Time evolution of protoneutron stars

Protoneutron stars are compact, hot and neutrinos rich object whose life duration is among the shortest in the Universe. There is indeed less than one minute between their birth following a successful gravitational supernova and the appearance of a black hole or a neutron star. Yet, a lot of complex phenomena happen during these seconds, since it is long enough for the protoneutron star to contract, cool down and to lose all its neutrino content. One of the key issues in the study of protoneutron stars is the determination of their rotation profile and its influence on their evolution. In this spirit, a team composed of researchers of the Paris-Meudon Observatory and the Universities of Valencia and Alicante (Spain) recently studied the thermodynamical evolution of rotating protoneutron stars, basing their work on the most recent results about massive stellar cores evolution and predicting in this way the possible appearance of hydrodynamical instabilities, that can be source of gravitational wave emission shortly after the peak in the neutrino luminosity. 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). Figure 1. A composite image of the Crab Nebula showing the X-ray (blue), and optical (red) images superimposed. The size of the X-ray image is smaller because the higher energy X-ray emitting electrons radiate away their energy more quickly than the lower energy optically emitting electrons as they move. The inner ring is about one light year across. (Credits : X-ray : NASA/CXC/ASU/J. Hester et al. ; Optical : NASA/HST/ASU/J. Hester et al.)Click on the picture to enlarge. Once the explosion ended and the external mass is ejected, the central remnant is a very dense object : a protoneutron star. Depending on the initial conditions, in the following seconds or minutes, it cools down to become a neutron star or collapses into a black hole. For the rest of this text, the birth of a neutron star is assumed, which is probably the most current outcome. The evolution of a protoneutron star is usually classified in three main stages : the mantle contraction during which fast cooling of the outer regions takes place in about 0.5 s, with probably significant accretion and convective motions ; deleptonization and consequently heating of the internal core as energetic neutrinos diffuse out leaving most of their chemical energy (analogously to Joule effect) on the way out ; cooling by means of diffusion of (mostly) thermal neutrinos, resulting in a decrease of temperature in such a way that the protoneutron star finally becomes transparent to neutrinos (when the temperature falls below 1 MeV). The final result is a young neutron star. 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. Figure 2. Illustration of rotation and density profiles reached with simulations of massive stars core collapses. Notice that the rotation profile is not constant (differential rotation) but that for every profile, the characteristic length is the same. Moreover, these profiles are well-fitted with a simple function also depicted on the figure. For more details, see Villain et al. (2004). Click on the picture to enlarge. The rotation profiles reached in this way were recently used to study the evolution of rotating protoneutron stars [Villain et al (2004)]. In this work, differential rotation, even if less strong than thought in the past, turns out to be quite relevant for several reasons, for instance possibly changing the shape of the star. Indeed, for rotation profiles characterized by variations of the angular velocity on short scales (some km), protoneutron stars seem to possibly acquire a non-convex shape, with a central density becoming smaller and smaller as the star accelerates while contracting. This phenomenon is illustrated on Figure 3 that depicts the shape of a rotating protoneutron star (1 s old) for 2 different rotation profiles. In the first case, the angular velocity is quite homogeneous. Thus, for high angular velocities, a classical shape is reached : the equator looks like a kind of "line made of singular points". This can be easily understood by the fact that the faster a star rotates, the higher is the centrifugal force acting on the matter. Thus, for every rotating star, there is a maximal angular velocity (called Kepler velocity) at which the gravitation just compensates the centrifugal force and the star starts losing matter. Figure 3 (left) then illustrates the typical shape of a star at the mass-shedding limit when matter is in a very unstable equilibrium at the equator. Figure 3 (Left) Iso-density lines for an 1 s old rotating protoneutron star in very rapid rotation (more than 99% of the Kepler velocity) but with very weakly differential rotation. The surface of the star is represented by a larger line. The shape is "usual". Click on the pictures to enlarge. Figure 3 (Right) Same picture for the same star but with strongly differential rotation. Although the central angular velocity is some 4.5 times larger than in the Figure of left, the equatorial matter is not about to be lost, but the shape is completely changed. 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)