Modelling the April 15 spectrum of Supernova 1993 J

We present the modeling of the ultraviolet and optical spectra obtained simultaneously on 1993 April 15 with the HST and at Lick Observatory. A Monte Carlo code is employed in the modeling and a comparison is made between models reported by different groups. With an atmosphere similar to the Sun in chemical composition, the observed spectral lines are well reproduced by a power law density structure of index around 20 except the strong H and HeI λ5876 lines which have peculiar absorption profiles. The photospheric velocity is found to be 9500 km/s and the blackbody temperature of the spectrum is 7990 K. For H and HeI λ5876, we suggest a two-component density structure which has a smoother layer located immediately outside the steeply decreasing inner envelope. The power law indices are most probably 20 and 3, respectively, with the transition point at about 13 000 km/s. In addition, this outer smooth layer serves to flatten the far UV spectrum as observed.     

Chaotic Diffusion And Effective Stability of Jupiter Trojans

It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, T_L, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of T_Land the escape time, T_E, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the T_E=1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between T_LandT_E is found.