Relationships between G magnitude, Johnson V magnitude, and spectral type of stars?

I'm simulating a population of binary stars for a summer research project. I'm adding uncertainties to my simulated observables such as angular position and radial (line of sight) velocity. I'm using astrometric and spectroscopic uncertainties from different telescopes to model what the data would look like if it were observed by different experiments. In my simulation, I'm including the fact that the values of the uncertainties for said observables depend on the magnitude (brightness) of the star. The fainter the star, the lower the precision with which we can measure its position, velocity, and so on. Makes sense.

Certain parameters of binary orbits such as the mass ratio distribution of the components depend on the spectral type of the primary, and I would like to include this in my simulation as well. In order to do this, I will generate a random spectral type for each orbit, and from there determine the mass of the primary, the mass ratio, and so on. As I understand it, spectral type, in general, is related to the magnitude of the star. My goal is, using the randomly generated spectral type (from a certain distribution) for each binary pair, to calculate the magnitude of the stars in order to assign the correct uncertainty in angular position and radial velocity.

One of the telescopes whose uncertainties I want to use to simulate observed data is GAIA. I came across this text and the associated paper by de Bruijne: Science performance of Gaia, ESA’s space-astrometry mission, which includes exactly what I'm looking for: the varying astrometric and spectroscopic uncertainties for stars of different magnitudes. The spectroscopic uncertainty depends on Johnson V magnitude, but the astrometric uncertainty varies with a different description of magnitude, a parameter $$G$$, e.g. $$G=15 {\rm mag}$$. I'm trying to relate these to spectral types, but when I researched it I wasn't able to find an explanation of G mag anywhere.

I did read about absolute, apparent, and Johnson V magnitudes, but I still don't understand where the parameter G comes from, or the relationship between spectral type and magnitude as it relates to my simulation. Can anyone pleae help me relate G, Johnson V magnitude, and spectral type? Or explain what is flawed about my simulation plan?

• The term magnitude is too unspecific, as there are absolute and apparent magnitudes. The apparent magnitude has no correlation to spectral type. You can test that by filtering a catalogue like the HR and apply the filter "3.5 .. 3.7" [two dots!!!] to the column "Vmag". The output will be stars of very different spectral type, but almost the same apparent magnitude. Feb 13, 2022 at 16:14