ЯДЕРНАЯ ФИЗИКА, 2008, том 71, № 6, с. 1114-1120
= ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
STELLAR MATTER IN SUPERNOVA EXPLOSIONS AND NUCLEAR MULTIFRAGMENTATION
© 2008 A. S. Botvina1), I. N. Mishustin2)'3)
Received August 21, 2007
During the collapse of massive stars and the type-II supernova explosions, stellar matter reaches densities and temperatures which are similar to the ones obtained in intermediate-energy nucleus—nucleus collisions. The nuclear multifragmentation reactions can be used for determination of properties of nuclear matter at subnuclear densities, in the region of the nuclear liquid—gas phase transition. It is demonstrated that the modified properties of hot nuclei (in particular, their symmetry energy) extracted from the multifragmentation data can essentially influence nuclear composition of stellar matter. The effects of the modification of nuclear properties on weak processes and on the nucleosynthesis are also discussed.
PACS:26.50.+x, 25.70.Pq, 21.65.+f
1. INTRODUCTION
Properties of matter at densities close to nuclear one are crucial for many natural processes. A spectacular event in astrophysics is the type-II supernova explosion which releases of about 1053 erg of energy, or several tens of MeV per nucleon [1]. When the core of a massive star collapses, it reaches densities several times larger than the normal nuclear density po & 0.15 fm_3. The repulsive nucleon—nucleon interaction gives rise to a bounce-off and creation of a shock wave propagating through the in-falling stellar material. This shock wave is responsible for the ejection of a star envelope that is observed as a supernova explosion. During the collapse and subsequent explosion the temperatures T & 0.5—10 MeV and baryon densities p & (10~5 — 2)p0 can be reached. As shown by many theoretical studies, a liquid— gas phase transition is expected in nuclear matter under these conditions. It is remarkable that similar conditions can be obtained in energetic nuclear collisions in terrestrial laboratories, which lead to multifragmentation reactions.
Multifragmentation, i.e., breakup of nuclei into many small fragments, has been observed in nearly all types of nuclear reactions when a large amount of energy is deposited in nuclei. It includes reactions induced by protons, pions, antiprotons, and by heavy ions of both relativistic energies (peripheral collisions)
'■'Institute for Nuclear Research, Russian Academy of Sciences, Moscow.
2)Frankfurt Institute for Advanced Studies, J.W. Goethe University, Frankfurt am Main, Germany.
3)Kurchatov Institute, Russian Research Center, Moscow.
and "Fermi" energies (central collisions) [2—9]. According to the present understanding, multifragmen-tation is a relatively fast process, with a characteristic time around 100 fm/c, where, nevertheless, a high degree of equilibration is reached. The process is mainly associated with abundant production of intermediate mass fragments (IMF, with charges Z & 3—20). However, at the onset of multifragmentation, also heavy residues are produced which have previously only been associated with compound-nucleus processes. At very high excitation energies, the IMF production gives way to the total vaporization of nuclei into nucleons and very light clusters.
2. LIQUID-GAS PHASE TRANSITION IN NUCLEAR MATTER
The multifragmentation reaction can be considered as an experimental tool to study the properties of hot fragments and the phase diagram of nuclear matter at densities p ~ 0.1p0 and temperatures around T & 3—8 MeV which are expected to be reached in the freeze-out volume. In Fig. 1 we demonstrate a schematic phase diagram of nuclear matter, which, as widely believed, contains a liquid-gas phase transition. In the density range (0.3—0.8)p0 the matter is in a mixed phase. This phase is strongly inhomo-geneous with intermittent dense and dilute regions characterized by different topologies. These configurations are generally called the nuclear "pasta" phases [10, 11]. They were recently under intensive theoretical investigation [12, 13]. However, at lower densities p < 0.3p0, which are considered in this paper, the matter breakup into compact clusters of nearly spherical shape. These low densities dominate
STELLAR MATTER IN SUPERNOVA EXPLOSIONS T, MeV
101
100
Nucleón gas
I
Is
0
1
S = 4 S = 2
S = 1
Multifragmentation
10-
10
-3
10
-2
10-
100 p/p0
Fig. 1. Nuclear phase diagram on the temperature—density plane. Solid and dotted curves give borders of the liquid—gas coexistence region and the spinodal region. The shaded area corresponds to conditions reached in nuclear multifragmentation reactions. The dashed curves are isentropic trajectories characterized by constant entropies perbaryon (S = 1, 2, and 4).
during the main stages of collapse and explosion. The shaded area indicates the region of densities and temperatures which can be studied in nuclear multifragmentation processes. We have also shown isentropic trajectories with S/B values of 1,2, and 4 typical for supernova explosions. One can see, for example, that a nearly adiabatic collapse of the massive stars with typical entropies of 1 —2 per baryon passes exactly through the multifragmentation area.
