Neutron Star and Black Hole
Initial Mass Function


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Contact: F.X.Timmes
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The neutron star and black hole initial mass function (1996)

In this article, using recently calculated models for massive stellar evolution and supernovae coupled to a model for Galactic chemical evolution, neutron star and black hole birth functions (number of neutron stars and black holes as a function of their mass) are determined for the Milky Way galaxy.

For those stars that explode as Type II supernovae, the models give birth functions that are bimodal with peaks at 1.27 and 1.76 M$_{\odot}$ and average masses within those peaks of 1.28 and 1.73 M$_{\odot}$. For stars that explode as Type Ib there is a narrower spread of remnant masses, the average being 1.32 M$_{\odot}$, and less evidence for bimodality. These values will be increased, especially in the more massive Type II supernovae, if significant accretion continues during the initial launching of the shock, and the number of heavier neutron stars could be depleted by black hole formation. The principal reason for the dichotomy in remnant masses for Type II is the difference in the presupernova structure of stars above and below 19 M$_{\odot}$, the mass separating stars that burn carbon convectively from those that produce less carbon and burn radiatively.

The Type Ib's and the lower mass group of the Type II's compare favorably with measured neutron star masses, and in particular to the Thorsett et al. (1993) determination of the average neutron star mass in 17 systems 1.35 $\pm$ 0.27 M$_{\odot}$. Variations in the exponent of a Salpeter initial mass function are shown not to affect the locations of the two peaks in the distribution function, but do affect their relative amplitudes. Sources of uncertainty, in particular placement of the mass cut and sensitivity to the explosion energy, are discussed, and estimates of the total number of neutron stars and black holes in the Galaxy are given. Accretion-induced collapse should give a unique gravitational mass of 1.27 M$_{\odot}$, although this could increase if accretion onto the newly formed star continues. A similar mass will typify stars in the 8-11 M$_{\odot}$ range (e.g., the Crab pulsar). The lightest neutron star produced is 1.15 M$_{\odot}$ for the Type II models and 1.22 M$_{\odot}$ for the Type Ib models.

Altogether there are about 109 neutron stars in our Galaxy and a comparable number of black holes.

Curiously, this effort has garnered attention post gravitational wave LIGO/VIRGO. Mostly not for its models, but for the one-line approximation in equation 8 relating baryonic and gravitational masses: $M_{\rm baryon} - M_{\rm grav} = \Delta M = 0.075 M_{\rm grav}^2$.

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