This figure shows a theoretical H-R diagram which includes effective temperature, Teff and luminosity, L, for a star I am studying, along with several evolutionary tracks from PARSEC 1.25 stellar models (Parsec).
The PARSEC models include various stellar parameters, and I want to use these closest models to estimate the mass, radius, and age of my study star. Zooming in, and plotting the values on a linear-linear plot we see the following:
Here we see a closeup portion of the three tracks for metallicity Z=0.02, and masses of 1.80, 1.85, and 1.9 Mʘ. On this scale, we can clearly see the discrete points in the evolutionary tracks. The black points on each track are the points closest the measures values for the study star. They might not look like the closest, but the scales on the two axes are not the same. The following shows an even closer view with the same scales on both axes.
Again, the black points are the closest to the measured data. Obviously, these are actually the closest of the discrete points. Remember that the parameters we want are the mass, radius, and age, and the values might not be at one of the discrete points. For the mass, the values do not change along the tracks, so a combination of interpolation and extrapolation along the vertical axis using only the difference in luminosity can provide three masses and uncertainties which can be combined in a weighted average to provide an overall estimate of the mass of the study star (if it has a metallicity Z≈0.02). The tracks are not quite horizontal, and it should be noted that the same interpolation and extrapolation procedure can be performed using differences in the temperature, but this will produce a large uncertainty. Combining the luminosity and temperature results in a weighted average produces an overall estimate that is very close to the luminosity value with a slightly larger uncertainty estimate.
Unlike the mass, the values of age and radius do change along each evolutionary track, and it is necessary to interpolate between the two nearest discrete points along each track to determine the values of age and radius at the actual closest approaches. These can then be used in the same interpolation/extrapolation process as that used for the mass.
The same procedure can be repeated for the Z=0.01 tracks, and the combined set of mass, age, and radius values should give insight into the evolutionary status of the study star.
Now that I’ve explained the process, I’d like to hear comments or suggestions for improvement. Thanks.
, their units are dex.