University Studies

Portland State University.

Day 3 - Hubble Expansion

All text in black is from other sources, yellow-green is my commentary.

This early diagram prepared by E. Hubble and M. Humason shows the relationship between galaxy velocity and distance. The slope of the relation has since been altered as data for more galaxies have been added and the measurement of distances has improved, but the general appearance of this figure is the same today.

A modern version of the Hubble law. Often, apparent magnitude is used on the horizontal axis instead of distance, because the two quantities are related, particularly if the diagram is limited to galaxies of the same type, as this one is. The small rectangle at the lower left indicates the extent of the relationship as Hubble first discovered it; today many more, much dimmer galaxies have been included. The most rapid galaxies are not actually traveling at the speed of light as this diagram implies, because relativistic corrections have not been applied (see the discussion in the next chapter).

So it appears that there is a linear relationship between how far a galaxy is from us and how fast it is moving—the faster a galaxy is moving away from us, the farther it has moved. This is just like driving a car. If you drive South at 60 Mph for an hour, can you tell me where you will end up? If you drive South at 120 Mph for an hour, can you tell me where you will end up (if not in jail)? How do we generalize what you already know how to do?

D = T V

This linear relationship between how far a car or a galaxy is from us and how fast it is moving, can be inverted to find the time of travel. The time it took your car to go 60 miles from here at 60 Mph was an hour.

A recessional-velocity calculation worksheet may be found at

http://www.physics.csulb.edu/hubrdshi.html

if you want your students to find {Plate scale is (5015-3888)Å/76.5 mm = 14.7 Å/mm.

Virgo: v = 11.7mm/10 × 14.7 Å/mm /3951Å c = 17.2 Å /3951Å c= .00435 c = .00435× 3× 10⁵ km/s = 1,310 km/s

Corona Borealis: v = 21mm × 14.7 Å/mm /3951Å c = 309 Å /3951Å c= 0.0783 c = 0.0783× 3× 10⁵ km/s = 23,500 km/s

Discussion groups on Hubble Time 30 min. Each group does the entire sequence.

1. The time it took M100 to go 56 million ly away from the Milky Way at 1210 km/s was (Note that if you rewrite the distance "ly" in the calculationally mnemonic form: 1 ly = 1 c× yr = 3×10⁵ km/s × 1 yr, this calculation is made much easier) {56 million cyr × 3× 10⁵ km/s yr/cyr /(1210 km/s) = 13.88 Billion yr.} {56 million cyr × 3× 10⁵ km/s yr/cyr /(1310 km/s) = 12.9 Billion yr.} {56 million cyr /(.00435 c) = 12.9 Billion yr.}

2. The time it took the Corona Borealis galaxy to go 945 million light-years away from the Milky Way at 21,600 km/s was {945 million cyr × 3× 10⁵ km/s yr/cyr /(21,600 km/s) = 13.13 Billion yr.} {945 million cyr × 3× 10⁵ km/s yr/cyr /(23,500 km/s) = 12.1 Billion yr.} {945 million cyr /(0.0783 c) = 12.1 Billion yr.}

3. The time it took the Hydra galaxy to go 2.67 Billion light-years away from the Milky Way at 61,200 km/s was {2.67 Billion cyr × 3× 10⁵ km/s yr/cyr /(61,200 km/s) = 13.10 Billion yr.}

4. What if I gave you another 10 galaxies and asked you to find the travel time to each distance. What would you guess would be the result? What if you got this answer for another 1000 galaxies; for a million galaxies?

5. What would our neighborhood have been like 13 Billion years ago?

We call this time t_o the Hubble Time, and its inverse is the Hubble constant H_o. It is actually an upper limit on the age of the universe because we believe that this quantity, though constant for all galaxies we see now, was not always constant in time. 10 Billion years ago the Hubble constant would have been different, a different constant for all galaxies then, if the expansion has been slowing down as the galaxies exert their mutual attraction.

