Astronomy 100, Week 3 Notes

Last week was a tough one for most students; this week involves critical information for the rest of the course and uses the week 2 information. The units in the book deal with OBSERVATIONS of the Sun and other stars, plus some information about the theoretical model of our Sun, including how the Sun produces the energy that it also radiates to space (in the form of electromagnetic radiation).

We observe that the Sun is sort of a typical star, so we suppose that study of the Sun’s surface features provides information typical of that of many other stars. The "typical" descriptor can be misleading, in that nature makes way more lower-mass stars than the Sun-like stars, and way fewer higher-mass stars. However, bear in mind that much more massive stars, as well as stars off the "main sequence" of the H-R diagram, have significantly different surface features than our Sun. So the info in the book, while supposedly about the Sun, is really about stars like our Sun, which means stars having "about" the same mass as our Sun.  The book also surveys and summarizes observed features of other stars.

The story that may turn out to be the most interesting science of all near-surface phenomena is one that is currently unfolding based on the lightly mentioned GONG project. Astronomers measure surface undulations for the Sun (using the Doppler effect at millions of points on the surface) and attempt to deduce what is going on beneath the surface of the Sun - i.e., what the material motions look like beneath the surface. Another source of the same kind of information concerns the solar magnetic field - analysis of surface magnetic field phenomena also leads to some conclusions about material flow beneath the surface. Your assignments include leads to follow to discover what solar astronomers are now seeing using data from various solar observing instruments.

One of the two main puzzles about the Sun until recently has been the high temperature in the solar corona - as described in one of your assignments. When astronomers observe the Sun’s X-radiation, they see that the corona emits X-rays that typify temperatures in the 1-3 million Kelvin range - MUCH higher than the surface temperature of about 6000 Kelvins. This puzzle is now replaced with trying to explain why the surface magnetic field loops form and break, thereby pumping energy into the corona, thereby heating it. The SECOND main puzzle about the Sun concerns the solar neutrino shortage.  A measurement reported during summer 2001 showed huge promise in explaining that apparent shortage in a natural way: (http://www.sns.ias.edu/~jnb/Papers/Popular/Nature01/nature.html).  
A later report using the same facility, but with a different neutrino detector, seems to have resolved the issue for good:
(http://www.sno.phy.queensu.ca/)
Some work also continues to understand more completely how the Sun's large-scale magnetic field evolves and correlates with active features observed on the Sun's surface - sunspots, prominences, and flares.

One focus to maintain is the distinction between surface features that one can always see on the Sun (passive Sun) versus features that correlate with the solar cycle - the active Sun. Granulation, spicules, coronal heating, and surface undulations are always present on the surface. Prominences, solar flares, sunspots, and increased coronal heating are features that come and go with the 11-year solar cycle. Also important is to understand qualitatively how we think the Sun’s magnetic field and differential rotation CAUSE the increase in solar activity. Your text mentions that we think Earth’s magnetic field explanation is similar to that for the Sun, but in my opinion our understanding of the Sun’s magnetic field exceeds our understanding of Earth’s field and associated observations. More on that later in the course. The cause for all this activity on the surface is, of course, what goes on much deeper in the Sun, and that comes next . We think the upwelling material arises because of thermal energy transfer from deeper layers to the surface via convection - the mode of heat transfer in a boiling pot of water.

When we look outward from our Sun to other stars, we have to 'travel' very long distances (compared with distances in our solar system) to find them. At these distances, we can only image the disc of very few, extremely huge, stars like Betelgeuse, and even then we cannot discern surface features like sunspots. Think for a moment what you CAN measure from a distant star. Through a telescope comes a certain amount of light, whose energy deposition rate and spectrum one can measure. The measured energy per week time is closely related to the "apparent magnitude" (or brightness from our location) of the star. From the spectrum, astronomers infer the surface temperature, composition, and other quantities as described last . Getting the stellar data for all stars on the same basis requires knowing the distance to all the stars we observe. Stellar distance measurements can be tricky to understand because there are several methods, and each method relies for accuracy on other methods - an interlaced network that ALL relies for accuracy on the most basic technique known as (geometric) parallax. The problem is that we can measure the geometric parallax (by triangulation) for a relatively small fraction (roughly a million as of 2003) of observable stars. Nevertheless, much of what we know about stellar evolution derives from study of this "near-by" collection of stars whose distances we know from parallax measurements. Stars in this collection all exhibit a tiny bit of transverse back-and-forth apparent motion (relative to the far more numerous 'fixed' stars) as Earth orbits the Sun. You can see a simple example of this parallax effect by holding your arm extended and seeing how your thumb changes location against a distant background as you look at it with one eye, then the other. If you measure your eye separation and the angular change in apparent thumb location, you can calculate the length of your arm. Without the aid of large, high-resolution telescopes, the early Greeks could not detect parallax of any stars and incorrectly concluded that all stars lay equally distant on one of the crystal spheres they imagined rotating about Earth at the center.

