Physics 101 Class Notes

Physics 101 - Astronomy - Spring 2019

Class notes for day 24, April 16, 2019

This lecture is about characterizing the stars. This lecture was a continuation of the material we did on Day 22, but students filled out a worksheet (for extra credit) as I went over the material.

We did a quick review, and then I had students go over a worksheet which had questions keyed to the slides. Here are the questions (you will need to figure out the answers if you didn't come to class):

1) Suppose that star X is known to be 10 parsecs away from us and star Y is 50 parsecs away. Which star has the greater parallax angle?
a) star X
b) star Y
c) neither – their parallax angles are the same.

2) The most important reason for measuring the parallax of a star is to help us find the stars'
a) direction of motion.
b) proper motion.
c) distance, so we can calculate the absolute magnitude.
d) radial velocity.

3) Two identical stars, one 10 light years from Earth, and a second 40 light years from Earth are discovered. How much fainter does the farther star appear to be?
a) 2 times fainter.
b) 4 times fainter.
c) 8 times fainter.
d) 16 times fainter.
e) the farther star does not appear fainter, since it is identical.

4) For two stars of the same apparent brightness, the star closer to us will generally have
a) a higher flux.
b) a hotter temperature.
c) a lower luminosity.
e) identical physical properties

5) Using the magnitude system of astronomy, how would the brightness of an 8th magnitude star compare to a 7th magnitude star?
a) 10 times brighter than the 7th magnitude star.
b) 10 times dimmer than the 7th magnitude star.
c) 2.5 times brighter than the 7th magnitude star.
d) 2.5 times dimmer than the 7th magnitude star.

6) The reason astronomers use the concept of the absolute magnitude is to allow stars to be compared directly, by removing the effects of differing
a) distance.
b) mass.
c) temperature.
d) radius.

7) Which property of a star would not change if we could observe it from twice as far away?
a) angular size.
b) color
c) apparent magnitude
d) parallax
e) proper motion

8) Suppose that two stars are at equal distance and have the same radius, but one has a temperature that is about twice as great as the other. The luminosity from the hotter star is
a) about 16 times greater.
b) about 16 times less.
c) about 20 per cent greater.
d) about 20 per cent less.
e) Not enough information given to answer the question.

9) Two stars have the same temperature, but the radius of one is twice that of the other. How much brighter is the larger star?
a) the same because luminosity depends only on temperature.
b) 2 times
c) 4 times
d) 8 times
e) 16 times

Continuing in the Powerpoint -

To characterize the stars, we measure the
1. apparent magnitude
2. distance (by parallax)
3. spectrum (to find the temperature)
and so we can deduce the luminosity and spectral class (OBAFGKM-LT).

The spectral classification uses letters for the spectral classes: OBAFGKM (and LT) based on the star’s temperature.

Then we start looking at the HR diagram. HR stands for Hertzsprung-Russell, just the names of two astronomers who invented the diagram in the 1920s.

We plot stars on a chart which has temperature on the horizontal axis and the luminosity on the vertical axis. We use units of solar luminosity on the vertical axis and units of Kelvin (for temperature) on the horizontal axis. So if a star has 3 times the luminosity of our Sun, we say it has a luminosity of 3 (solar luminosity units). Notice the luminosity is a special kind of scale called a logarithmic scale, in powers of ten. The horizontal temperature axis is plotted in reverse: hot on the left, cooler on the right, and typically ranges from 30,000 K down to 3000 K.

Look at the diagrams in the PowerPoint. First are some well-known stars, then an HR diagram of the nearest stars seen from the Earth. Now this diagram shows the Main Sequence of stars that are in the shaded region. Stellar size is indicated by the diagonal lines. (These dotted lines are a result of the luminosity-radius-temperature equation). Then you see an H–R Diagram of the 100 Brightest Stars. This is biased in favor of giants, which are very luminous, so we see all the giants in a large volume of space, and don’t see the smaller stars in such a large volume. As a result, very few smaller stars show up on this plot. Then you see a Hipparcos H–R Diagram, using a large database of stars. This is a more representative set of stars for a plot like this, so this is what the diagram should look like if we include all the stars in a galaxy, for example.

Extension of the methods of determining distance requires a non-geometric approach, since parallax is only good out to 200 pc or so. Spectroscopic parallax is really a misnomer, it is not a direct measurement, but empirical, based on a statistical estimate, the most likely distance for a star based on luminosity and color.

Luminosity class is an additional criterion, based on spectral line width and its correlation to gas pressure in the star’s photosphere. We get several types of stars, listed in the Table on Stellar Luminosity Classes. This is starting to get confusing, and I certainly don't remember the details, just the fact that we can do quite a bit of classifying if we look at spectral details.

Stellar masses can be determined most easily in Binary Stars. There are basically three types: visual, spectroscopic, and eclipsing, depending on how we see them. It turns out that Stellar masses determine a star’s position along the main sequence, more than other properties do. So if you know the star's mass, you know how it will develop over its lifetime.

Stellar Radii and Luminosities: Radius is proportional to mass and Luminosity is proportional to (mass)^{(4th power)}
These relationships are hard to explain because they require a detailed understanding of the stellar interior and the properties of the gases, etc.

Main sequence stars show some trends: The small mass stars tend to be cooler and so they burn hydrogen more slowly in their core. Hence they have longer lives, in some cases, lives that will be much longer than the present age of the Universe (trillions of years).