The main activity of stars during their whole life is to fight against gravity, despite it was the responsible of their birth. Indeed, the history of every star begins with an initially dispersed cloud which contracts due to its own weight. With time, temperature and density increase, and nuclear reactions are ignited if the total mass of the cloud (and thus the pressure) is high enough : the mass of the cloud has to be at least 10% of the mass of the Sun. In the core of what is now a protostar, hydrogen is burning, and heavier elements, the first of which is helium, are produced. Because of these nuclear reactions, energy is generated which creates pressure to counter-balance gravity. The star has just entered in what is called "the main sequence". The duration of the period during which the star no longer evolves, just burning hydrogen, depends of its rate of burning which is ruled by the initial mass : for more massive stars it lasts just some millions of years, but it could take up to 10 billions for less massive stars. When the main part of the hydrogen of the core has disappeared, the latter becomes steril. Then, hydrogen of the surrounding layers starts to be consumed, which is done simultaneously with the expansion and the cooling of the external layers. The star leaves the main sequence. In the core, the degeneracy pressure of electrons is now the main source of resistance to gravitation. Yet, the slow contraction goes on, and after about one billion years, the helium of the core starts to react too, producing heavier elements as carbon, nitrogen and oxygen. The next step in the evolution of the star depends on its initial mass : if this mass was too small, the star becomes sterile once every possible "fuel" has burnt. In this case, we are left (after some adventures) with a small (a radius similar to the Earth radius), dense (the same mass as the Sun, something like one million times the Earth mass) corpse with a variable composition (a layers structure whose central element is the one which was the heaviest produced) : a white dwarf, damned to slowly cool down ; but if the initial mass of the star is high enough (which will be assumed in the following), there are nuclear reactions up to the production of iron nuclei that concentrates in the middle of the "onion-like structure" of the star. The 56Fe element is the most stable and cannot produce anything else. This iron then starts to accumulate, and when the mass of the iron core reaches the threshold value of Chandrasekhar ( 1.2 solar masses), the core suddenly collapses due to its self-gravity. This collapse implies an increase of the density that creates the appearance of electron captures e + p -> &#957 + n that makes some electrons disappear, which decreases the main source of resistance to gravitation and hence accelerates the collapse. Yet, when the density reaches values of the order of 1011 grammes per cube centimeters, for a temperature around 1011 K, the matter suddenly becomes opaque to the produced neutrinos (&#957). Thus, the collapse is now adiabatic until some 10 ms after its beginning, moment when the central density is close to the saturation density &#9610 2.6 1014 g.cm-3. This value is in fact also typical of nuclear matter inside atomic nuclei, which is not by chance : it corresponds to a mean distance between nucleons that minimizes the energy per nucleons. Thus, if the matter is compressed beyond this density, the strong interaction becomes repulsive. As the iron core is freely falling and collapsing, it can have such a huge kinetic energy that even the strong interaction does not stop the collapse and a black hole may appear. Yet, if the kinetic energy is not high enough, the fall of the matter ends with a bounce of the inner part while the outer part is still falling. This creates a shock-wave that expels the external layers with a strong electromagnetic emission : a type Ib, Ic or II supernova happens (see Figure 1 which depicts the remnant of a type II supernova now known as the famous Crab nebula).

The preceding story is well-known, as far as we forget about rotation. But neutron stars are rapidly rotating objects, since the angular momentum is (almost) conserved during the collapse of the iron core. Thus, their period at birth could be as small as some milliseconds. But, the effects induced by rotation in protoneutron stars such as lower inner densities, which results in faster diffusion of neutrinos and heat could be quite important. The protoneutron star could slow down, speed up or even change dramatically its evolution (becoming unstable). Furthermore, the collapse of the iron core does not happen in an exactly spherical way, which should generate a quite complex profile of rotation, showing to differential rotation. This expected prediction is now supported by recent numerical simulations of core collapse of massive stars, as shown on Figure 2.

On the other hand, what appears on Figure 3 (right), is that if one "accelerates more and more" a protoneutron star with strongly differential rotation, before the object reaches a shape characteristic of the Kepler velocity [Figure 3 (left)], the central density decreases making the fluid to adopt a doughnut-like shape. This phenomenon had already been predicted by other theoretical studies in the past for rotating fluids (among them protoneutron stars), but up to now it was not proved to be relevant for realistic scenarios of evolving protoneutron stars. Furthermore, the possibility to "observe" such a phenomenon (by its implications on some radiations for instance) strongly depends on the rotational kinetic energy (and then angular momentum) contained in a baby protoneutron star. But this value is still poorly known, the effect of magnetic field during the iron core collapse being also quite undetermined. Hence, some recent calculations [see Heger et al. (2003)] predict that the magnetic braking could be very efficient to slow down the core. Yet, even in this case, the evolution of the resulting rotating protoneutron star could involve an even more interesting phenomenon potentially detectable in the gravitational waves detectors currently operating or in the final stages of calibration : the fast growth of a hydrodynamical instability some seconds after the peak in the neutrino luminosity (detectable by neutrino detectors such as SuperKamiokande) [Villain et al. (2004)]. The detection of such a gravitational wave event in coincidence with the detection of neutrinos coming from a galactic supernova would be a very useful source of information to improve both our knowledge of the structure of the matter at very high densities and our knowledge of the initial states of black holes and neutron stars. But for this dream to happen, a lot a work is still needed, both in the theoretical study of relativistic stars and data analysis.

References

• L. Villain, J.A. Pons, P. Cerdá-Durán and E. Gourgoulhon, Evolutionary sequences of rotating protoneutron stars, Astron. & Astrophys., in press astro-ph/0310875 J.A. Pons et al. , Evolution of PNSs, ApJ, 513, 780-801 (1999) A. Heger et al. , astro-ph/0301374 to appear in Stellar Collapse (Astrophysics and Space Science) edited by C.L. Fryer (2003)

Contact

• Loïc Villain (Universitat de Valencia and Observatoire de Paris, LUTH)
• Eric Gourgoulhon (Observatoire de Paris, LUTH)