No this is not a political rant. This is a follow-up to my earlier post of Space, 9/12/12

http://habitablezone.com/?prosc_taxopt=topics%3Aspace&s=hertzprung

I discuss there how stars are classified by spectral class, O,B,A,F,G,K,M in descending order of temperature from hottest (O, blue) to coolest (M, reddish orange). Each class is further subdivided into subclasses designated by a number, so for example, our own sun is a G2. The class can be determined by visual inspection of the spectrum, by seeing which spectral lines are prominent and which are missing. This can be done from a black-and-white photograph of the spectrum, but it requires a highly trained eye willing to do back-breaking and terribly monotonous work at no pay by staring at spectra on film emulsions through a microscope: i.e, a graduate student. As you go from O to M, the stars are cooler and the spectral lines change as pressure, temperature, density and flux conditions change in the star’s photosphere. For example, in G stars like Sol the H and K absorption lines of singly ionized Calcium are particularly prominent.

The work is important because the spectral class tells you the conditions at the surface, particularly temperature–stars are close to being black-body radiators, that is, their temperature can be determined by their color. But the difficulty of determining spectral class from spectrum inspection is considerable, so long ago astronomers developed a clever technique to gauge color for many stars at once using photography: the color index. The method takes advantage of a property of film emulsions that the size of a stellar image is directly proportional to its magnitude. This relation is independent of the optical system used, and the length of the time exposure, or the development chemistry, provided you use the same film emulsion.

Magnitude, you will recall is a power law defined so that the log of the light intensity ratio of two stars = 0.4 times the magnitude difference. Another way of saying this is that a first magnitude star is exactly (by definition) 100 times brighter than a sixth magnitude star. Yet another way of saying this is that the difference in magnitudes between two stars m1 – m2 = -2.5 log i1/i2. where i1 and i2 are the corresponding intensities. The reason for this cumbersome system are historical, traditional, and due to the physical reality that the human eye and photographic film are not linear detectors, they are logartihmic. But we’re stuck with it in this day of direct flux detectors like CCDs because a lot of old data is still out there that we have to compare with modern observations. And its no more confusing than the decibel system audio weenies use.

If we photograph a star field with any telescope, the relative magnitude of every star on it can be determined by simply measuring the size of each image on the photographic plate. If you know the actual brightness (measured by some other method) of one star on the plate, you can calibrate the plate and determine the magnitude of all the others–and one photographic plate may contain thousands of stellar images! To do this you must use a standard emulsion, and the Kodak company used to make it for astronomers at a financial loss (bless their hearts), manufactured to strict quality control standards. I practically cried when Kodak went out of business. They were fine corporate citizens.

But how do you determine the color of a star, since the photographic emulsion used for this purpose was panchromatic (black and white)? You do it by exposing two identical plates, one through a filter that passes yellow-green light only (astronomers call it V, for Visual) and one through a filter that passes only Blue (or B). The filters were also manufactured by Kodak to excruciating standards so they were as similar as possible. Residual differences between lots were detected by examining standard stars of known color and the results corrected mathematically.

By measuring the stellar images, you derive a B and a V magnitude for each star. And simply subtracting the second from the first you get the color index. Since stars are black body radiators and their thermal properties are highly correlated with their color, the B-V number is a very accurate measure of their spectral class and their color.

Today, of course, you have photosensitive diodes and charge coupled devices to do your measurements directly, in milliwatts, but by the time they came along we had catalogued the color indices of hundreds of thousands of stars which can now be easily compared to modern measurements.

We still use the B-V color index system, and several others such as the UBV (U is for Ultraviolet, it gives a better fit for very hot stars) to characterize stellar temperatures. If you see these arcane astronomical numbers, I hope this will give you a bit of an understanding of their historical origins. Here are some examples

Spectral Class-Temperature (deg K)-Color Index

O5 38,000 -0.32
O9 31,900 -0.31
B0 30,000 -0.30
B9 12,400 -0.06
A0 10,800 0.00
A7 8,190 0.20
F0 7,240 0.33
F8 6,200 0.53
G0 5,920 0.60
G2 5,780 0.64 (Sol)
G8 5,490 0.72
K0 5,240 0.81
K7 4,160 1.30
M0 3,920 1.41
M8 2,660 2.00

Astrophysical Formulae, Kenneth R. Lang.