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If supernovas can be predicted depending on the mass of the a star, (If its more than about 8 times the mass of sun it will eventually go supernova - https://www.space.com/23756-white-dwarf-stars.html), can we use that data to predict if a neutron star will later form from this supernova and if that neutron star will turn into a black hole later on? A neutron star can only turn into a black hole if it reaches a density of 4 × 10^14 I think (https://chem.libretexts.org/Ancillary_Materials/Exemplars_and_Case_Studies/Exemplars/Physics_and_Astronomy/Density_of_Black_Holes) or basically has a mass greater than 2 or 3 solar masses since density typically increases proportionately with mass in neutron stars. I feel like there is a way to connect all three of these stages of a neutron-formed black hole in a simple equation I am just not sure how or where to find more information into it. Let me know what you think!

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There is no simple equation and different researchers do not agree in detail about which massive stars end their lives as neutron stars and which end up as black holes. Any simple mass criterion is complicated by the uncertain physics of neutrinos and radiative transfer in the core of a supernova; the rotation rate and the strength of any magnetic fields present and the uncertain details of the prior episodes of mass loss from the star, which are also dependent on the mass, composition and rotation of the star. i.e. mass is not the only important parameter.

OK, so after injecting a note of realism, that doesn't stop people trying to calculate a remnant mass versus initial mass relationship. Here are recent examples taken from the review of core-collapse supernovae by Limongi (2017) for stars with two representative initial "metallicities" (the fraction of the initial stellar material made up by elements heavier than helium); on the left, a metallicity similar to the solar composition and the enriched interstellar medium that might form massive stars now; on the right, a metallicity of one thousandth of this, to represent stars formed in the early universe. The red lines represent the relationships you are looking for between remnant mass (on the y-axis) and the initial mass of the star (on the x-axis), and the ranges forming neutron stars or black holes are indicated.

Remnant mass Vs initial mass from Limongi et al. (2017).

But I think you want to go further than this - to estimate the mass of the progenitor and the remnant from the properties of the supernova. This is at present a completely theoretical and hence model-dependent exercise because of all the uncertainties I mentioned above. Nevertheless, you can look at Kasen & Woosley (2009), where

Formulae are developed that describe approximately how the model observables (light curve luminosity and duration) scale with the progenitor mass, explosion energy, and radioactive nucleosynthesis.

For example, they give the following expressions to relate the observable parameters of type IIp (plateau) core-collapse supernovae - the luminosity at 50 days, $L_{50}$, and the length of the light curve plateau, $t_p$, in terms of the energy of the explosion $E_{51}$ (in units of $10^{51}$ ergs) and the progenitor mass, $M_{in,10}$ in units of 10 solar masses. $$L_{50} = 1.49\times 10^{42} E_{51}^{0.82} M_{in,10}^{0.77}\ {\rm erg/s}\ , $$ $$t_p = 128E_{51}^{-0.26} M_{in,10}^{0.11}\ {\rm days}. $$

In principle, you could measure these two parameters from multi-colour light curves and invert these equations to obtain the explosion energy and progenitor mass and then use the Limongi diagram (or something similar) to see whether that progenitor mass led to a neutron star or black hole.

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