If a galaxy is moving at 146,000 km/s, how far should it be according to this graph? (2000 Mpc)

Can also use an equation.

Where H_o = 73 km/s per Mpc. Check:

V = 73 km/s per Mpc × 1000 Mpc= 73,000 km/s

Suppose D is 2000 Mpc, what would we expect V to be? 146,000 km/s

see also http://oposite.stsci.edu/pubinfo/background-text/hnought.txt

No. 94-23 For release: Friday, September 30, 1994

Contact: Julie Corless or James Cornell (617) 495-7461

A Cosmic "Custom Yardstick" Yields Age of 14 Billion Years

MEASUREMENTS OF DISTANT SUPERNOVAE PRODUCES NEW AGE FOR UNIVERSE

CAMBRIDGE, MA--A new cosmic distance scale derived from measurements of expanding supernova atmospheres suggests that the Universe may be approximately 14 billion years old, considerably younger than the 20-billion-year age preferred by many theorists but ancient enough to have allowed evolution of the oldest observed stars.

Based on observations of the expanding photospheres of five Type II supernovae made at the Cerro Tololo Inter-American Observatory (CTIO) in Chile, and 13 more from earlier work, [18] an international collaborative effort between two groups of astronomers located at Harvard and in Chile has established a new value for the Hubble Constant, or expansion rate of the universe, at 73 (+/-6) kilometers per second per Megaparsec, a rate that translates into a maximum age of 14 billion years.

Robert Kirshner of the Harvard-Smithsonian Center of Astrophysics (CfA), leader of the group at Harvard, describes the distance measurements as "completely independent of, but complementary to, other attempts to determine the Hubble Constant, such as using the the calibration of Cepheids in nearby galaxies." (The Cepheids are variable stars with a well-defined period-luminosity relationship that allows measurement of their absolute magnitudes to yield accurate distances to nearby galaxies.)

These methods require a step-by-step, ladder-like, progression to increasing depths of the universe, first by establishing a distance to an object, then using that measurement as a rung to reach more distant objects, often with different calibration methods at each step. Consequently, the climb to new rungs can add considerable uncertainty to the final figure.

The measure of the Hubble Constant is made more difficult by the fact that the universe does not expand smoothly in our galaxy's local neighborhood, where gravitational forces of nearby clusters may affect the rate. Thus, it is necessary to measure distances to galaxies far beyond our own, and astronomers have sought for many years a "standard candle" by which distances to far objects could be compared with those nearer by.

The "expanding photosphere method" employed by the US-Chilean group is a direct, one-step process, based on a single and simple geometric measurement of bright objects in galaxies far beyond the local group.

Models of the temperature and density of the atmosphere of an exploding star calculated by Ronald Eastman of the Lawrence Livermore National Laboratory provide observers with the precise dimensions of the emerging blast of light. Using the color of a supernova and its brightness as measured at Earth, Eastman's models give the angular size of the exploding star. When combined with measurements of the velocity in the expanding gas, this yields a solution for the supernova's distance.

Brian Schmidt of the CfA, who made several of the observations, notes that the technique works equally well with both nearby and distant supernovae. For example, Supernova 87A in the Large Magellanic Cloud was one target of this study, but others at distances of more than 500 million light years were also measured.

"Since supernovae are a million times brighter than Cepheids," Schmidt explains, "we can see them much farther away."

All the supernovae in this survey were Type II, that is, a type with a hydrogen-rich atmosphere which explodes when the core of a massive star collapses. Such supernovae are thought to form neutron stars and pulsars. However, the size and type of the original progenitor stars is not crucial to this measurement technique, according to Schmidt, since the observed atmospheric temperature, brightness, and velocity provide an accurate size for the expanding shell.

As Kirshner describes it, the expanding photosphere method is not so much a "standard candle" as a "custom yardstick."

The chief limitation on the method is the need to make observations within the first few weeks after a supernova's explosion, that is, before the atmosphere cools, thins and and turns transparent.