The results presented in this news release have just been complemented by a third article which demonstrates that the gamma function is invariable also for planets like our own, super-Earths, neutron stars, hybrid stars and quark stars. (The latter is a hypothetical type of star which results from the decay of a neutron star when the neutrons that compose it, due to the high pressure generated by the star’s own gravity, break up into their constituent elements: quarks).  

It has likewise been found that the stability criterion for neutron stars defined in previous articles, which describes the conditions necessary for stars to remain stable and not collapse into black holes, applies equally to hybrid stars, quark stars and neutron stars in their preliminary phases.  

Finally, Antonio Claret (IAA-CSIC) simulated a supernova explosion of a star of forty solar masses in order to study the behaviour of the gamma function at the onset of formation of black holes and found that it does indeed vary during the implosion of supernova nuclei as well as during rebounds (during which a peak is reached). Applying the stability criterion born of his previous work, stars can be seen to lose stability and finally collapse into black holes.

However, just before this happens the star recovers the gamma value present in the phases prior to the main sequence.  “Thus, the gamma function is recovered like a fossil at the end of the life of a star, any star, including black holes,” the researcher concludes.


A. Claret. Neutron, quark, and proto-neutron stars at the onset of formation of black-holes: the memory effect. Astronomy & Astrophysics . DOI: http://dx.doi.org/10.1051/0004-6361/201322024


Stars experience changes in mass, pressure, composition and internal structure throughout their life and, as combustible material runs out, give rise to compact objects such as white dwarfs, neutron stars or black holes. One might expect that such an agitated development, which includes explosive episodes like supernovae in the case of massive stars, would prevent stars from preserving in their old age any feature characteristic of their initial stages. However, a study by Antonio Claret of the Institute of Astrophysics of Andalusia (IAA-CSIC) concludes that, in a certain sense, stars have “memories”.

Gráfico que muestra los distintos caminos evolutivos de las estrellas dependiendo de su masa. Fuente: NASA/CXC/M. Weiss

These memories (called, in mathematical terms, the gamma function) are related to three stellar parameters: potential energy of the star, derived from the fact that stars are self-gravitating gaseous spheres, moment of inertia, which describes resistance to rotation and is linked to internal distribution of mass (just like the rotary speed of an ice skater is linked to the stretching or bending of her limbs), and level of compactness.

“We have studied the behaviour of gamma functions from initial to final stages of stellar development and have come to the conclusion that, while they remain constant during the initial stages of the main sequence or juvenile stage, the constancy disappears entirely during the adult phase; it varies dramatically and can reach values thousands of times greater than in the initial stages” says Antonio Claret (IAA-CSIC).

The fascinating thing, however, is that after the final adult stages and the violent processes that occur when the combustible material runs out, when stars reach the state of compact objects (white dwarf or neutron star) they recover the constant values they possessed in the juvenile stage. “It is interesting that this function should be lost during adulthood and reappear during the final stages. It is behaviour akin to fossils: after virtually disappearing, they re-surface and give us information about the original organisms,” Claret observes. 

The study by Claret, published in two scientific articles, also delves into the reasons for the effacement and later resurgence of these constants in the life of stars. There is a correlation between the amount of energy generated in the nucleus of a star and the variations of a gamma function. “We have also extended this research to giant planets between one and fifty times the mass of Jupiter, and they follow the same pattern, the only difference being that their gamma function remains constant throughout their life because they have no nuclear activity. This really seems to be a universal function,” Claret concludes.  


This research has been of special interest with regard to neutron stars, an extremely compact type of object which may have a mass equivalent to that of the sun compressed into a diameter of approximately 14 kilometres. 

Neutron stars are one way massive stars can end their life after ejecting every layer in a supernova explosion and keeping only the nucleus. If the mass of the original star is less than twenty solar masses it will give rise to a neutron star; if it is greater than that it will contract until its density becomes infinite and finally produces a black hole.  

“It is very surprising to find that a gamma function is recovered even after a supernova explosion,” says Claret (IAA-CSIC). Based on his study Claret has been able to establish a stability criterion for neutron stars which not only describes what conditions they must fulfil to preserve their stability and not collapse into a black hole but also makes it possible to choose between available models the one that best describes the internal structure of these objects. “We are presently investigating the implications of those conditions for the onset of black hole formation,” he adds.

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