ASTRONOMY 1040

Class Notes #6    ALL NOTES ARE SUBJECT TO CHANGE

Our knowledge of the stars is based on the Sun, but that is not all we know. Much is based on our model of the Sun, but there are various parameters what we can know or at least deduce from direction measurement.

Chapter 11

Characteristics of Stars

In terms of directly observable characteristics of stars, we are a bit limited, but we can measure:

• apparent magnitude, or how bright stars appear (this however, really tells nothing about the true nature of the star
• energy flux, or the amount of energy we receive from the star in a given time (not the total amount it emits, bu tjust the amount that we receive at Earth's distance). If it  varies in magnitude and energy flux this is an average.
• surface temperature using Wien's Law, from about 3000 K to 50,000 K (the Sun's surface is about 5800 K)
• Chemical composition, using spectroscopy (most stars are mostly hydrogen and helium)

Distances

The Cosmic Distance ladder  -- each step is less accurate that the one before

• Stellar parallax, or distance based on how a star's apparent location varies with the observer's location
•     most accurate method, but limited to only the nearest stars
•     only about 2000 stars as seen from Earth, although hundreds of thousands as viewed from spacecraft
• Cepheid variables, based on the "period luminosity" characteristics of certain stars
•     Cepheids are stars whose total brightness (luminosity) varies with specific periods
•     The period is related to the star's absolute magnitude or luminosity. Luminosity is a measure of how bright the star truly is at all wavelengths.[By comparison, light bulbs come in various luminosities, such as 60 watts or 100 watts. A 60 watt light bulb will appear much brighter at 5 feet than at 50 feet, but it will still have a 60-watt luminosity. If you know what the luminosity is, and can measure the apparent brightness, you can determine the distance by a simple mathematical relation.] By observing the star's period, we know its luminosity (which is directly related to another quantity called "absolute magnitude", which you should look up. By then comparing the known luminosity to the apparent brightness, the distance can be found by applying the inverse square law [just as you could determine the distance to a 60-watt light bulb if you could measure how bright it appears at your distance].
• Spectroscopic parallax and related techniques based on spectral classification and the HR diagram (below). That is, if we know the spectral type of a "normal" star, we know its luminosity (actual total energy output at all wavelengths). This is because stars follow a pattern. That is, all G-type "normal" (non-Giant) stars are like all other G-type stars. All B-type normal stars are like all other B-type normal stars. More specifically, all G2 normal stars (such as our Sun) have approximately the same luminosity. Thus, if we can identify a star as being a G2 from its spectrum. Then we know its luminosity, because we know that it is essentially the same as the Sun's. If we know the luminosity, we can compare that to the apparent (observed) brightness to deduce mathematically the actual distance.

Several other techniques for determining distances beyond our Milky Way Galaxy

•     Cepheid variables (only for nearby galaxies)
•     Supernova magnitudes (which tend to be only in a limited range)
•     The Tully-Fisher relationship, by which the mass of spiral galaxy is related to its rotation rate
•     Red-Shift, whereby the distance of distant galaxies is related to the shift in its spectral lines. 

(Only after we determine a distance can we determine other characteristics such as those in 3 below)

• Normal stars are much like the Sun, but vary greatly in terms of physical characteristics:
• mass, ranging from roughly one tenth to 200 times the mass of the Sun. If you don't understand what mass means, ask!
• physical dimensions (size) ranging from roughly one tenth to one thousand times the Sun's diameter
• luminosity (total energy output), ranging from about one thousandth to about one million times that of the Sun
• luminosity is related to "absolute magnitude" or how bright a star would appear at a set distance (10 pc*)
• once we know distance, calculating luminosity or absolute magnitude aids in comparing stars
• age, ranging from newborn stars to some very old red dwarfs which could be 12-13 billion years old

The characteristics above are typically determined from a mathematical model of stellar characteristics. 
Stellar characteristics were originally determined by studying perhaps a few hundred stars.

The Spectral Sequence

The Spectral Sequence classifies stars with a letter, OBAFGKM, going from hottest (O) to "coolest" (M). The sequence is further broken down into numbers, 0-9, again hottest to "coolest". The Sun is a "G2", and as such is toward the cool end of the middle range (it's pretty average all round). You can remember the sequence with this old phrase:   "Oh, Be A Fine Girl (Guy), Kiss Me." Topday there are a few other letters for unusual stars, but don't worry about them.

The Hertzspung-Russel (FR) Diagram

Luminosity plotted against spectral classification forms the Hertzsprung-Russell (HR) diagram.  Luminosity (or absolute magnitude) is on the vertical axis, going upward from least to most. Spectral classification (or temperature) is on the horizontal axis, left to right (OBAFGKM, hot to cool).  Most stars fall along a line from the lower right to upper left called the "Main Sequence.".This tells us that normal stars (the vase majority of all stars) follow a pattern and are not random.  A few stars (white dwarfs, red giants) do not fall into this pattern and have different luminosities.  Using the HR diagram, we can plot most stars through their spectral type (fairly easy to determine). Once a star is plotted we can measure its luminosity directly from the chart.  Knowing luminosity, we can compare how bright the star appears to how bright is really is. This comparison yields distance. It is like comparing the brightness of a streetlight a few blocks away to how bright it is up close.

Any Questions?

* NOTE: a "pc" is a "parsec" or the distance at which the radius of Earths orbit would cover one second of arc. This amounts to 3.262 light years, so absolute magnitudes are calculated as if the star were 32.62 light years away

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  (Some graphics copyright by Richard W. Pogge and used with permission. Other graphics are copyright by Larry C. Sessions or are believed to be in the public domain. Contact me at the email address below with questions or if you find a copyrighted image uncredited or inappropriately used.)