Source and code associated to the research note arXiv:2201.10519 to appear in RNAAS, created with showyourwork.
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We want to develop a new mapping between star (and core) mass and compact object remnant for population synthesis calculations.
Our aim is to have one way to calculate this across the entire mass range (from neutron stars to black holes above the pair-instability mass gap). Moreover, we want the mapping to be continuous. This is not because it is a priori unphysical to have discontinuities, but because we don't want to artificially introduce features. Free parameters can be added later to control the appearance of discontinuities.
The idea is to calculate the mass of the compact object remnant as total mass minus varius mass loss terms:
M_\mathrm{comp.\ obj} = M_\mathrm{pre-CC} - \left(\Delta M_\mathrm{SN} + \Delta M_{\nu, \mathrm{core}} + \Delta M_\mathrm{NLW} + \Delta M_\mathrm{PPI} + \cdots \right)
In this way, pre-explosion binary interactions reduce M_\mathrm{pre-CC}
already (and possibly modify the core structure, Laplace et a. 2021), and then each mass loss
process at core-collapse can be added separately. This can also be
extended to add other mass loss mechanisms at core-collapse
Note that while "building" the compact object mass from the bottom up (e.g., the Fryer et al. 2012 approach of starting with a proto neutron star mass and accrete the fallback on it) makes it very difficult to use observationally informed values for some of the terms in parenthesis. Conversely, in our approach of "building" the compact object "top down" by removing from the total mass the ejecta, we can use observationally informed quantities for each term here if they are available.
If one (or more) of these terms have a stochastic component, this can naturally produce the scatter in compact object masses expected because of the stochasticity in supernova explosions (e.g., Mandel& Mueller 2020).
The script src/figures/fit_DM_PPI.py generates the fitting formula,
its tex expression, and the figure in the research note automatically
through showyourwork.
The data from Table 1 in Farmer et al. 2019 are automatically downloaded from zenodo (see datafile1.txt) and cleaned by the script.
This is the resulting fit (see also Fig. 1):
\Delta M_\mathrm{PPI} = (0.0006\log_{10}(Z)+0.0054)\times (M_\mathrm{CO}-34.8)^3-0.0013\times (M_\mathrm{CO}-34.8)^2
See more details in the main text with the article badge above.
Recently Mehta et al. 2021 have produced more simulations showing the nuclear data tables adopted in stellar evolution calculations (like those in Farmer et al. 2019) might be under-resolved. They showed that this can impact the predicted BH masses. This may introduce an uncertainty, depending on the source of the nuclear physics data, in the maximum black hole mass below the pair-instability gap of ~20%, which is comparable to the accuracy of our fit.