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Amazing infinities

"The mass of the moon in a soup spoon"

Since the recent detection of gravitational waves during the merger of two neutron stars by the LIGO-VIRGO collaboration, neutron stars have been propelled to the forefront: but what do we know about these so particular stars which, while having a spatial extension comparable to that of the city of Marseille, can be the seat of gravitational fields so intense that they could be detected from the distant galaxy NGC 4993 in the constellation of Hydra at 130 million light-years from our earth, by tiny oscillations of our interferometers ?

Francesca Gulminelli

Première observation de la coalescence de deux étoiles à neutrons, avec les signaux gravitationnel et électromagnétique associés. National Science Foundation/LIGO/Sonoma State University/A. Simonnet.)

First observation of the coalescence of two neutron stars, with associated gravitational and electromagnetic signals. National Science Foundation/LIGO/Sonoma State University/A. Simonnet.)

Like a cosmic phoenix, the neutron star is born from the ashes of dead stars, when these exceed the mass of about ten stars comparable to our sun.  When such stars have completely burned their nuclear fuel, one of the most spectacular phenomena of our cosmos takes place: the ashes of this combustion, made up essentially of iron atoms, are so massive that they collapse under the weight of their own gravity, threatening to make the residual star and its planetary systems disappear forever into the elusive depths of a black hole. But in many cases, and according to a dynamic which is not entirely understood, the strong interaction between the atomic nuclei in free fall is sufficiently important to reverse the dynamics of the collapse: the matter rebounds, and this rebound generates a shock wave which violently expels the gravitational energy accumulated during the collapse, as well as the outer layers of the star which were not yet dissociated, and thus scatters in the cosmos complex elements, dust which will be reused to build new stars, and with them new planetary systems. We can try to visualize the extreme violence of the event by knowing that its luminosity is comparable to that of a hundred billion stars, that is to say, to the luminosity of an entire galaxy: when Betelgeuse, the brightest star in the constellation of Orion, some 650 light-years away, explodes into a supernova, the event will be visible in broad daylight for several days (but 650 years later, of course…)!

It is this observation by the Kamiokande detector that allowed for the first time to demonstrate the veracity of neutrino oscillations, and thus open a wide avenue towards new physics beyond the standard model

These images, largely confirmed by observations and modelling, give however only a very incomplete idea of the event: theoretical models assure us that the energy used by the shock wave and the luminous flash corresponds only to less than 1% of the 1046 Joules of gravitational energy accumulated in the collapse, the remainder being expelled in the form of neutrinos. If a handful of these events have been recorded by astronomers and historians around the world since the first observation in China in 182 AC, most of the observational information we have on the phenomenon comes from the first and so far only detection with modern instruments and a multi-messenger mind: it is SN1987a, a famous supernova observed both in its electromagnetic spectrum and in its neutrino emission in a nearby galaxy, the Large Magellanic Cloud. It is this observation by the Kamiokande detector that allowed for the first time to demonstrate the veracity of neutrino oscillations, and thus open a wide avenue towards new physics beyond the standard model. Today, large international projects such as DUNE, Hyper-K and Halo1kT are eagerly awaiting a new detection: theorists estimate that an event of this kind should occur on average every 50 years in our galaxy, but of course the potential for discovery increases with the sensitivity of the instruments that allow to probe more and more remote regions of space. From a theoretical point of view, the possibility to extract from the neutrino signal fundamental information about its nature or properties, relies entirely on the reliability and accuracy with which we are able to model the interactions of neutrinos with the extremely dense, often non-uniform, supernova matter, as well as the elementary processes that produce neutrinos in the first place, namely the electronic capture by nuclei. This is one of the many fields where the microphysics of nuclear reactions and the macrophysics of large scale hydrodynamic evolutions meet and work hand in hand to join the two ends of the golden ribbon of the Two Infinities. We will quote many others!

Four teaspoons of neutron star in your cup ...
and you have as much matter as in the whole moon in your tea

Much more discreet, but even more astonishing than the great crashing noise of a supernova explosion, is the small, dark and compact object that remains as the residue of the explosion: the neutron star. This extraordinary star is the seat of all excesses and, even more than the supernova, the privileged playground of theorists and astrophysicists who seek to understand the extreme conditions of existence of matter. In the great Guinness Book of Records of the Cosmos, the neutron star accumulates only gold medals. Considered as a star, because it is nothing else than the residue of the explosion of a visible star, and remains detectable with extreme precision by the electromagnetic radiation it emits, its size (about ten kilometers) is comparable to that of an asteroid, although its mass equals or exceeds that of our sun. Four teaspoons of neutron star in your cup … and you have as much matter as in the whole moon in your tea.  

