Merging Neutron Stars and the relation with Gold

Klaas S. de Boer     Argelander Institut für Astronomie, Univ. Bonn

On 16 October 2017, it was made public that gravitational waves had been detected with LIGO/VIRGO from the merging of a pair of neutron stars. The press release said, that with such mergers gold is produced, gold that from earlier similar events has landed on Earth.
This statement in the press release is correct, but the connection is tenuous and requires a lot of explaining. With this essay it will be attempted to provide the missing links.

What happened?

On 17 August 2017, the LIGO/VIRGO detector for gravitational waves recorded ripples in "space-time", lasting more than 1½ minute. This event (GW170817) was soon recognised as due to the merging of two very close neutron stars encircling each other at high speed.

Having determined the direction in the sky from where the gravitational waves came (using the LIGO/VIRGO detections *) telescopes with a wide array of instrumentation could be pointed at that event. The subsequent measurements revealed its exact position as well as confirmed earlier predictions about the behaviour of a neutron star merger.

To understand why the merging of two neutron stars leads to, as the press release indicated, the making of gold, one has to have some knowledge of:  1. gravitational waves;  2. stellar evolution, essentials of nucleosynthesis;  3. evolution of binary stars;  4. formation of stars and planets;  5. evolution of the young Earth, plate tectonics, volcanism.

1. Gravitational waves

When two very heavy objects (really heavy, like heavy stars) rotate around each other, they move inside their overlapping gravitational potential wells. Following relativity theory, such heavy objects "deform" the "fabric of space-time" in their vicinity. When these objects rotate around each other, that periodic deformation propagates through space. If they circle each other really fast, the ripples of the deformation can become strong enough to also be detected at Earth. For the first ever direct detection of gravitational waves in 2015 the prime scientists at the Laser Interferometer Gravitational-Wave Observatory received in 2017 the Nobel Prize in Physics. This is all explained in the essay on Gravitational Waves.

The essential aspect of two orbiting heavy stars is that, with time, they get closer in such a manner, that they will coalesce: they become one object. Note that the merger of two black holes cannot be seen, because no radiation whatsoever can escape from a black hole. But in the case of the event made public on 16 October, the heavy objects are neutron stars having a mass quite less than that of black holes. Therefore, radiation set free during the merger of neutron stars can be detected! For the first time, data are obtained about such events. To understand all this, and the gold, some mechanisms need explaining.

2. Stellar evolution, essentials of nucleosynthesis

The energy needed for the radiation we see from stars is foremost generated by fusion of hydrogen (H) into helium (He) in a star's centre (4 H → 1 He + radiation). After this long and stable phase, further steps in evolution involve furter steps in nuclear fusion, all providing energy to let the star radiate. Each step leads to the making of heavier elements, as follows.

After a long time most of the hydrogen in the stellar core has been burned to He and then the star adjusts it structure: it expands and now burns hydrogen in a shell around the helium-filled core. In this way, more helium is added to the core, thereby making the centre of the star denser. Then, in its very hot and dense centre, helium starts to "burn",

Reaction network to form the indicated heavier nuclei. Decay is possible, too (from de Boer & Seggewiss, 2008).

it is transformed to carbon (3 He → 1 C + radiation). This is possible only when the star has sufficient mass: the density and temperature in its centre must be high enough to come to this fusion at all.

In the same way, further fusion processes may start, clearly only when the pressure and temperature in the stellar core are high enough to also get a next fusion reaction going. In this way, He+C makes O, Ne, Mg, Si, etc. And from these elements (see Figure) a whole set of similar elements can be made. If all goes well, also iron (Fe) is made, the most dense element in the sequence. The rule is: the heavier the star, the easier it is to produce the heavier elements, but only up to Fe. In these processes there is a net gain for the star: the fusions sets more energy free than the energy needed to get it going.