Astronomers accumulated stellar spectrum data for many decades until Hertzsprung and Russell of H-R diagram fame discovered the now-famous correlation between luminosity L (or total power radiated to space in all directions) and surface temperature T (related to spectral type). We calculate luminosity based on the measured radiation energy (including spectrum) and measured distance. As you saw in section 6-2 of your text, we determine T by measuring the wavelength of the peak intensity of the star’s spectrum and using Wien’s law to compute temperature. A plot of L versus T shows that 90% of stars lie along a correlation curve called the main sequence. In the next chapter, you will see that this fact leads to an interpretation that stars spend about 90% of their total lifetime sitting at this point on the H-R diagram. How they get to that point on the H R diagram is the theory of star formation, and leaving the main sequence is the saga of stellar death. Thus, the 10% of stars that we do NOT observe on the main sequence part of the H-R diagram are doing something BESIDES living the 90% part of their life (this includes white dwarf stars, red giant/supergiant stars, and stars still in their formation stage). The red giants are about to die, and the white dwarfs are the final remains of lower mass stars. The remains of even higher mass stars are neutron stars and black holes, and their luminosity (zero in the case of bare black holes) and surface temperature are too extreme to show up on a conventional H-R diagram.

It turns out that the stellar property we most want to know is the most difficult to measure - the total mass. The only stars for which we can determine the mass directly are part of a binary pair. Essentially, we use the mutual gravitational influence of two stars on each other to determine the individual masses. If everything about the mutual orbit is known, we can determine the mass of each star. For many binary pairs, only some of the orbital information is measurable, and we can only infer the total mass of the binary system with accuracy. Fortunately, over half of all stars appear in pairs, so for that near-by collection whose parallax is measurable we can determine the mass of many stars. The huge importance of star mass will become apparent later when you learn about stellar models and structural theory.

It is critical that you understand how to interpret the H-R diagram, and you need to be focusing on this aspect. It is important from several evolutionary points of view to know that nature makes far more low mass stars than high mass stars.  The red dwarfs, orange, yellow, green, blue, etc. stars on the main sequence are dominated by the red dwarfs in number.  The O type stars are the most rare. The white dwarf stars also show up as being fairly numerous - these are stellar corpses that have accumulated from the death of stars similar to our Sun since the beginning of the universe.  At a very distant point in the future (hundreds of billions of years) white dwarf stars will greatly outnumber all other types of objects.   In next week's reading you'll revisit this stellar population distribution.

In summary, remember that this week is mostly about observed stellar properties and quantities calculated from those observed properties, and the observed H-R diagram correlation. The next couple of weeks are mostly about models and theories of stellar evolution, including birth, main lifetime, and death.

The following table lists approximate values for the mass-luminosity relationship, with a modification at low mass to match the data more closely.  For mass above about 40 solar mass, and for mass below about 0.4 solar mass, I'm pretty skeptical about the values - both these star categories present limited and tough observational opportweekies.  Also remember that the luminosity of a main-sequence sun-like star will increase by a factor of about 2 while the star is still on the main sequence.

Solar Mass	Approx. Main Sequence Luminosity
0.1	1.0 x 1003
0.2	1.0 x 10-02
0.4	1.6 x 10-01
0.6	1.7 x 10-01
0.8	4.6 x 10-01
1	1.0 x 1000
2	1.1 x 1001
4	1.3 x 1002
6	5.3 x 1002
8	1.4 x 1003
10	3.2 x 1003
15	1.3 x 1004
20	3.6 x 1004
25	7.8 x 1004
30	1.5 x 1005
40	4.0 x 1005
60	1.7 x 1006
80	4.6 x 1006
100	1.0 x 1007