Phononic Rogue Waves

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schroedinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue wave like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.Comment: 9 pages, 4 figure

The Formation of High-Mass Black Holes in Low Mass X-ray Binaries

In this note we suggest that high-mass black holes; i.e., black holes of several solar masses, can be formed in binaries with low-mass main-sequence companions, provided that the hydrogen envelope of the massive star is removed in common envelope evolution which begins only after the massive star has finished He core burning. That is, the massive star is in the supergiant stage, which lasts only $\sim 10^4$ years, so effects of mass loss by He winds are small. Since the removal of the hydrogen envelope of the massive star occurs so late, it evolves essentially as a single star, rather than one in a binary. Thus, we can use evolutionary calculations of Woosley & Weaver (1995) of single stars. We find that the black holes in transient sources can be formed from stars with ZAMS masses in the interval 20-35\msun. The black hole mass is only slightly smaller than the He core mass, typically \sim 7\msun.Comment: 19 pages, substantial changes, accepted in New Astronom

Evolution and Merging of Binaries with Compact Objects

In the light of recent observations in which short gamma-ray bursts are interpreted as arising from black-hole(BH), neutron-star(NS) or NS-NS mergings we would like to review our research on the evolution of compact binaries, especially those containing NS's. These were carried out with predictions for LIGO in mind, but are directly applicable to short gamma-ray bursts in the interpretation above. Most important in our review is that we show that the standard scenario for evolving NS-NS binaries always ends up with a low-mass BH (LMBH), NS binary. Bethe and Brown (1998) showed that this fate could be avoided if the two giants in the progenitor binary burned He at the same time, and that in this way the binary could avoid the common envelope evolution of the NS with red giant companion which sends the first born NS into a BH in the standard scenario. The burning of He at the same time requires, for the more massive giants such as the progenitors of the Hulse-Taylor binary NS that the two giants be within 4% of each other in ZAMS mass. Applying this criterion to all binaries results in a factor 5 of LMBH-NS binaries as compared with NS-NS binaries. Our scenario of NS-NS binaries as having been preceded by a double He-star binary is collecting observational support in terms of the nearly equal NS masses within a given close binary.Comment: 32 pages, 1 figure, substantial changes from v