surface of the balloon?