Courbe de lumière enregistrée pendant les 8 jours suivant l’événement multi-messager de 2017, montrant que la coalescence d’étoiles à neutrons est bien le site principal du processus r de production d’éléments lourds dans l’univers. Tiré de R.M.Drout et al , Science, 16 Octobre 2017

Light curve recorded during the 8 days following the 2017 multi-messenger event, showing that neutron star coalescence is indeed the main site of the heavy element production r process in the universe. From R.M.Drout et al , Science, 16 October 2017

The idea of a star at a temperature close to absolute zero, which could be composed entirely of neutrons, at such a density that the gravitational pressure could be entirely counterbalanced by the quantum pressure of the zero point and the repulsive part of the nuclear force, was put forward as early as 1934 by W. Baade and F. Zwicky, shortly after the discovery of the neutron. At that time, it was essentially an exercise of thought, because it was not at all clear where all these neutrons could come from: indeed, the universe is essentially composed of hydrogen, and the neutron is an unstable particle that turns into a proton after a few minutes! 

The first detection of a neutron star was made in 1967 by the famous astrophysicist Jocelyn Bell, who was working on her doctoral thesis at Cambridge University at the time. The observation of perfectly regular, temporally spaced radio pulses from a region of space where no light candidates could be observed was so disturbing that the operation was called LGM (“Little Green Man”) and initially kept under military secrecy for the possible implications in terms of communication with intelligent extraterrestrial life.

Today we know that the periodic nature of the radio pulses is due to the presence of huge magnetic fields on the surface of the stars, fields that we believe can reach a million billion Gauss in their interior (by comparison, the Earth’s magnetic field is about half a Gauss). These magnetic fields, unequalled in the cosmos, whose origin is still a subject of vast debate, concentrate the radiation of the star along the lines of the fields close to the axis of rotation of the star, which thus behaves like a lighthouse. The measurement of the period of the pulses and its variation allows us to know the period of rotation of the star. And without surprise we know today that the fastest rotating objects in our galaxy, with a speed at the equator of about a quarter of the speed of light, as well as the fastest stars, with speeds exceeding a thousand km per second, are all neutron stars! 

It would be constituted of an unpublished matter elsewhere in the universe

That large classes of objects, classified differently by astronomers according to the characteristics of their radiation as pulsars, magnetars, X-ray binaries, gamma-ray repeaters, etc., are all neutron stars, in different phases of their lives and in different environments, is also now largely accepted thanks to the work of nuclear theorists who have been able to explain all the observed phenomena within the framework of a single model of the star.  It would be constituted of a matter unseen elsewhere in the universe: a quantum plasma in strong interaction where protons, electrons and neutrons are in a state of equilibrium with respect to all nuclear reactions. 

In the understanding of the internal structure of the neutron star, the continuous and close collaboration between observers and nuclear theorists is an almost shadowless success story. A convincing example is the measurement of masses. Indeed, many of these stars are found in binary systems, either with another neutron star, or with a “traditional” star that can be followed in its orbital movements with standard astronomical methods. The interpretation of the trajectory of the companion star given by Kepler’s laws, corrected to take into account the effects of general relativity, allow to estimate with an accuracy of only a few percent the mass of the neutron star. However, the very principle of equilibrium imposes that, for a given radius, the mass of the star is exclusively determined by the internal pressure exerted by its constituents, called “equation of state”. Thus, the nuclear physics models that allow to estimate the equation of state can be directly confronted with the observational measurements of neutron stars. To cite only one example of the abundant discoveries of the last few years, these observations have already made it possible to exclude an important contribution of strange particles (kaons, hyperons) in the core of neutron stars.

The most spectacular confirmation of the quality of theoretical predictions concerns
the much publicized discovery of gravitational waves during the merger of
two neutron stars on August 17, 2017. 

The very existence of such a signal, its modification in the last seconds before the merger due to the tidal deformation of the two massive bodies at very small distance, and especially the associated electromagnetic signal in the form of a gamma-ray and X-ray burst in the seconds following the merger, all these signals were predicted by the theory for many years. Even more spectacular, the combined observation of light in the visible range by a large number of ground-based telescopes around the world has confirmed the “kilonova” scenario, according to which a large part of the synthesis of elements rich in neutrons heavier than Iron, called the “r” process, would be produced by the rapid capture of neutrons in the core of the star on the Iron nuclei that compose its solid surface, a capture made possible by the high densities and temperatures involved in the fusion.

A next major challenge concerns the possible presence of deconfined matter, i.e. a plasma of quarks and gluons, such as it existed only at the very beginning of our universe and seeks to be ephemerally reproduced in very high energy colliders. The combined observations of masses and radii will probably allow to answer this question in the very near future. Once the composition of the neutron star core is clarified, the precise anatomy of the equation of state will allow us to address even more fundamental questions, such as the viability of different alternative gravity theories. 

In this vast project of study of the hyper-dense matter, the two infinities continuously rub shoulders and enrich each other.

On the infinitely small side we can mention the combined effort of laboratory experiments on core matter such as the measurement of the charge radius of the Lead nucleus and the collective motions in heavy ion collisions, as well as the constant progress in the reliability of ab-initio nuclear calculations. The increasingly accurate models that arise from these studies will be able to be confronted with a number of observations that come from the macro-cosmos: more statistical observations of fusion events by the new LIGO-VIRGO campaigns, the combined analysis of X-ray emission for radius measurements by NICER, and especially the observations by the new Einstein Telescope project of gravitational waves emitted by the super-massive and highly distorted neutron star that results from the coalescence.

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