# Goldplating Planets with Kilonovas

One of Alice's interstellar jaunts will take her to a Gold Planet. It's a planet that was recently covered in a meter deep layer of gold dust (for realism, it is mixed with silver, platinum, teensy bits or uranium and the like)

I've been thinking about how to do this -- since planets don't naturally tend to refine gold and deposit it as nice uniform layers. My latest idea involves using a Kilonova, or double neutron star collision. This should generate an expanding cloud of gold and other Lanthanides (a few thousand Earth masses), hopefully enough to plate a nearby word.

I am slightly worried however of what having a kilonova going off within gold dusting distance might reasonably be expected to do to a planet(ary system).

Would it make sense to expect a kilonova gold dusting to lay a 1 meter layer of gold dust on a planet, or would the side-effects (have been)/be a bit too dramatic?

• Since colliding neutron stars are suspected to be the cause of gamma ray bursts, some of the most powerful naturally occurring phenomena in the universe, I suspect that if you would be close enough to be in the shockwave of the event (which would be the mechanism to deliver heavy elements), you would not have a planet covered in dust, but rather the planet would be turned into dust by the radiation and shockwaves. – Thucydides Oct 17 '17 at 17:48
• @Thucydides, I was not able to find much literature on the topic, but unless I misread it, the energies seem to be relatively mild (compared to a supernova gamma burst for instance) – Serban Tanasa Oct 17 '17 at 17:50
• I doubt you can "electroplating" gold onto a planet this way, but I liked the way u think. When 2 neutron stars each at least 1.4x mass of Sun but squeezed into a ball of 10 miles diameter merged, it scatters radioactive debris into space when free neutron can stick onto an already heavy elements to form gold and it goes up the periodic table unlike supernova which goes up to iron. Thereafter gravity takes over and everything is history... – user6760 Oct 18 '17 at 6:02
• I can't find anything that says that Lanthanides make up a large fraction of a kilonovas output. This is different then the output of kilonovas making up a large fraction of Lanthanides which is what is stated in all the references I could find. This is an important distinction without more information you'll end up coating the planet in material that is a higher percentage gold but possibly still mostly lighter elements which wouldn't have the desired effect. – Lex Oct 19 '17 at 1:27

## How much gold are we talking about?

Well, let's use the approximation $$\Delta V\approx4\pi r^2\Delta r$$ If $$r$$ is about the radius of Earth and $$\Delta r$$ is $$1\text{ meter}$$, then $$\Delta V\approx5\times10^{14}\text{ m}^3$$. The density of gold is $$\rho\approx19320\text{ kg/m}^3$$, and so $$\Delta m=\rho\Delta V\approx10^{19}\text{ kg}$$.

Let's say that the cloud of material expands isotropically outward from the source with a total mass $$M$$, radius $$R$$ (at a given time) and a thickness $$\Delta R$$. It therefore has a volume $$V\approx4\pi R^2\Delta R$$ and an area mass density of $$\sigma=\frac{M}{4\pi R^2}$$ The planet has a cross-section of $$A=\pi r^2$$,1 meaning that the total amount of mass that hits the planet is $$\Delta m=\sigma A=\sigma\pi r^2=\frac{1}{4}M\frac{r^2}{R^2}$$ If we set this equal to our earlier value of $$\Delta m$$, then we find $$\frac{M}{R^2}\approx10^6\text{ kg/m}^2$$

The typical amount of gold produced in a kilonova via the r-process is . . . not well-known. We've got a limited dataset. That said, if we assume (conservatively!) that $$M\approx100M_{\oplus}$$, then we need $$R\approx2\times10^{9}\text{ m}$$, or roughly $$0.01\text{ AU}$$. The planet would almost certainly be in orbit around the binary system, which could be dangerously close. I certainly wouldn't want to be anywhere nearby!

## Things you could do to solve the problem

You do have some options here:

• Lower the thickness of the gold coating you want!
• Lower the density of the coating. I honestly don't know what a good value would be; my $$\rho$$ assumed that the gold would be totally solid (which is probably not an excellent approximation).

Both of these let you place the planet further from the melee.

It's worth noting, by the way, that only the half of the planet facing the binary system would be significantly coated, unless an accretion disk of sorts was the form around it. Additionally, the depth of the coating would be non-uniform.

## What would be the effects on the planet from the merger?

Radiation from such a merger should be emitted isotropically, i.e. most of should spread out equally in all directions.2 It's possible that some emissions could be constrained to thin beams, but this certainly won't be the case for all of the electromagnetic emission.

Let's look at the energies and luminosities involved:

• Gamma rays: $$\sim10^{39}\text{ J}$$, $$\sim10^{40}\text{ W}$$[1]
• X-rays: $$\sim10^{32}\text{ W}$$[2]

By comparison, the luminosity of the sun is $$\sim10^{26}\text{ W}$$. This sort of event is brief but very violent. I don't know what the long-term effects of this radiation will be for the planet, but short-term, it won't be pleasant. The deposition of radioactive isotopes might also be a problem, but I don't know just how bad it would be.

