14 research outputs found
A precise measurement of the magnetic field in the corona of the black hole binary V404 Cygni
Observations of binary stars containing an accreting black hole or neutron star often show x-ray emission extending to high energies (>10 kilo–electron volts), which is ascribed to an accretion disk corona of energetic particles akin to those seen in the solar corona. Despite their ubiquity, the physical conditions in accretion disk coronae remain poorly constrained. Using simultaneous infrared, optical, x-ray, and radio observations of the Galactic black hole system V404 Cygni, showing a rapid synchrotron cooling event in its 2015 outburst, we present a precise 461 ± 12 gauss magnetic field measurement in the corona. This measurement is substantially lower than previous estimates for such systems, providing constraints on physical models of accretion physics in black hole and neutron star binary systems.
This article has a correction. Please see: http://science.sciencemag.org/content/360/6386/eaat927
On the approximability of the L(h, k)-labelling problem on bipartite graphs (Extended abstract)
Given an undirected graph G, an L(h, k)-labelling of G assigns colors to vertices from the integer set {0,.. lambda(h,k)}, such that any two vertices v(i) and v(j) receive colors c(v(i)) and c(v(j)) satisfying the following conditions: i) if v(i) and v(j) are adjacent then vertical bar c(v(i)) - c(v(j))vertical bar >= h; ii) if v(i) and v(j) are at distance two then vertical bar c(v(i)) - c(v(j))vertical bar >= k. The aim of the L(h, k)-labelling problem is to minimize lambda(h,k)- In this paper we study the approximability of the L(h,k)-labelling problem on bipartite graphs and extend the results to s-partite and general graphs. Indeed, the decision version of this problem is known to be DIP-complete in general and, to our knowledge, there are no polynomial solutions, either exact or approximate, for bipartite graphs. Here, we state some results concerning the approximability of the L(h,k)-labelling problem for bipartite graphs, exploiting a novel technique, consisting in computing approximate vertex- and edge-colorings of auxiliary graphs to deduce an L(h, k)-labelling for the input bipartite graph. We derive an approximation algorithm with performance ratio bounded by (4)/D-3(2), where, D is equal to the minimum even value bounding the minimum of the maximum degrees of the two partitions. One of the above coloring algorithms is in fact an approximating edge-coloring algorithm for hypergraphs of maximum dimension d, i.e. the maximum edge cardinality, with performance ratio d. Furthermore, we consider a different approximation technique based on the reduction of the L(h, k)-labelling problem to the vertex-coloring of the square of a graph. Using this approach we derive an approximation algorithm with performance ratio bounded by min(h, 2k)root n + o(k root n), assuming h >= k. Hence, the first technique is competitive when D O(n(1/4)) These algorithms match with a result in [2] stating that L(1,1) labelling n-vertex bipartite graphs is hard to approximate within(n1/2-)epsilon, for any epsilon > 0, unless NP=ZPP. We then extend the latter approximation strategy to s-partite graphs, obtaining a (min(h, sk)root n + o(sk root n))-approximation ratio, and to general graphs deriving an (h root n + o(h root n))-approximation algorithm, assuming h >= k. Finally, we prove that the L(h, k)-labelling problem is not easier than coloring the square of a graph