How does the number in stellar classification indicate properties within the range of that class?

I am doing some research for a video game and I wanted to store stellar data on a star, such as its Stellar Classification, and then from that derive a physical appearance in the game. These are fictional stars.

My original thought had been to store the star's classification, For example G2V and then at runtime I could use that data to determine things like surface temperature, brightness, radius, and mass. From temperature I can also derive color.

However when I sat down to start coding a first pass on this I noticed something that confused me.

According to Wikipedia, our Sun, Sol, is a G2V star. The number is supposed to indicate a "sub" classification. A G2 star would be 20% between a G star and a K star. A table there lists a G type star as having a surface temperature between 5,200 K and 6,000 K. Therefore I figured a G2 star would have a temperature of about (I know nothing here is EXACT) 5,360 K (20% of the way between 5,200 and 6,000) but apparently it actually has a temperature of 5,800 K which is about 75% between the given range. So why is Sol not a G7 of G8 star?

And then once I hit that irregularity, I had to assume that things like Radius and Mass are probably also not linearly interpolated along the range.

Is there a feasible way to derive properties such as I am looking at based on the Stellar Classification?

• I think low numbers indicating hotter stars. So G2 would be more like 5840K if you interpolate between 5200K and 6000K. – SpaceBread Sep 21 '19 at 0:18
• Well that's an embarrassing mistake! – jwvanderbeck Sep 21 '19 at 1:40
• Confirmation of above: en.wikipedia.org/wiki/G-type_main-sequence_star – userLTK Sep 21 '19 at 3:31
• There is no linear relationship between spectral classes and stellar parameters. Spectral classification is based on the appearance of the spectrum. Your solution is a look-up table. – Rob Jeffries Sep 21 '19 at 6:52
• There are some tables in Zombeck's Handbook of Astronomy and Astrophysics, though these are perhaps a bit crude. ads.harvard.edu/books/hsaa/toc.html A problem that you have is that there is NO one-to-one mapping between mass and spectral type. For that you would have to define an age or use the ZAMS. The easiest way to get a mass temperature relationship is download some stellar model calculations. e.g. astro.ulb.ac.be/~siess/pmwiki/pmwiki.php?n=WWWTools.Isochrones – Rob Jeffries Sep 21 '19 at 19:52

Here is a table taken from the models of Siess et al. (2000). It is appropriate for zero age main sequence stars of about the solar metallicity. Note that any correspondence between spectral type, mass and radius will be age dependent.

You can generate tables for different metallicities, or get more detailed information at http://www.astro.ulb.ac.be/~siess/pmwiki/pmwiki.php?n=WWWTools.Isochrones

Computation of the ZAMS Metallicity : Z = 0.02 , no overshooting

 ST       L         R        Teff     Mass     age       Bol    BC     B-V    V-R    V-I    Mu     Mv     Mb     Mr     Mi     Mj     Mh     Mk     Ml  flag  check

M6   8.290E-04  1.137E-01   2781.   0.100  2.270E+10  12.45  -5.97   2.28   2.76   5.68  22.15  18.42  20.70  15.66  12.75  10.49   9.77   9.32   8.85   1     1

M5   6.689E-03  2.187E-01   3300.   0.200  1.785E+08  10.19  -2.95   1.72   1.37   3.15  16.12  13.14  14.85  11.76   9.99   8.33   7.72   7.42   7.16   0     0

M3   1.488E-02  2.950E-01   3528.   0.300  1.343E+08   9.32  -1.88   1.54   1.05   2.33  13.94  11.20  12.73  10.14   8.86   7.64   7.00   6.77   6.59   0     0

M2   2.656E-02  3.612E-01   3683.   0.400  1.120E+08   8.69  -1.51   1.48   0.96   2.03  12.89  10.20  11.68   9.24   8.17   7.10   6.43   6.23   6.08   0     0

M1   4.633E-02  4.293E-01   3829.   0.500  1.019E+08   8.09  -1.24   1.43   0.90   1.82  11.98   9.32  10.75   8.42   7.51   6.56   5.88   5.71   5.58   0     0

M0   8.292E-02  5.215E-01   4008.   0.600  8.320E+07   7.45  -1.05   1.37   0.86   1.67  11.08   8.50   9.87   7.64   6.83   5.97   5.31   5.16   5.04   0     0

K6   1.481E-01  6.369E-01   4287.   0.700  6.587E+07   6.82  -0.75   1.21   0.75   1.39   9.88   7.57   8.78   6.83   6.18   5.40   4.79   4.67   4.56   0     0

K4   2.804E-01  7.561E-01   4698.   0.800  5.212E+07   6.13  -0.51   1.00   0.60   1.11   8.47   6.64   7.64   6.04   5.54   4.82   4.27   4.17   4.08   0     0

K2   4.877E-01  8.656E-01   5047.   0.900  4.173E+07   5.53  -0.38   0.86   0.51   0.94   7.35   5.91   6.77   5.40   4.96   4.36   3.88   3.79   3.73   0     0

K0   8.102E-01  9.973E-01   5334.   1.000  3.326E+07   4.98  -0.30   0.80   0.45   0.85   6.48   5.28   6.07   4.82   4.43   3.90   3.46   3.39   3.33   0     0

