So far during the course, you have escaped the usual harangue about distance determination, and the information in these chapters is a little thin on this subject. Because of the importance in the history of knowledge about galaxies, I feel a compulsion to add to that material, so here goes. First, recall that the only DIRECT method for determining distance to stars is the geometric parallax method - chapter 8 material. Parallax works out to the point at which we can no longer accurately measure the shift of stars against the background of more distant stars - about 100 pc (or 300 light years) or a little more. From this collection of near-by stars, astronomers measured properties and discovered the H-R diagram correlation between color (or surface temperature) and magnitude (or luminosity or radiated power). About 90% of those near-by stars are on the main sequence.  Over half of these stars are in binary pairs, a fact which astronomers have been able to exploit to estimate stellar masses.  Therefore, these near-by stars allowed astronomers to construct and validate the theory stellar evolution as we know it today.

If we assume that stars everywhere obey the same statistics, then we can use the H-R diagram correlation as a rule to obtain distances further out into the universe. The limit for this so called spectroscopic method corresponds to our ability to resolve individual stars in large groups of stars (such as star clusters and galaxies) and measure spectra for individual stars - out to about 10,000 pc (30,000 light years):  in other words, only stars within our own galaxy. In the spectroscopic method of estimating stellar distance, astronomers assume that measured surface temperature correlates with luminosity according to the 'known' main-sequence correlation.  In other words, compute surface temperature based on a star's spectrum measurement, then simply look up the luminosity for the star assuming it lies on the main sequence.   Careful analysis of the spectral absorption lines generally allows the astronomer to assess the validity of the main sequence assumption (remember that 9 out of 10 stars lie along the main sequence).  Comparison of the luminosity with measured apparent brightness allows determination of the star's distance.  This method does involve using the main sequence correlation, which really is a 'band' rather than a line - and the distance determined with this method suffers from this lack of certainty of the luminosity.  Distance uncertainties using this method are on the order of plus or minus 25% - sometimes better if statistical analysis of a large number of stars is possible.

Within the 10,000 pc of applicability of the spectroscopic parallax method lie some variable stars. Astronomers have shown that a RR Lyrae or a Cepheid variable is a star in a late stage of evolution that is temporarily (i.e., several thousand years) unstable. The stars pulsate radially (that is, they expand and contract, thereby changing their light output) in a very regular pattern. The time between successive brightenings is the period of pulsation. {Do not confuse this type of pulsation with that associated with pulsars - pulsars are rotating neutron stars, and pulses of light sweep over Earth if the neutron star magnetic axis is pointed the right way.} Your text relates how Shapley used Cepheid variables to measure distance to Milky Way’s globular clusters, but all other texts give a different version of that story. I will relate the different version, and in a homework assignment you get the chance to think through this issue for yourself.

First, your text gives the impression that Henrietta Leavitt was an astronomer comparable with Harlow Shapley. In actuality, astronomers of that day (white males) hired educated women (at very low wages) to analyze the tremendous number of images the men were collecting. For women of that time, the work was interesting and they got to work regular hours in congenial groups in the cramped quarters of the Harvard Observatory. A couple of women are known for technical work that has high historical importance, and Ms. Leavitt is one of them (the other is Annie Cannon, who proposed the still-used spectral classification system (O B A F G K M). Ms. Leavitt did discover the correlation between average (over a period) brightness and pulsation period for variable stars in the Small and Large Magellanic Clouds (nearby galaxies - although at the time of her discovery astronomers only knew them as star systems because galaxy was not a known concept in 1908). She assumed that, for a given cloud, the variables were all at about the same distance from us, and plotted APPARENT magnitude versus pulsation period (which was easy to measure) for several hundred Cepheid variables. Most of these stars have periods from 3 to 50 days, with luminosities from 1,000 to 10,000 times that of our Sun. Perhaps the best known star that is a Cepheid is our North star (Polaris), which has a period of about 4 days and changes brightness by about a tenth of a magnitude (around 20% brightness variations). The correlation shows that the stars with shorter periods are the least luminous, and vice versa. (See figures 12-3 and 12-4). Today astronomers know that the least luminous Cepheids are the least massive, and vice versa. So the largest (most massive) stars pulsate slowly and have long periods, as befits their large size. The light-curve is very unique and distinct from the RR Lyra light curve (not shown in your text). The light curve of the RR Lyrae is 'spikier,' with a sharp rise, sharp drop, and a time of relatively constant magnitude before the next rise. Also, the period of most of the Lyra stars is about a day or less, and the average luminosity is only about 100 times that of the Sun. This 100 factor is very suggestive - it is the same factor by which our own Sun will brighten when it lands on the "horizontal branch" of the H-R diagram (when it is converting helium in the core to carbon). So astronomers believe that the Lyrae variables are sun-like stars (around one solar mass) in a brief unstable period near the second equilibrium phase on the horizontal branch. Similarly, we believe the Cepheids are more massive stars in a brief unstable period during their late stage evolution.

Now comes the historical glitch mentioned early in these notes. Your text implies that Shapley used Cepheid variables to estimate distances to Milky Way globular clusters. All other books say he used RR Lyrae variables - in fact these are the only types of variable in globular clusters. You get to decide which scenario is more likely. However, remember that the globular clusters in our galaxy are very old (about 10-12 billion years old), and also remember your stellar evolution stories and the fact that nature makes more low-mass stars than high mass stars. In any case, Shapley did measure globular cluster distances, then he ASSUMED the center of our galaxy was at the center of that distribution of clusters and for the first time came up with a decent estimate for the size of our home galaxy.