To make elements heavier than Fe, there looms a problem. These more massive nuclei require energy to be formed, so energy is taken from the star to make these nuclei. This evidently does not work. Neutron capture solves the problem. If neutrons are available, they may hit charged nuclei and are taken in effortlessly, bringing the mass of the nucleus one point up. This leads to heavier elements. But this process is, inside stars, exceedingly slow.

When two neutron stars merge, the explosive nature of the merger means that also large amounts of neutrons are spread around. With ample neutrons, the neutron capture process speeds up along all nuclear routes possible. So, because in the space around two merging neutron stars all material is swamped by neutrons, all Fe-nuclei may pick up neutrons repeatedly. This leads, step by step, to the formation of all the elements heavier than iron, including copper (Cu), zinc (Zn), silver (Ag), cadmium (Cd), tin (Sn), lanthanium (La), the lanthanides (Ce, Pr, etc.) and on to osmium (Os), platinum (Pt), gold (Au), mercury (Hg), lead (Pb) and more (see periodic table). Summarizing: two merging neutron stars spread huge amounts of neutrons that can, when captured by heavy nuclei, form yet heavier nuclei, thus building elements heavier that Fe.

3. Evolution of (binary) stars

Most stars are born as pairs, even in groups. Stars in a pair circle around each other. When their

When one of two close orbiting stars evolves to the expanded red giant state, its outer layers may flow over the saddle of their joined potential well onto the other star. (image by author)

mutual distance is not too large, the outer layers of a star that had to expand because of its evolution, can float material over the saddle of the joint potential well onto the other star.

Binary stars have a multitude of possible evolution paths. What will happen exactly, depends on the initial mass of each star and on their original separation, i.e., how close they orbit each other. The more massive star of the two will expand first, but it then heaps mass on the other star to become the more massive one. Pairs starting within the right range initial conditions may end up as a pair where first one, then the other, will explode as supernova, each leaving a neutron star.

Neutron stars in a gravitational potential well will exert mutually forces on their outer layers. This friction means a loss of energy and the system therefore must become tighter. Ultimately, the two neutron stars will merge. That process will cause the above mentioned gravitational waves (in the same way as in the merger of two black holes). And such neutron star mergers will be explosive, releasing the above mentioned flood of neutrons capable of making all the heavier elements we know.

4. Formation of stars and planets

Gas was/is the building material for the formation of a galaxy. Most gas was used up in the formation of stars but plenty of gas remained free. Later, stars blowing off their outer layers or stars exploding as supernova again add to the free gas. Also the explosion being part of the merger of two neutron stars contributes to the free gas. All these gases, being dispersed into the initial gas, bring their respective mix-in of heavier elements, elements produced by nuclear fusion in the stars, during supernova explosions and in the merging process of binary neutron stars.

Heavy elements are for that reason present in the free gas of galaxies. These elements include the full range from carbon through iron up to the elements formed through the bombardment with neutrons, such as zinc (Zn), gold (Au), lead (Pb) and uranium (U). These heavy elements, in part in the form of small molecules like oxides (foremost of magnesium and silicon), slowly build up very small dust particles floating in space, making stars behind the dust look dimmer.

Stars are formed in rather dense and cool clouds of dusty gas. The cloud contracts, always with some rotation, and in its centre a proto-star may form. The remaining material ends up in a swirling dusty disk with the freshly born star at its centre. That young star will be rather hot in its central zone, and if it has enough mass, nuclear fusion will start in its core.

In the disk cool clumps will coalesce and in this way planets are formed. When planets form, their centres will be warm, even hot enough for the solid material to melt. The denstest atoms and molecules will sink to the core of the proto-planet. Since there is a lot of it, the core contains mostly iron, the atom with the highest density nucleus. Elements that are rather inert, like gold and silver, will also sink down. The lighter material, such as the silicon oxides, will float and form the outer layer of a planet. If the planet were a heavy one, its gravitational pull would also bind gases, such as oxygen and nitrogen, forming an atmosphere.

5. Evolution of the young Earth, plate tectonics, volcanism

During the formation of the Earth, the dense molten iron sank to its centre to make the core. This took with it the vast majority of the planet's other heavy elements, including the precious metals, such as gold and platinum. What remained at the surface was a thick layer of lighter material, foremost silicates, that became the crust of the Earth.