G8   1.297E+00  1.166E+00   5556.   1.100  2.653E+07   4.47  -0.25   0.73   0.42   0.80   5.72   4.71   5.44   4.30   3.91   3.44   3.04   2.97   2.92   0     0

G5   2.004E+00  1.332E+00   5788.   1.200  2.214E+07   4.00  -0.21   0.65   0.39   0.75   5.02   4.20   4.85   3.82   3.45   3.06   2.71   2.65   2.60   0     0

G0   2.946E+00  1.476E+00   6070.   1.300  1.915E+07   3.58  -0.18   0.56   0.35   0.70   4.33   3.75   4.32   3.41   3.05   2.71   2.41   2.36   2.31   0     0

F7   4.281E+00  1.656E+00   6284.   1.400  1.617E+07   3.17  -0.16   0.49   0.31   0.62   3.82   3.33   3.82   3.02   2.71   2.38   2.08   2.04   2.00   0     0

F5   6.065E+00  1.848E+00   6498.   1.500  1.370E+07   2.79  -0.14   0.41   0.27   0.53   3.33   2.93   3.34   2.66   2.40   2.13   1.90   1.86   1.82   0     0

F3   8.117E+00  1.968E+00   6770.   1.600  1.196E+07   2.48  -0.12   0.37   0.24   0.48   2.97   2.59   2.96   2.35   2.12   1.91   1.73   1.70   1.67   0     0

F1   1.087E+01  2.062E+00   7120.   1.700  1.031E+07   2.16  -0.10   0.32   0.21   0.43   2.61   2.26   2.58   2.05   1.83   1.70   1.56   1.53   1.50   0     0

A9   1.405E+01  2.129E+00   7476.   1.800  9.064E+06   1.88  -0.10   0.25   0.15   0.35   2.29   1.98   2.23   1.83   1.64   1.51   1.41   1.38   1.35   0     0

A8   1.784E+01  2.202E+00   7832.   1.900  8.004E+06   1.62  -0.12   0.20   0.10   0.27   2.02   1.74   1.93   1.63   1.47   1.34   1.26   1.23   1.20   0     0

A7   2.226E+01  2.268E+00   8176.   2.000  7.125E+06   1.38  -0.13   0.17   0.08   0.21   1.77   1.51   1.68   1.43   1.30   1.17   1.10   1.07   1.04   0     0

A3   3.330E+01  2.395E+00   8824.   2.200  5.731E+06   0.94  -0.19   0.08   0.03   0.07   1.26   1.13   1.21   1.10   1.06   0.97   0.95   0.94   0.93   0     0

A0   5.441E+01  2.512E+00   9705.   2.500  4.298E+06   0.41  -0.38  -0.02   0.00  -0.03   0.73   0.80   0.78   0.80   0.82   0.84   0.85   0.86   0.87   0     0

A0   7.341E+01  2.618E+00  10241.   2.700  3.595E+06   0.09  -0.49  -0.04  -0.01  -0.05   0.42   0.57   0.53   0.58   0.63   0.68   0.70   0.72   0.73   0     0

B9   1.059E+02  2.720E+00  11048.   3.000  2.815E+06  -0.31  -0.63  -0.07  -0.01  -0.07   0.06   0.32   0.26   0.34   0.40   0.49   0.53   0.55   0.58   0     0

B8   1.843E+02  2.940E+00  12094.   3.500  1.944E+06  -0.91  -0.82  -0.09  -0.02  -0.09  -0.48  -0.09  -0.19  -0.08   0.00   0.15   0.19   0.23   0.26   0     0

B7   3.172E+02  3.240E+00  13208.   4.000  1.387E+06  -1.50  -1.06  -0.11  -0.02  -0.09  -0.97  -0.45  -0.56  -0.42  -0.35  -0.15  -0.10  -0.04  -0.02   0     0

B6   6.822E+02  3.530E+00  15334.   5.000  7.917E+05  -2.33  -1.45  -0.14  -0.04  -0.11  -1.61  -0.89  -1.03  -0.85  -0.78  -0.53  -0.47  -0.37  -0.40   0     0

B4   1.343E+03  3.910E+00  17291.   6.000  4.852E+05  -3.07  -1.75  -0.17  -0.05  -0.14  -2.17  -1.32  -1.48  -1.26  -1.18  -0.91  -0.83  -0.73  -0.75   0     0

B3   2.366E+03  4.320E+00  19281.   7.000  3.223E+05  -3.69  -2.06  -0.20  -0.07  -0.17  -2.60  -1.62  -1.82  -1.55  -1.46  -1.14  -1.05  -0.97  -0.95   0     0


The ZAMS is defined as the time, after deuterium burning, when Lnucl > 0.99 L (i.e. Lgrav < 0.01 L)

L,R and M are expressed in solar units, Teff in K

Bol represents the bolometric magnitude Colors are given in the Cousins system. We used the conversion table of Kenyon et al. (1994, AJ, 108, 251)
check = 1 means that the colors are out of the table and have been extrapolated flag = 1 means that the request was not successful. The data corresponds to the last entry found in the file

• Thanks for that @JamesK – Rob Jeffries Sep 22 '19 at 21:09