(47171) 1999 TC36, A Transneptunian Triple

We present new analysis of HST images of (47171) 1999 TC36 that confirm it as a triple system. Fits to the point-spread function consistently show that the apparent primary is itself composed of two similar-sized components. The two central components, A1 and A2, can be consistently identified in each of nine epochs spread over seven years of time. In each instance the component separation, ranging from 0.023+/-0.002 to 0.031+/-0.003 arcsec, is roughly one half of the Hubble Space Telescope's diffraction limit at 606 nm. The orbit of the central pair has a semi-major axis of a~867 km with a period of P~1.9 days. These orbital parameters yield a system mass that is consistent with Msys = 12.75+/-0.06 10^18 kg derived from the orbit of the more distant secondary, component B. The diameters of the three components are dA1= 286(+45,-38) km, dA2= 265(+41,-35 km and dB= 139(+22,-18) km. The relative sizes of these components are more similar than in any other known multiple in the solar system. Taken together, the diameters and system mass yield a bulk density of p=542(+317,-211) kg m^-3. HST Photometry shows that component B is variable with an amplitude of >=0.17+/-0.05 magnitudes. Components A1 and A2 do not show variability larger than 0.08+/-0.03 magnitudes approximately consistent with the orientation of the mutual orbit plane and tidally-distorted equilibrium shapes. The system has high specific angular momentum of J/J'=0.93, comparable to most of the known Transneptunian binaries.Comment: 16 pages, 8 figures, 6 tables. Accepted to Icaru

The Correlated Colors of Transneptunian Binaries

We report resolved photometry of the primary and secondary components of 23 transneptunian binaries obtained with the Hubble Space Telescope. V-I colors of the components range from 0.7 to 1.5 with a median uncertainty of 0.06 magnitudes. The colors of the primaries and secondaries are correlated with a Spearman rank correlation probability of 99.99991%, 5 sigma for a normal distribution. Fits to the primary vs. secondary colors are identical to within measurement uncertainties. The color range of binaries as a group is indistinguishable from that of the larger population of apparently single transneptunian objects. Whatever mechanism produced the colors of apparently single TNOs acted equally on binary systems. The most likely explanation is that the colors of transneptunian objects and binaries alike are primordial and indicative of their origin in a locally homogeneous, globally heterogeneous protoplanetary disk.Comment: 28 pages, 4 figure, 4 tables. accepted to Icaru

Scheduling jobs with release times on a machine with finite storage

Consider a single machine with a buffer which can store up to b waiting jobs for some fixed b. Given the release times, the weights and the processing times of n consecutive jobs, a maximum weight subset of jobs is to be found that is schedulable without violating the buffer's capacity constraint. A polynomial algorithm for the unweighted loss-delay problem is presented. The weighted case is shown to be NP-hard as well as an unweighted two-machine version

A greedy on-line algorithm for the k-track assignment problem

Given a collection [.] of n jobs that are represented by intervals, we seek a maximal feasible assignment of the jobs to k machines such that not more than c(M) intervals overlap pairwise on any machine M and that a job is only assigned to a machine if it fits into one of several prescribed time windows for that machine. We analyze an on-line version of this NP-complete problem and exhibit an algorithm that achieves at least half of the (theoretical) optimum. In a more detailed analysis, we bound the performance of our algorithm by an additive term that only depends on the time window structure of the machines (but not on the number of jobs). In the case where each machine M has capacity c(M) = 1, our bound implies that our algorithm loses at mostk − 1 jobs relative to the optimum. We show by an explicit construction that the bound is tight for greedy on-line algorithms