The removal of gold to the core should leave the outer portion of the Earth bereft of bling. However, precious metals are many times over more abundant in the Earth's silicate mantle than what would follow from the sinking down scenario. The planet's accessible reserves of precious metals are the result of the ongoing bombardment of meteorites.

Plate tectonics and its consequences. An oceanic plate is subducted below a continental crust. Magma chambers form and volcanoes erupt (from Wikipedia)

Millions of years after the Earth had formed, the crust became cool and stable enough to withstand that bombardment and fresh material from the dusty disk (in which star and planets had just formed) was piled up on the crust. [Text adapted from Willibold & Elliott, 2011.]

Hundreds of millions of years later, plate tectonics set in. Plate tectonics is the breaking and then moving of solid plates of crust on the softer/plastic mantle. When such plates collide, mostly one is forced to dive under the other, the other one being lifted. This is the process by which mountain ranges are formed. Then the forced down material heats up, partially melts, and froms magma. This magma will break into cracks higher up, the vertical motion being just like convection in the Earth atmosphere (warmer air rising up).

The top part of such a magma chamber will be cooled by the surrounding crust material. That forces part of the material to a condition in which it can cristallize, and the condensed and heavier cristals

Olivine cristal (left), pyrite cristal cubes, gold nugget. Images from Wikipedia.

slowly sink down to the bottom of the magma chamber. Which kind of material will cristallize, e.g. pyrite, FeS₂, or olivine, (Mg²⁺,Fe²⁺)₂SiO₄, depends on density and temperature. So each kind of cristallizing material will sink down together, concentrating each material crudely into a layer. In this manner elements that originally were spread very thinly in the crust may form layers of the stuff. In subsequent volcanic eruptions, lava flows may deposit these concentrated minerals near the surface of the Earth. These likely will de burried under further volcanic debris as well as infalling meteoritic material. All these processes will happen again and again over geological time.
This then happens to gold (Au) too, an element that hardly forms chemical bonds. It is therefore found in various places on Earth in pure form.

Nobody has actually seen the geological processes just described in operation. Their nature has been inferred from numerous studies, e.g., on the density structure of the crust (using the way shock-waves or earthquake-waves propagate), on the appearance of layers of granite, on volcanos, on lava flows, etc. etc.

The road from gold produced around two merging neutron stars  to  earthly gold nuggets is long, windy and complicated!

*   For each of the three LIGO/VIRGO detection sites, each with the two detection tubes oriented under 90 degrees, can one crudely determine a strip on the sky for the source of the signal (see Gravitational Waves). These three directions together provide a rather exact sky position. VIRGO in Europe detected only a weak signal on 17. Aug. 2017, even though its system was fully operational. Explanation: the gravitational waves arrived at VIRGO from a direction almost perpendicular to the two detection tubes, so there was hardly any stretching/shrinking of the VIRGO tubes. This provided nevertheless quite good direction information. The intersection of the LIGO/HAN, LIGO/LIV and VIRGO sky directions narrowed the search area sufficiently that optical searches discovered a "kilo-nova"-like star within a day.

Sources
Angulo, C., et al., 1999, Nuclear Physics A, 656,3
Cambridge Encyclopedia of Earth Sciences
de Boer, K.S., Seggewiss, W., 2008, "Stars and Stellar Evolution", EdPSciences
LIGO and VIRGO collaboration, 2017, Astrophys. J. 848, L12
McCaugrean, M.J., O'Dell, C.R., 1996, Astronom.J. 111, 1977
Willibold, M., Elliott, T., 2011, Nature; phys.org/news/2011
Magma chamber: https://en.wikipedia.org/wiki/Magma_chamber
Plate tectonics: https://en.wikipedia.org/wiki/Plate_tectonics

2017.11.14   neutrongold.html  Small adjustments and additions made since first posting on 2017.08.27