**Spectral Types vs Spectral Classes**

While there doesn't seem to be an "official" distinction between the terms “spectral type” and “spectral class”, I'm making a distinction in this volume; to wit, the spectraltypeis the alphabetic designation (e. g. O, B, A, F, G, K, M, and certain others), whereas the spectralclassis the spectral type with the numerical value appended (e. g. G2, F9.5, etc.). We might think of these in the same terms as biologic taxonomy, with the spectral type corresponding to the genus and the spectral class corresponding to the species. The decimal fraction part of the spectral class, then, would correspond to subspecies.

**The Harvard And MK Classification Systems**

There are actually a number of different ways in which stars are classified; some focus on their absorption and emission spectra, others on their color/temperature, yet others on their luminosities. For our purposes, we're mostly concerned with temperature and luminosity, and thus this volume focuses on the Harvard and MK classification systems, as well as the The Hertzprung-Russell Diagram. In the Harvard system, stars are organized according to their surface temperatures, with seven distinctive groupings: O, B, A, F, G, K, and M (often remembered by students through the mnemonic ( Oh, Be A Fine Girl/Guy, Kiss Me). These were first codified in the modern order by between 1901 and 1912, and adopted formally by the International Astronomical Union on May 9, 1922.Annie Jump Cannon |

This is a one-dimensional system, which concerns itself

*only*with the characteristics of the spectra of the stars. It has been expanded to include spectral types L, T, and Y, which classify the infrared spectra of very cool stars (to include brown dwarfs), as well as types C for carbon stars (red giants near the end of their lives) and S for stars falling between M and C and which have excess amounts of zirconium <1>.It was

This ran counter to the popular theory of her time that the Sun was composed of the same elements in the same proportions as was the Earth, and her publishing of this discovery was discouraged.

*(née Cecilia Helen Payne) who conclusively demonstrated in the 1920s that the***Cecilia Payne-Gaposchkin***OBAFGKM*designations specifically related to stars'*surface temperatures*. Applying work on the ionization of elements first performed by Indian astrophysicist*, she was also the first to recognize, in 1924, that the Sun is composed primarily of hydrogen, and that this would necessarily be true of all stars.***Meghnad Saha**

This ran counter to the popular theory of her time that the Sun was composed of the same elements in the same proportions as was the Earth, and her publishing of this discovery was discouraged.

*(see below) confirmed in 1929 that she had been correct; though he acknowledged her prior work and conclusions in a paper he published that year, Gaposchkin's contribution was largely overlooked until recently.***Henry Norris Russell****The Morgan-Keenan Classification**

The Morgan–Keenan (MK) classification system was developed by

*and***William W. Morgan***, and expands the Harvard classification, adding a luminosity class (see below), notated in Roman numerals, from zero to VII. This***Philip C. Keenan***two-dimensional*classification scheme relates to spectral lines and surface gravity (which is related to temperature), whilst the Harvard classification is based on surface temperature alone. Differences in the spectra of stars can thus be interpreted as luminosity effects, allowing analysis of the spectrum to lead to the assignment of luminosity classes.**The Hertzsprung-Russell (H-R) Diagram**

The H-R Diagram is a scatter plot which maps surface temperature against brightness, and is thus a two-dimensional system which synthesizes the Harvard system and the MK system.

It was created around 1910 by

It was created around 1910 by

*and***Ejnar Hertzsprung***when they were exploring the relationships between different characteristics of stars. The H-R Diagram was a major advance in helping astronomers to understand the processes of stellar evolution, and thus helped pave the way for our modern understanding that stars are not permanent, but have a lifetime during which their characteristics change.***Henry Norris Russell**The H-R Diagram above plots temperatures from low-to-high across the bottom, which is reversed from the usual scheme, but more intuitive. It also indicates stellar radii in terms of the Sun as well as masses in solar masses.