1 Okay, it's a bit more than that because gravity's involved, so there's going to be some accretion. In particular, gravitational focusing will give an effective cross-section (p. 22) (see also here) of $$A_{eff}=A\left[1+\frac{v_{esc}^2}{v_0^2}\right]$$ where $$v_{esc}$$ is the scape velocity at the surface of the planet and $$v_0$$ is the initial relative velocity of the gas and the planet. Let's assume that the planet's escape velocity is the same as that of Earth, $$\sim11\text{ km/s}$$. The speed of the ejected gas is expected to be $$0.1-0.2c$$. This means that $$v_0\gg v_{esc}$$, and so $$A_{eff}\approx A$$.
2 For what it's worth, there will be delays before the radiation is emitted, even without the effects of interstellar dispersion. It probably won't help you that much, though - the planet will still be orbiting the remnant.

• planet cachement area would be significantly larger than planet surface, as there's this thing called gravity. :) – Serban Tanasa Oct 18 '17 at 20:09
• @SerbanTanasa I did consider that, but then had no idea how to calculate how much would land on the planet because I couldn't get a good idea of the velocity of the gas, and therefore, how much would escape. I'll add a note to that effect. You know, it reminds me of work on stellar collisions, where the cross-section does take gravity into account because the effect's significant. So maybe this could be helpful. – HDE 226868 Oct 18 '17 at 21:35
• @SerbanTanasa I've edited it. Turns out that the velocity of the gas should be extremely high, so the effective cross-section is actually still just about the cross-section of the planet. – HDE 226868 Oct 19 '17 at 16:10
• Aha, had not considered the relativistic speed of the gas – Serban Tanasa Oct 20 '17 at 16:44
• Can you edit to add how much kilonova mass one can expect to accrete on the planet? Or a layer width – Serban Tanasa Oct 20 '17 at 16:47

Planets don't refine gold and deposit in in nice layers. Microbes do.

Have the dust be the dried bed of an ancient ocean, the floor of which was covered with polymetallic nodules.

Microbial metabolism can convert dissolved metal salts into metallic nuggets. This is best described for manganese but can happen with other metals, sometimes all in the same nugget.

Marine biominerals: perspectives and challenges for polymetallic nodules and crusts Xiaohong Wang, Werner E.G. Müller. Trends in Biotechnology Volume 27, Issue 6, p375–383, June 2009

Deep sea minerals in polymetallic nodules, crusts and hydrothermal vents are not only formed by mineralization but also by biologically driven processes involving microorganisms (biomineralization). Within the nodules, free-living and biofilm-forming bacteria provide the matrix for manganese deposition, and in cobalt-rich crusts, coccolithophores represent the dominant organisms that act as bio-seeds for an initial manganese deposition.

Could this sort of thing form nodules of solid gold? Absolutely, and I think it probably happens. There have been discovered organisms that metabolize gold salts and excrete tiny gold nuggets - probably just another type of the microbial metal metabolism described above. That only has to go on for a few million years before you have a lot of gold nuggets.

http://www.nature.com/nature/journal/v495/n7440_supp/full/495S12a.html?foxtrotcallback=true

Take a solution of gold chloride, a compound toxic to most forms of life. Add a colony of Cupriavidus metallidurans, one of the few bacteria able to survive amid compounds of heavy metals in mines across the world. As the bacteria accumulate the gold salt from the solution, biochemical processes within the organisms reduce it to the pure metal, which the bacteria excrete in the form of tiny gold nuggets — nanoparticles of pure gold. The bacteria produce the gold as protection from the toxic gold complexes that would otherwise destroy their cells.

Could it work with uranium? Yes. http://www.nature.com/nature/journal/v350/n6317/abs/350413a0.html

So at the bottom of your ocean, dissolved metal inputs leached over eons are accumulated into nuggets. When the oceans went away, wind gradually weathered these nodules of gold, uranium and other metals down to dust. Thus it is when Alice arrives.

• Aaaah, Biology. – Joe Bloggs Oct 17 '17 at 15:53
• @JoeBloggs The universe is more inventive than we will ever be. I want to upvote science, but I'll settle for a willing proxy. – Frostfyre Oct 17 '17 at 16:32

Not sure how you would work out the stellar mechanics, but if there was a black hole/neutron star eclipsing the kilonova and exactly halfway between the planet and the explosion, then the matter cloud could be gravitationally lensed around and back to the planet. This would also increase the amount of matter intercepted significantly. If the eclipting body also has a strong magnetic field, you would in effect have a stellar scale mass spectrometer, with which you could filter out the undesired lighter ions. Assuming they exit the nova at the same velocity, and I have no idea whether or not that would be the case.

• Note: I would not consider this answer "hard science." Even in writing it, I can think of many holes that would need to be addressed and may sink the idea out right. But for soft science, it may contain sufficient plausibility to pass suspension of disbelief. – Lex Oct 17 '17 at 20:18