Contracting Systems of Hyperons and the Evolution of Stars
Abstract Generated abstract
The paper examines the speculative possibility that hyperon matter may lack nuclear saturation and therefore contract into compact strongly interacting objects termed collapsons. It argues that such objects, if formed during neutronization at stellar densities, could absorb nucleons or neutrons through strong interactions with substantial energy release, potentially affecting gravitational collapse and the late evolution of massive stars. A simple balance model is also developed for a self-sustaining neutron absorption process in mixed matter containing collapsons and ordinary nuclei, yielding threshold conditions for its occurrence. The paper suggests that these mechanisms could provide energy sources for quasars or galactic nuclei, while emphasizing that the underlying assumptions about hyperon interactions remain unproved.
Full Text
Contracting Systems of Hyperons and Stellar Evolution
V. A. Filimonov
(Presented by the Scientific-Technical Seminar of the High-Energy Laboratory of the Research Institute of Nuclear Physics)
Despite considerable efforts, it has so far not been possible to determine fully the reasons preventing the contraction of nuclear matter into a region of the size of the range of action of nucleon-nucleon forces. The difficulties of establishing a definite mechanism to explain saturation in nuclear matter make it possible to regard this property as accidental, inherent only in nucleons and not necessarily applying to other baryons. For example, one cannot be certain that systems of hyperons will behave like ordinary nuclei. Therefore one should take into account the possibility that such systems do not possess the property of saturation [1, 2].
In the absence of saturation, a system of hyperons will form a compact object of a size on the order of the Compton wavelength of the \(\pi\)-meson, resembling a strongly interacting particle. Such objects were called collapsons [3].
In [4] some properties of contracted systems of hyperons were considered. It was found that, under certain assumptions concerning the forces acting inside a collapson, it will be stable if its baryon number \(A>A_y\approx 50\). In this case nuclei with \(A>A_y\) acquire the possibility of collapse through the weak interaction with the transformation of nucleons into hyperons. This is an \(A_y\)-th order process in the weak interaction. The estimated lifetime of nuclei with respect to such a process is \(\tau \sim 10^{12A_y-33}\) years. This lifetime is so large that such a transformation of nuclei should be regarded as impossible.
At present, because of the absence of a theory of strong interactions, it is impossible to predict the properties of collapsons. But one can propose some features of their behavior. First of all, one should note their ability to absorb nucleons in the strong interaction with the formation of \(K\)-mesons in order to balance hypercharge:
\[ C^A + N \to C^{A+1} + K + n\pi . \tag{1} \]
In (1), \(C\) denotes a collapson, \(\hat A\) its baryon charge. We shall assume that in process (1) the rest mass of the nucleon is transformed into the mass of the \(K\)-meson, pions, and the kinetic energy of the final products.
The conditions necessary for reaction (1) to occur depend on the charge of the collapson. For a given \(A\) there exists a charge \(Z\) at which the collapson has the least mass and, consequently, is stable. In the plane \((A, Z)\), stable collapsons will corre-
some line. This line is schematically shown in Fig. 1 by the solid curve. In vacuum, collapsons will decay, approaching in the \((A, Z)\) plane the stability line along vertical straight lines. In matter, a negatively charged collapson will be captured by nuclei and will absorb nucleons. Its baryon number then increases, and in the \((A, Z)\) plane it moves to the right along a certain trajectory, which in Fig. 1 is schematically indicated by a dashed line. The process of absorption of nucleons by the collapson will continue until its charge becomes positive. Then, after undergoing decays, the collapson will reach the stability line and will remain in this position for practically an infinitely long time, since its interaction with nuclei will be suppressed by the Coulomb barrier. A positive collapson behaves in matter like ordinary nuclei. (Under certain conditions, in matter consisting of two components—the collapson and nuclear components—a self-sustaining process of neutron absorption may arise. This possibility will be considered below.)
Fig. 1. Trajectory of a collapson (dashed curve) in the \((A, Z)\) plane during absorption of nucleons and decays.
The energy generated by a negative collapson in matter is determined by the mean time between two successive acts of reaction (1). If this time is taken to be \(t \sim 10^{-10}\) s, then the generated energy will be \(\sim 10^{7}\) erg/s. Positively charged collapsons will be active in a neutron medium. In neutron matter at nuclear density the time of occurrence of processes under the action of strong interactions is \(\sim 10^{-22}\) s. The generation of energy by a single collapson in such a medium may proceed at a rate of \(10^{19}\) erg/s.
Collapsons cannot arise as a result of decays of ordinary nuclei. But they may form at a certain stage of stellar evolution in the process of neutronization of matter. As calculations show [5], when neutron matter reaches a density of \(\approx 3 \cdot 10^{14}\) g/cm\(^3\), a hyperon component begins to arise in it. It is usually assumed—without sufficient grounds—that it behaves like nucleon matter and, in particular, possesses the same property of saturation. In the absence of saturation, hyperons will contract into collapsons, and the latter will interact energetically with neutrons. Neutronization of matter occurs as a result of gravitational compression. The attainment of densities at which collapsons begin to form will lead to the switching on of a powerful mechanism of energy generation due to process (1). Since the rate and magnitude of the energy release are large, such a process may not only halt further gravitational collapse, but also disperse the matter compressed by gravitational forces.
In light of what has been said, one cannot regard as sufficiently substantiated the conclusions that the final stage of the evolution of high-mass stars is the formation of a self-closed object—a “black hole.” This is only one of many possibilities allowed by the existing uncertainties in the understanding of the strong interactions of elementary particles.
