arXiv subjects
Publications and source records attributed to Bradley Meyer.
We compute the nonabelian $\mathrm{SL_2}(\mathbb{C})$-character varieties of the rational knots $C(2n+1,2m,2)$ in the Conway notation, where $m$ and $n$ are non-zero integers. By studying real points on these varieties, we determine the left orderability of the fundamental groups of the cyclic branched covers of $C(2n+1,2m,2)$.
A critical constraint on solar system formation is the high $^{26}$Al/$^{27}$Al abundance ratio of 5 $\times 10^{-5}$ at the time of formation, which was about 17 times higher than the average Galactic ratio, while the $^{60}$Fe/$^{56}$Fe value was about $2 \times 10^{-8}$, lower than the Galactic value. This challenges the assumption that a nearby supernova was responsible for the injection of these short-lived radionuclides into the early solar system. We show that this conundrum can be resolved if the Solar System was formed by triggered star formation at the edge of a Wolf-Rayet (W-R) bubble. Aluminium-26 is produced during the evolution of the massive star, released in the wind during the W-R phase, and condenses into dust grains that are seen around W-R stars. The dust grains survive passage through the reverse shock and the low density shocked wind, reach the dense shell swept-up by the bubble, detach from the decelerated wind and are injected into the shell. Some portions of this shell subsequently collapses to form the dense cores that give rise to solar-type systems. The subsequent aspherical supernova does not inject appreciable amounts of $^{60}$Fe into the proto-solar-system, thus accounting for the observed low abundance of $^{60}$Fe. We discuss the details of various processes within the model and conclude that it is a viable model that can explain the initial abundances of $^{26}$Al and $^{60}$Fe. We estimate that 1-16% of all Sun-like stars could have formed in such a setting of triggered star formation in the shell of a WR bubble.
We present a systematic study of the pure deflagration model of Type Ia supernovae using three-dimensional, high-resolution, full-star hydrodynamical simulations, nucleosynthetic yields calculated using Lagrangian tracer particles, and light curves calculated using radiation transport. We evaluate the simulations by comparing their predicted light curves with many observed SNe Ia using the SALT2 data-driven model and find that the simulations may correspond to under-luminous SNe Iax. We explore the effects of the initial conditions on our results by varying the number of randomly selected ignition points from 63 to 3500, and the radius of the centered sphere they are confined in from 128 to 384 km. We find that the rate of nuclear burning depends on the number of ignition points at early times, the density of ignition points at intermediate times, and the radius of the confining sphere at late times. The results depend primarily on the number of ignition points, but we do not expect this to be the case in general. The simulations with few ignition points release more nuclear energy $E_{\mathrm{nuc}}$, have larger kinetic energies $E_{\mathrm{K}}$, and produce more $^{56}$Ni than those with many ignition points, and differ in the distribution of $^{56}$Ni, Si, and C/O in the ejecta. For these reasons, the simulations with few ignition points exhibit higher peak B-band absolute magnitudes $M_\mathrm{B}$ and light curves that rise and decline more quickly; their $M_\mathrm{B}$ and light curves resemble those of under-luminous SNe Iax, while those for simulations with many ignition points are not.
Nucleosynthesis of heavy nuclei in metal-poor stars is generally thought to occur via the r-process because the r-process is a primary process that would have operated early in the Galaxy's history. This idea is strongly supported by the fact that the abundance pattern in many metal-poor stars matches well the inferred Solar r-process abundance pattern in the mass range between the second and third r-process abundance peaks. Nevertheless, a significant number of metal-poor stars do not share this standard r-process template. In this Letter we suggest that the nuclides observed in many of these stars are produced by the r-process, but that it is prevented from running to completion in more massive stars by collapse to black holes before the r-process is completed, creating a "truncated r-process," or "tr-process." We find that the observed fraction of tr-process stars is qualitatively what one would expect from the initial mass function, and that an apparent sharp truncation observed at around mass 160 could result from a combination of collapses to black holes and the difficulty of observing the higher mass rare earths. We test the tr-process hypothesis with r-process calculations that are terminated before all r-process trajectories have been ejected. We find qualitative agreement between observation and theory when black hole collapse and observational realities are taken into account.