Below is a table which lists the specific temperature ranges, in Kelvin, associated with the various spectral types:

Below is a table which lists the specific temperature ranges, in Kelvin, associated with the various spectral types:

Stellar surface temperatures as assigned to spectral types are not a linear progression across the entire range, nor do they follow an exponential or geometric progression, as can be seen in the graph below:

The equation <2> for determining the exact numerical component of the spectral class is:

Where:

𝜏 = a constant value representing the maximum temperature for the spectral type in question (in Kelvin);

The 𝜏 and

*Sc*= the numerical portion of the spectral type designation;𝜏 = a constant value representing the maximum temperature for the spectral type in question (in Kelvin);

*K*= the actual surface temperature of the star in question (in Kelvin);*q*= a constant value associated with each spectral typeThe 𝜏 and

*q*values for each spectral type are given in the following table:If the star's effective (surface) temperature is known, the above equation and constants can be used to determine the numerical portion of its spectral class. Use the table above to locate the appropriate spectral type by letter, then use the equation to determine the numerical portion of the star's spectral class.

For example, the Sun's surface temperature is listed in most sources as about 5800 K. However, if we didn't already know that it's a G-class star, we could consult the first table, and find that 5800 is in the G-type range. We can then use this value in the equation for spectral type G:

For example, the Sun's surface temperature is listed in most sources as about 5800 K. However, if we didn't already know that it's a G-class star, we could consult the first table, and find that 5800 is in the G-type range. We can then use this value in the equation for spectral type G:

... to arrive at a spectral class of G2.498.

Conversely, if you already know the numerical portion of the spectral class, you can calculate the exact surface temperature of the star in question with the following equation.

Conversely, if you already know the numerical portion of the spectral class, you can calculate the exact surface temperature of the star in question with the following equation.

Thus: the Sun is typically listed as a G2 spectral class, so

*S**c**= 2.0*; searching the table for spectral type G, we arrive at 𝜏*= 6000*, and*k**= 1.249 × 10⁻²*, and so the precise value returned by this equation for the surface temperature of a G2-class star is:… which—for all practical purposes—can be rounded to 5840 K.

As a further example, the star Zeta Tucanae is listed as F9.5.

Consulting the first table, we see that spectral type F has a temperature range of 6000—7500 K. Using the numbers from Zeta Tunanae's spectral class in the appropriate equation from the table above:

As a further example, the star Zeta Tucanae is listed as F9.5.

Consulting the first table, we see that spectral type F has a temperature range of 6000—7500 K. Using the numbers from Zeta Tunanae's spectral class in the appropriate equation from the table above:

… we calculate a surface temperature that is quite close (within ≈2%) to the "official" value of 5956 K.

**How Accurate Is This System?**

Using the same list of 13 stars as above, we can compare the measured Kelvin temperatures to the values calculated using the above equation and constants:

The luminosity classes (see below), range from supergiants to main sequence dwarfs, and the accuracy if the calculations spans 27.12%, between [77.02% , 104.14%] of measured values.

The mean plus-or-minus the population standard deviation spans 16.46%, between [86.47%, 102.93%] of measured values. The accuracy is almost exactly 100% for G-type stars and shows increasing variation as the temperatures both increase and decrease, though cooler stars show a greater variation than hotter stars.

Thus, this method of calculating the Kelvin temperatures of stars based on their spectral class is accurate enough for Worldbuilding purposes.

The mean plus-or-minus the population standard deviation spans 16.46%, between [86.47%, 102.93%] of measured values. The accuracy is almost exactly 100% for G-type stars and shows increasing variation as the temperatures both increase and decrease, though cooler stars show a greater variation than hotter stars.

Thus, this method of calculating the Kelvin temperatures of stars based on their spectral class is accurate enough for Worldbuilding purposes.

As always, if you are using a known star as the primary for your star system, you should use the measured values for that star’s characteristics, rather than calculated values.

## Notes

- "Stellar Classification," Wikipedia, July 21, 2018, , accessed July 21, 2018, https://en.wikipedia.org/wiki/Stellar_classification.
- Please note that I derived this equation by analyzing empirical data; as far as I know, it is in no way related to a any official method for assigning spectral types/classes to stars—thus
*caveat emptor*.