Saturday, 28 December 2019

nuclear physics - Age of the Earth and the star that preceded the Sun


One of the great unheralded advances made in the history of science was the ability to determine the age of Earth based on the decay of isotopic uranium. Based on the apparent abundance of uranium in the early Earth, what conclusions can be drawn about the star that preceded the Sun?



Answer



Dear Humble, the cosmic nucleosynthesis (first three minutes) only produced hydrogen, helium, lithium, and beryllium. All heavier elements came from slow fusion inside living stars and, especially the heaviest ones, originate from dying stars.


The periodic table


Regular fusion-related processes inside stars (see the list at the bottom of the answer) only produce elements up to $Z=70$ or so: I included the periodic table for your convenience. The even heavier elements, especially gold and uranium, were produced by three extra processes




  • s-process

  • r-process

  • rp-process


The s-process depends on the existence of elements in the iron group. An extra neutron may be absorbed (probably coming from reactions inside red giants), increasing $A$ by one, and if an unstable element is produced in this way, a neutron in the nucleus beta-decays by emitting an electron. Additional neutrons may be absorbed and the process may continue. Nuclei in the "valley of beta stability" can be produced in this way. "S" stands for "slow".


On the contrary, the r-process is "rapid". The neutrons are absorbed in a similar way but in the cores of supernovae. The seed nucleus is usually Ni-56. The rp-process, which may occur in the neutron stars and elsewhere, is also rapid, "r", but the particle is that absorbed is a proton, therefore "p" in "rp". Logically, unlike the previous two, it produces nuclei on the "proton-rich side" of the stable valley.


The uranium we observe on the Earth probably comes from all these processes - and from many stars - there is arguably no "the star" that preceded the Sun. In particular, our Earth hasn't orbited any other star before the Sun because it is as old as the Sun, at least this is what is believed. The hydrogen used by our Sun couldn't have been "recycled" and it began to burn soon after the sufficient collapse - it couldn't have been recycled from elsewhere. The heavier elements were recycled from many places. There was probably no "permanent region" that was inheriting the brand "Solar System". These issues were discussed yesterday:



How many times has the stuff of the Sun been recycled? How many times has the "stuff" in our solar system been recycled from previous stars?




Let me mention that it's not a problem for the heavy material to spread across large distances of the Cosmos. For example, an exploding supernova shoots most or all the matter by the speed 1% of the speed of light. So in 400 years, the material from the Sun - if it went supernova (it won't) - reaches Proxima Centauri and in less than 100 million years, it may reach almost any point in the Milky Way. Even the Solar System is moving at speed of 0.1% of the speed of light which is enough to move matter by light years in thousands of years. It's silly to imagine that the material had to wait on the same place from an "ancestor star", being saved for some humans on some Earth.


It may be useful to list all processes of stellar nucleosynethesis, not only those linked to uranium:



pp-chain / CNO cycle / α process / Triple-α / Carbon burning / Ne burning / O burning / Si burning / R-process / S-process / P-process / Rp-process



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