Neutron stars and distribution of heavy elements

Question

In the news, of course, is the theory that much of the mass of the heaviest elements in Earth would have come from colliding neutron stars. This graphic gives one such analysis:

^{Origin of the Elements in the Solar System by Jennifer Johnson is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. (Larger version at http://www.astronomy.ohio-state.edu/~jaj/nucleo/)}

I don't know how accurate this is, but the URL looks good. Also, this seems to be a new theory, and AFAIK this is the first actual evidence for it.

If this is correct, what are the implications for the quantity of heavy elements that would be found on planets outside our solar system? In particular, I guess, the very heavy ones: gold, platinum, thorium, uranium...

We've been watching the skies for signs of neutron star collisions for several years now (IIUC), and I guess we're starting to get an idea of the frequency of this event. And I've seen estimates of how much gold etc. was produced by this particular event. How many planets would one such collision supply with the quantity of heavy elements in Earth?
(I guess we only really know about gold in the Earth's crust, and to some extent in the mantle; are these elements concentrated in the core? Any idea about heavy elements in other planets of our solar system?)

So: given the frequency of the event per galaxy, the estimated number of stars with planets in a galaxy, etc., is it likely that most planets are deficient in heavy elements, as compared with Earth?

(Side comment: if so, then nuclear wars might be rare or impossible on those planets.)

Answer 1

I may do some more detailed calculation, but I think there is a misconception that has provoked your question.

The content of (e.g) gold, with respect to other elements in the solar system can be readily measured in meteorites. The Earth is expected to contain a similar abundance, but is very depleted in hydrogen and helium and somewhat depleted of lighter elements like carbon and sodium. The surface abundance of gold in the Earth is then a bit lower, because it sinks during the Earth's formation.

We expect the relative abundances of chemical elements to be quite smoothly distributed in space and time. Material that is produced in supernovae and neutron star collisions is mixed quite quickly in the interstellar medium. Thus the material that makes up the solar system is contaminated by the excreta of as many as a billion stars that lived and died before it's birth. Even if a neutron star merger occurred right next to the molecular cloud that formed the Sun, that cloud may have contained a million solar masses of gas, that would have diluted the signature of the kilonova event. We expect this to be true for all stars born in our Galaxy, except those that were born right near the beginning, where individual "pollution" events might become apparent.

The rate of these events in the local universe is only known observationally to an order of magnitude. In the past, it is also rather poorly known, but can be indirectly deduced from the rate of short Gamma ray bursts (of which we see only a small, uncertain fraction), if we assume that all sGRBs are merging neutron stars and that all merging neutron stars produce sGRBs. The rate in our Galaxy is extrapolated from the properties of the meagre number of identified double neutron stars and their orbital decay rates and is about 1 every 50,000 years (so about 200,000 over the lifetime of the Galaxy).

These rates require that about 0.0001 to 0.001 solar masses of very heavy elements is produced in each of these explosions to reproduce the solar system abundances. In the recent event, the amount of heavy elements in the ejecta appear to be in that range.