Shadowing-based reliability decay in softened n-body simulations

A shadow of a numerical solution to a chaotic system is an_exact_ solution to the equations of motion that remains close to the numerical solution for a long time. In a collisionless n-body system, we know that particle motion is governed by the global potential rather than by inter-particle interactions. As a result, the trajectory of each individual particle in the system is independently shadowable. It is thus meaningful to measure the number of particles that have shadowable trajectories as a function of time. We find that the number of shadowable particles decays exponentially with time as exp(-mu t), and that for eps in [~0.2,1] (in units of the local mean inter-particle separation $\bar n$), there is an explicit relationship between the decay constant mu, the timestep h of the leapfrog integrator, the softening eps, and the number of particles N in the simulation. Thus, given N and eps, it is possible to pre-compute the timestep h necessary to acheive a desired fraction of shadowable particles after a given length of simulation time. We demonstrate that a large fraction of particles remain shadowable over ~100 crossing times even if particles travel up to about 1/3 of the softening length per timestep. However, a sharp decrease in the number of shadowable particles occurs if the timestep increases to allow particles to travel further than 1/3 the softening length in one timestep, or if the softening is decreased below ~0.2$\bar n$.Comment: 4 pages, 5 figure

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We present new high-precision Stromgren photometry and Ca ii H and K spectrophotometry of HD 192263

� 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A. BLACK HOLE MASS AND SPIN COEVOLUTION BY MERGERS

Massive black holes appear to be present in the nuclei of almost all galaxies, but their genesis and evolution are not well understood. As astrophysical black holes are completely characterized by their masses and spins, the observed joint distribution of these quantities contains important clues to their history. We examine the coevolution of mass and spin in binary merger growth scenarios. We find that holes are typically spun down by mergers. Rapid rotation results only if the binary's larger member already spins quickly and the merger with the smaller hole is consistently near prograde, or if the binary's mass ratio approaches unity. If, as some observations have suggested, observed black holes spin rapidly, then this limits the importance of merger scenarios for the growth of black holes

� 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A. A CORRELATION BETWEEN INCLINATION AND COLOR IN THE CLASSICAL KUIPER BELT

We have measured broadband optical BVR photometry of 24 classical and scattered Kuiper belt objects (KBOs), approximately doubling the published sample of colors for these classes of objects. We find a statistically significant correlation between object color and inclination in the classical Kuiper belt using our data. The color and inclination correlation increases in significance after the inclusion of additional data points culled from all published works

� 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A. A NEW FORMATION MODEL FOR M32: A THRESHED EARLY-TYPE SPIRAL GALAXY?

The origin of M32, the closest compact elliptical galaxy (cE), is a long-standing puzzle of galaxy formation in the Local Group. Our N-body/smoothed particle hydrodynamics simulations suggest a new scenario in which the strong tidal field of M31 can transform a spiral galaxy into a compact elliptical galaxy. As a low-luminosity spiral galaxy plunges into the central region of M31, most of the outer stellar and gaseous components of its disk are dramatically stripped as a result of M31's tidal field. The central bulge component, on the other hand, is just weakly influenced by the tidal field, owing to its compact configuration, and retains its morphology. M31's strong tidal field also induces rapid gas transfer to the central region, triggers a nuclear starburst, and consequently forms the central high-density and more metal-rich stellar populations with relatively young ages. Thus, in this scenario, M32 was previously the bulge of a spiral galaxy tidally interacting with M31 several gigayears ago. Furthermore, we suggest that cE's like M32 are rare, the result of both the rather narrow parameter space for tidal interactions that morphologically transform spiral galaxies into cE's and the very short timescale (less than a few times 10 yr) for cE's to be swallowed by their giant host galaxies (via dynamical friction) after their formation

� 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A. EXPECTED CHARACTERISTICS OF THE SUBCLASS OF SUPERNOVA GAMMA-RAY BURSTS

The spatial and temporal coincidence of gamma-ray burst (GRB) 980425 and supernova (SN) 1998bw has prompted speculation that there exists a subclass of GRBs produced by SNe ("S-GRBs"). A physical model motivated by radio observations lead us to propose the following characteristics of S-GRBs: (1) prompt radio emission and an implied high brightness temperature close to the inverse Compton limit, (2) high expansion velocity (*50,000 km s ) of the optical photosphere as derived from lines widths and energy release larger than usual, (3) no long-lived X-ray afterglow, and (4) a single-pulse GRB profile. Radio studies of previous SNe show that only (but not all) Type Ib and Ic SNe potentially satisfy the first condition. We investigate the proposed associations of GRBs and SNe within the context of these proposed criteria and suggest that #1% of GRBs detected by BATSE may be members of this subclass