# How are the numerical stellar subclassifications determined?

From Wikipedia:

The spectral classes O through M, as well as other more specialized classes discussed later, are subdivided by Arabic numerals (0–9), where 0 denotes the hottest stars of a given class. For example, A0 denotes the hottest stars in the A class and A9 denotes the coolest ones. Fractional numbers are allowed; for example, the star Mu Normae is classified as O9.7. The Sun is classified as G2.

So our Sun is a G2V yellow dwarf.

The G identifies its temperature as within the range of 5,200-6,000K. The V tells us it is on its main sequence.

That leaves us with the 2. The 2 tells us that the sun is warmer than a G3 star and cooler than a G1. I get that. My problem: I just can't seem to figure out how the ranges of these specific numerical subclasses are determined. Are they explicitly defined? Logarithmic? Is there a way to calculate it exactly? Why is Mu Normae a O9.7?

My best guess is to take the range of the stellar class and divide it into 10 subsections but I can't find any source to confirm that.

• I don't have a definitive answer. However, the fractional spectral types usually arise when someone measures a spectral type dependent property (e.g. a line ratio) and then uses a calibration relation to estimate the spectral type. Apr 22 '17 at 7:18
• There are also not always 10 subclasses. Nobody really uses K8 and K9 for example. Apr 22 '17 at 7:31
• The subdivisions were part of an attempt by Annie Jump Cannon to adjust the existing system based on Lyman alpha hydrogen line strength to one based on temperature (thus the reason for not being in alphabetical order). The temperatures are estimated by the line ratios mentioned by Rob. I'm not sure how so I'm not calling this an answer. The subdivisions were a "fine tuning" by temperature and some classifications warranted finer tuning (thus the M1.5 or whatever). Hydrogen line strength now follows a curve that is lower for hot O stars, then peaks at A stars and gradually tapers with temp.. May 12 '17 at 17:25
• May 27 at 1:57