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Are spectral subclasses logarithmic? I can't seem to find any source on whether they're linear or logarithmic. For reference, by spectral subtypes I mean, for example, G2 vs G3 stars.

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Strictly speaking, neither. The types and sub-types are qualitatively defined in terms of spectral features (the presence or absence of various lines) and the relationship to photosphere temperature is a derived and secondary property.

In practice the relationship is mixed. In the graph below the logarithm of temperatures (source) are plotted against spectral type.

enter image description here

If there were a simple logarithmic relationship, you would expect a straight line. That works reasonably well for the G, F and A stars, and also for the B stars (but at different parameters) but the M and K stars have a linear interpolation (giving a curved section of the graph), and the O type stars are a little scattered too.

The evidence from these data is that the scaling of sub-types from 9-to-0 isn't done by simple mathematical scaling applied equally to all types, unlike (for example) the logarithmic magnitude or decibel scales.

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