29:50 Modern Astronomy
Fall 1999
Lecture 11 ...September 17, 1999
Binary Stars and Other Topics
In the skies this week:
(1) On Thursday, (September 23) at 6:31 CDT we have the Autumnal Equinox.
Notice that the Sun (and Full Moon) rise and set due east and west.
Diagram.
(2) On Sunday, Venus reaches maximum brilliance, with apparent magnitude of -4.6
Last time I mentioned that binary stars are of primary interest because we can use them to measure stellar masses. To do this, we use the circular orbit equation, or a generalization of this equation. This equation crops up all the time in astronomy. It is a relation between V, the speed at which the star moves, M the mass of the massive star, and R, the radius of the circular orbit. The circular orbit equation is
where 
is the gravitational constant, one of the
``Fundamental Physical Constants'', which in this case tells us how strong gravity is.
We can manipulate this equation to give us the mass M if we know V and R.
Let's work an example. We observe a little (nonmassive) star orbiting a big (massive) star in a circular orbit. The radius of the orbit is 5 million kilometers. The speed of the little star in its orbit is 283 kilometers per second. What is the mass of the big fella?
We use the equation 
. Before plugging in numbers, we have to be picky and
convert the radius to meters, and the velocity of meters per second. Soooo...
283 kilometers per second = 
. And
R = 5 million kilometers 
meters.
Now we are ready to plug in numbers.
kilograms.
That is three times the mass of the Sun.
Demonstration of Cavendish experiment.
The Mass-Luminosity Relation
From observations of binaries we have masses of a few hundred stars. If one plots up the masses
and luminosities of stars on the Main Sequence, you find a remarkable result, termed
the Mass-Luminosity Relation. It is shown in Figure 16-22 of your textbook.
Transparency of Figure 16-22.
This transparency shows that the stellar luminosity goes up extremely fast as the mass increases. If we express this in terms of a formula, we write
If we look at this diagram, we see that a star with 10 times the mass of the
Sun is not merely 10 times as luminous, but instead several thousand times as luminous.
We know of stars that are as much as 25 times as massive as the Sun. This relationship
tells us that their luminosity would be 78,000 times that of the Sun.
The mass luminosity relation leads to an extremely important conclusion about stellar lifetimes. Stars use their own mass as their source of fuel. Since massive stars are using it up at a prodigious rate, they cannot last as long as lower mass stars.
Let's work out an illustration. Take two cars. A volkswagen has a gas tank of 10 gallons, and gets a mileage of 50 miles per gallon. A Cadillac ``Bon Vivant'' has a 20 gallon gas tank, but gets 4 miles to the gallon. Even though the ``Bon Vivant'' has twice as much fuel, it doesn't travel as far as the volkswagen because it if using up the fuel at a much faster rate.
The same kind of reasoning works for stars. A 10 solar mass star has ten times as much fuel as the Sun, but it is using it up at about 5000 times the rate of the Sun. This means that the ``lifetime'' of the star will be much less, about 1/500 the lifetime of the Sun.
This is illustrated in Figure 19.9 of your textbook.
Info on stellar lifetimes versus mass.
The mass-luminosity relation says that if we see a very massive main sequence star,
it must have formed rather recently.
This result will help in understanding both where
stars come from, and what they do after the Main Sequence.
Stellar Birth and Death Let's start with the formation of stars. How does such an object get organized? Where do they come from?
SC1 Chart from winter sky.
Let's choose an example from the sky. The region throughout the constellations of Taurus,
Auriga and Gemini, is quite interesting. It includes the star cluster the Pleiades.
a picture of the Pleiades is given on p511 of your textbook. The brightest stars in the
Pleiades are ``early'' B stars. Astronomers who have studied these stars conclude that
they, and the Pleiades cluster, must only be about 70 million years old.
Picture of Pleiades
Image of Pleiades This star cluster must be close to the place it formed, and thus should give us some hints about star formation. You can see what appears to be wisps of gas that might be ``leftovers''.
