Is there a way to calculate the mass of of a stellar remnant given the initial mass of the star? Assume there is a star in a completely empty region of space, away from any outside influence.
Is there a way to calculate the mass of a resulting stellar remnant, a white dwarf, neutron star, or black hole(variations is accuracy are completely fine) that will result after a star dies, only given the star's mass around the time in which will die? (like an equation or something)
And, is there a way to calculate the resulting remnant's mass only given the star's initial mass during its formation?
It would be appreciated if one were to provide a concrete method or graph for determining such.
Thanks in advance!
For massive stars and their remnants, one can only be guided by theoretical measurements at present, since we do not have any masses for isolated neutron stars and black holes and no measurements of the masses of the progenitors of any neutron stars or black holes (only limits). Here are two plots taken from the extensive review by Limongi (2017). These show the relationships you want (the red lines) between the final remnant mass (on the y-axis) and the initial progenitor mass on the x-axis. The calculations are highly dependent on metallicity, so plots are given here (there are more in the paper) for solar metallicity ([Fe/H]=0) and a thousandth of solar metallicity ([Fe/H]=-3). There is also a dependence on rotation, which may be important.

You have to appreciate that these red curves are highly uncertain and model-dependent.
The situation is much clearer at lower masses. The masses of white dwarfs, even isolated white dwarfs, can be estimated quite well and their presence in binary systems and clusters of stars gives the means to estimate their ages. Combining this with their cooling ages gives a good estimate of the time that their progenitor spent as a &quot;normal&quot; star and then stellar evolution models give an estimate of the progenitor mass. Both the modelling and measurements are much more secure and so the initial-final mass relation for white dwarfs is in quite good shape.
The plot below is from a summary by Kalirai (2013). It is likely to be superseded in the next year or two by the wealth of data coming in on white dwarfs from the Gaia satellite. The names on the plot are the clusters in which the calibrating white dwarfs were found. You will see on the plot that Kalirai gives a simple formula that represents this relationship and might be what you are looking for. I believe the dashed line is from some stellar evolution model.