Electromagnetic power of merging and collapsing compact objects

[Abridged] Electromagnetic emission can be produced as a precursor to the merger, as a prompt emission during the collapse of a NS and at the spin-down stage of the resulting BH. We demonstrate that the time evolution of the axisymmetric force-free magnetic fields can be expressed in terms of the hyperbolic Grad-Shafranov equation. We find exact non-linear time-dependent split-monopole structure of magnetosphere driven by spinning and collapsing NS in Schwarzschild geometry. Based on this solution, we argue that the collapse of a NS into the BH happens smoothly, without natural formation of current sheets or other dissipative structures on the open field lines and, thus, does not allow the magnetic field to become disconnected from the star and escape to infinity. Thus, as long as an isolated Kerr BH can produce plasma and currents, it does not lose its open magnetic field lines, its magnetospheric structure evolved towards a split monopole and the BH spins down electromagnetically. The "no hair theorem", which assumes that the outside medium is a vacuum, is not applicable in this case: highly conducting plasma introduces a topological constraint forbidding the disconnection of the magnetic field lines from the BH. Eventually, a single random large scale spontaneous reconnection event will lead to magnetic field release, shutting down the electromagnetic BH engine forever. We also discuss the nature of short Gamma Ray Bursts and suggest that the similarity of the early afterglows properties of long and short GRBs can be related to the fact that in both cases a spinning BH can retains magnetic field for sufficiently long time to extract a large fraction of its rotation energy and produce high energy emission via the internal dissipation in the wind

Infrared spectroscopy of Landau levels in graphene

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show \textit{in situ} half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs are resolved. Their transition energies are proportional to $\sqrt{B}$ and the deduced band velocity is $\tilde{c}\approx1.1\times10^6$ m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

Rotation and X-ray emission from protostars

The ASCA satellite has recently detected variable hard X-ray emission from two Class I protostars in the rho Oph cloud, YLW15 (IRS43) and WL6, with a characteristic time scale ~20h. In YLW15, the X-ray emission is in the form of quasi-periodic energetic flares, which we explain in terms of strong magnetic shearing and reconnection between the central star and the accretion disk. In WL6, X-ray flaring is rotationally modulated, and appears to be more like the solar-type magnetic activity ubiquitous on T Tauri stars. We find that YLW15 is a fast rotator (near break-up), while WL6 rotates with a significantly longer period. We derive a mass M_\star ~ 2 M_\odot and \simlt 0.4 M_\odot for the central stars of YLW15 and WL6 respectively. On the long term, the interactions between the star and the disk results in magnetic braking and angular momentum loss of the star. On time scales t_{br} ~ a few 10^5 yrs, i.e., of the same order as the estimated duration of the Class~I protostar stage. Close to the birthline there must be a mass-rotation relation, t_{br} \simpropto M_\star, such that stars with M_\star \simgt 1-2 M_\odot are fast rotators, while their lower-mass counterparts have had the time to spin down. The rapid rotation and strong star-disk magnetic interactions of YLW15 also naturally explain the observation of X-ray ``superflares''. In the case of YLW15, and perhaps also of other protostars, a hot coronal wind (T~10^6 K) may be responsible for the VLA thermal radio emission. This paper thus proposes the first clues to the rotation status and evolution of protostars.Comment: 13 pages with 6 figures. To be published in ApJ (April 10, 2000 Part 1 issue

Interestingness of traces in declarative process mining: The janus LTLPf Approach

Declarative process mining is the set of techniques aimed at extracting behavioural constraints from event logs. These constraints are inherently of a reactive nature, in that their activation restricts the occurrence of other activities. In this way, they are prone to the principle of ex falso quod libet: they can be satisfied even when not activated. As a consequence, constraints can be mined that are hardly interesting to users or even potentially misleading. In this paper, we build on the observation that users typically read and write temporal constraints as if-statements with an explicit indication of the activation condition. Our approach is called Janus, because it permits the specification and verification of reactive constraints that, upon activation, look forward into the future and backwards into the past of a trace. Reactive constraints are expressed using Linear-time Temporal Logic with Past on Finite Traces (LTLp f). To mine them out of event logs, we devise a time bi-directional valuation technique based on triplets of automata operating in an on-line fashion. Our solution proves efficient, being at most quadratic w.r.t. trace length, and effective in recognising interestingness of discovered constraints

A Spherical Model for "Starless" Cores of Magnetic Molecular Clouds and Dynamical Effects of Dust Grains

In the standard picture of isolated star formation, dense ``starless'' cores are formed out of magnetic molecular clouds due to ambipolar diffusion. Under the simplest spherical geometry, I demonstrate that ``starless'' cores formed this way naturally exhibit a large scale inward motion, whose size and speed are comparable to those detected recently by Taffala et al. and Williams et al. in ``starless'' core L1544. My model clouds have a relatively low mass (of order 10 $M_\odot$) and low field strength (of order 10 $\mu$G) to begin with. They evolve into a density profile with a central plateau surrounded by a power-law envelope, as found previously. The density in the envelope decreases with radius more steeply than those found by Mouschovias and collaborators for the more strongly magnetized, disk-like clouds. At high enough densities, dust grains become dynamically important by greatly enhancing the coupling between magnetic field and the neutral cloud matter. The trapping of magnetic flux associated with the enhanced coupling leads, in the spherical geometry, to a rapid assemblage of mass by the central protostar, which exacerbates the so-called ``luminosity problem'' in star formation.Comment: 27 pages, 4 figures, accepted by Ap

The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.Comment: Latex file, uses epsf.sty, 15 pages and 3 eps figures. Paragraph on role of smooth functions rewritten. Four references added. To appear in Classical & Quantum Gravit

A complete classification of spherically symmetric perfect fluid similarity solutions

We classify all spherically symmetric perfect fluid solutions of Einstein's equations with equation of state p/mu=a which are self-similar in the sense that all dimensionless variables depend only upon z=r/t. For a given value of a, such solutions are described by two parameters and they can be classified in terms of their behaviour at large and small distances from the origin; this usually corresponds to large and small values of z but (due to a coordinate anomaly) it may also correspond to finite z. We base our analysis on the demonstration that all similarity solutions must be asymptotic to solutions which depend on either powers of z or powers of lnz. We show that there are only three similarity solutions which have an exact power-law dependence on z: the flat Friedmann solution, a static solution and a Kantowski-Sachs solution (although the latter is probably only physical for a1/5, there are also two families of solutions which are asymptotically (but not exactly) Minkowski: the first is asymptotically Minkowski as z tends to infinity and is described by one parameter; the second is asymptotically Minkowski at a finite value of z and is described by two parameters. A complete analysis of the dust solutions is given, since these can be written down explicitly and elucidate the link between the z>0 and z<0 solutions. