Multifragmentation model for the production of astrophysical strangelets

Determination of the baryon number (or mass) distribution of the strangelets, which may fragment out of the warm and excited strange quark matter tidally ejected in the merger of strange stars in the compact binary stellar systems in the galaxy, is attempted here using a statistical disassembly model. Finite mass of strange quarks is taken into account in the analysis. Resulting charges of the strangelets and the corresponding Coulomb corrections are included to get a plausible size distribution of those strangelets as they are produced in stellar mergers, thus getting injected in the galaxy. From this mass distribution of strangelets at their source, an approximate order of magnitude estimate for their possible flux in the solar neighborhood is attempted by using a simple diffusion model for their propagation in the galaxy. Such theoretical estimate is important in view of the ongoing efforts to detect galactic strangelets by recent satellite-borne experiments.

Figure 1

Multiplicity ($ln\omega$) distribution of strangelets for massless ($m_s=0$) and massive ($m_s=95$ MeV) $s$-quarks for constant values of the bag constant ($B^{1/4}=145\mathrm{MeV}$) and the total baryon number ($A_{\mathrm{b}}=1\times {10}^{53}$) at a specific temperature ($T=10\mathrm{keV}$) at freeze-out. The $u$- and $d$-quarks are considered to be massless in both cases. The results are displayed for (a) the full range of the available baryon numbers and (b) for a limited range of baryon numbers of the strangelet fragments. Panel (b) is included to focus on the lower cutoff ($A\approx 11$ for $m_s=95$ MeV) in the baryon numbers, as well as the baryon number ($A\approx 4$) at which the peak of the distribution (for $m_s=0$) is obtained. Here, the idealized $m_s=0$ case (marked by the broken line) is included for the sake of a comparison.

Figure 2

$ln\omega$ vs $A$ for strangelets with $B^{1/4}=145\mathrm{MeV}, m_s=95\mathrm{MeV}$, and $A_b=1\times {10}^{53}$, at three different temperatures at freeze-out. Variations are displayed for (a) the full range of the possible baryon numbers and for (b) a limited range of the baryon numbers of the fragments.

Figure 3

$ln\omega$ vs $A$ for strangelets with $m_s=95\mathrm{MeV}, A_b=1\times {10}^{53}$, and $T=10$ keV, at two different values of the bag constant as indicated in the diagrams. Approximate values of the quark number chemical potential (${\mu }_b$) of the bulk matter before fragmentation, that correspond to different values of the bag constant at zero external pressure and zero temperature, are also displayed.

Figure 4

Variation of the energy per baryon ($E/A$) against the changing baryon number ($A$) of the strangelet fragments (with $m_s=95\mathrm{MeV}$) for three different values of the bag parameter, at a specific temperature ($T=1$ MeV) at freeze-out. Corresponding value of the quark number chemical potential (${\mu }_b$) of the initial bulk matter, at zero pressure ($P_{\mathrm{ext}}=0$) and zero temperature, is displayed against each bag value for the sake of comparison. The solid (red) horizontal lines mark the energies per baryon of ${}^{56}\mathrm{Fe}$, nucleon and ${\mathrm{\Lambda }}^0$-hyperon, respectively, that delineate the thresholds for absolute stability, metastability, and instability of the fragments. The total baryon number considered to draw this diagram is the same as in the previous figures.