Let us now consider the above-mentioned self-sustaining process of neutron absorption by collapsars in matter. Suppose there is matter consisting of two components. One component has, as atomic nuclei, positively charged collapsars; the second consists of ordinary nucleon nuclei. When a collapsar absorbs an incidental neutron, a reaction of “annihilation” of the neutron (1) occurs, with the formation of a \(K^+\)- or \(K^0\)-meson and several \(\pi\)-mesons. Additional \(\pi\)-mesons arise in the decay of \(K\)-mesons. On average, for one act of neutron “annihilation,” one should expect the formation of approximately one negatively charged \(\pi\)-meson. If the density of matter is sufficiently large \((>1\ \mathrm{g/cm^3})\), \(\pi^-\)-mesons will be captured by nuclei. Absorption of \(\pi\)-mesons by nuclei proceeds mainly through the quasi-deuteron mechanism, according to the scheme \(\pi^-+d\to n+n\), with the formation of at least two neutrons. The emitted neutrons, in turn, have a certain probability of being captured by collapsars, etc. As a result, a self-sustaining process of neutron absorption may arise.
This process will lead to the appearance of neutron and \(\pi^-\)-meson fluxes with certain flux densities \(j_{\mathrm n}\) and \(j_\pi\), respectively. Let us introduce the notation: \(\sigma_{\mathrm{nN}}\), \(\sigma_{\mathrm{nK}}\), \(\sigma_{\pi\mathrm{N}}\), \(\sigma_{\pi\mathrm{K}}\) are the average cross sections for absorption of neutrons and \(\pi^-\)-mesons by nuclei and collapsars; \(\rho_{\mathrm N}\), \(\rho_{\mathrm K}\) are the numbers of nuclei and collapsars per unit volume, respectively; \(\nu_\pi\), \(\nu_{\mathrm n}\) are the mean yields of \(\pi^-\)-mesons and neutrons per act of absorption of a neutron by a collapsar and of a \(\pi^-\) by a nucleus, respectively. Then in the steady state we shall have
\[ j_{\mathrm n}\left(\sigma_{\mathrm{nN}}\rho_{\mathrm N}+\sigma_{\mathrm{nK}}\rho_{\mathrm K}\right) -j_\pi\sigma_{\pi\mathrm N}\nu_{\mathrm n}\rho_{\mathrm N}=0, \]
\[ j_{\mathrm n}\sigma_{\mathrm{nK}}\rho_{\mathrm K}\nu_\pi -j_\pi\left(\sigma_{\pi\mathrm N}\rho_{\mathrm N}+\sigma_{\pi\mathrm K}\rho_{\mathrm K}\right)=0. \tag{2} \]
From the solvability conditions for this system follows the condition under which the existence of a self-sustaining process is possible:
\[ \nu_{\mathrm n}\nu_\pi \geq 1+x+2\sqrt{x}, \tag{3} \]
\[ x=\frac{\sigma_{\mathrm{nN}}\sigma_{\pi\mathrm K}}{\sigma_{\mathrm{nK}}\sigma_{\pi\mathrm N}}. \]
If one takes \(\nu_{\mathrm n}\nu_\pi \approx 2\), then for the maximum possible value of \(x\) we obtain the estimate \(x_{\mathrm m}\approx 0.17\). The minimum possible value of the collapsar density will then be
\[ \rho_{\mathrm K\,min}= \left(\sigma_{\mathrm{nN}}/\sigma_{\mathrm{nK}}\right)\rho_{\mathrm N}/x_{\mathrm m}^{1/2}. \tag{4} \]
Absorption of neutrons by nuclei proceeds by radiative capture, whereas absorption of neutrons by collapsars is effected through the strong interaction (1). Therefore one may assume that \(\sigma_{\mathrm{nN}}/\sigma_{\mathrm{nK}}\sim 0.01\). Then, for the minimum concentration of collapsars at which establishment of a self-sustaining process is possible, we shall have the estimate
\[ \rho_{\mathrm K\,min}\sim 0.02\rho_{\mathrm N}. \tag{5} \]
In constructing models of quasars and galactic nuclei, the principal difficulty that must be faced is the absence of sufficiently long-acting energy sources capable of sustaining the observed radiation of these objects. In the cases considered here
processes, energy is generated on scales exceeding the energy release in all other known phenomena occurring in ordinary matter. It may be supposed that varieties of collapse processes take place inside quasars and galactic nuclei.
According to existing estimates, the mass of a quasar is \(M \sim 10^{43}\) g, and the power of its radiation is \(\sim 10^{47}\) erg/s [6, 7]. To provide such radiation through the absorption of neutrons by collapsars in neutron matter, it is necessary to admit the existence in it of \(\sim 10^{28}\) collapsars, which amounts to \(10^{-39}\) of the number of nucleons. It is believed that the lifetime of a quasar is \(\sim 10^{14}\) s. During this time the baryon charge of each collapsar in the medium will increase by \(10^{36}\) units.
If the self-sustaining process of neutron absorption considered above is taken as the energy source of quasars, then in this case a high density of matter is not required, but a high concentration of collapsars is necessary (5). The energy released is determined by the expression
\[ \frac{dE}{dt}=j_{\mathrm{n}}\sigma_{\mathrm{n}я}Mc^{2}/A_{я}X^{1/2}, \tag{6} \]
where \(A_{я}\) is the mean mass number of nuclei. To maintain the observed radiation of a quasar, neutron fluxes are necessary:
\[ j_{\mathrm{n}}\sim 10^{9}\ \mathrm{s}^{-1}\ \mathrm{cm}^{-2}. \]
Everything discussed here is based on the assumption of the specific character of hyperon interactions. At the present level this assumption can neither be proved nor refuted. But all other assumptions discussed in the literature concerning the behavior of matter at densities above nuclear density are of exactly the same character. The possibility considered here does not contradict any fundamental laws of physics, and its realization in nature is entirely admissible.
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