As a model which can provide connection between nuclear multifragmentation and astrophysical processes we take the Statistical Multifragmentation Model (SMM), for a review, see [2]. As demonstrated by many analyses [3—9], the model describes experimental data very well. Since the SMM can be applied both for finite systems and in the thermodynamical limit for infinite systems, it may be generalized for supernova conditions, where a nuclear statistical equilibration is usually expected. This generalization was performed in [14, 15] by including effects of electron, neutrino, and photon interactions in stellar matter. Under supernova conditions one can use the Grand Canonical approximation, therefore, one can write the density of nuclear species (pAZ) with mass
A and charge Z as
Vf A3/2
PAZ =gAZ
VX3T
exp
iFAZ - ßAz)
(1)
Here, gAz is the ground-state degeneracy factor of
1 /9
species (A, Z), XT = (2nh9/mNT) 1 is the nucleon thermal wavelength, mN k> 939 MeV is the average nucleon mass. Vf is so-called free volume, which accounts for the finite size of nuclear species in the actual volume V. FaZ is the free energy of fragments which is calculated under model assumptions [14]. The chemical potentials haZ one can find from the baryon number and charge conservations for a considered electron fraction in the matter. In the case of the full equilibrium including electroweak processes, these potentials are connected with electron and neutrino chemical potentials [14].
The SMM describes a coexistence of large nuclei and nucleon gas at subnuclear densities by calculating all produced species. It is instructive to investigate details of the phase transition, in particular, how do large nuclei disintegrate into nucleons by increasing temperature, or by decreasing density. In Fig. 2 we demonstrate the results of SMM calculations both
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Relative yield
Fragment mass number A
Fig. 2. Relative yields of fragments per nucleon (top panel) in multifragmentation of Au sources and (bottom panel) in supernova environment at the electron fraction Ye = 0.2 per nucleon and the density of 0.1 po. The calculations at (top) excitation energies of 3, 5, and 8 MeV per nucleon, and (bottom) different temperatures T are shown by different curves. Effects of the reduced symmetry-energy coefficients y are also demonstrated (top and bottom).
for multifragmentation of Au sources at different excitation energies and for a stellar matter with density, electron fraction, and temperatures expected during the collapse of massive stars and supernova explosions. One can see that the evolution of mass distributions with increasing excitation energy is qualitatively the same for both the nuclear multifragmentation reactions and the supernova process. The smooth transition with energy (and with temperature) from the "U-shaped" mass distribution to the exponential distribution is taking place in both cases. This is a characteristic feature of the nuclear liquid—gas phase transition. In the both cases we obtain very broad distributions of produced fragment. However, in the supernova environments much heavier and neutron-rich nuclei can be produced because of screening effect of surrounding electrons.
In Fig. 3 we show evolution of the mass distribution of fragments produced in stellar matter at typical conditions of low densities and a temperature,
where we also expect the phase transition. We do not have any sudden disintegration of heavy nuclei, but a continuous modification with decreasing density. Actually, at the density of transition from the "U-shape" 0.18p5 = 0.18 x 10-5p0 shown in the figure, the mass distribution can be parametrized by a so-called A-T law. At this point the т reaches a minimum which can be connected with properties of fragments and the phase transition [16]. These examples clearly demonstrate that it is not possible to approach correctly the phase-transition region by characterizing the "liquid" phase only by one "average" nucleus, as some models assume [17].
3. IN-MEDIUM MODIFICATION OF NUCLEAR PROPERTIES
Multifragmentation opens a unique possibility to investigate the coexistence part of the nuclear phase
STELLAR MATTER IN SUPERNOVA EXPLOSIONS
1117
Relative yield
Fig. 3. Fragment evolution during the phase transition: mass yields of fragments (per nucleon) produced at Ye = 0.4 and T = 1 MeV at small densities shown by curves.
diagram. In particular, the "in-medium" modifications of properties of hot nuclei are very important for astrophysical applications [14, 15]. Recently, the symmetry energy of hot nuclei was extracted in [18], and it was demonstrated that it decreased considerably from the values expected for cold isolated nuclei with increasing exci
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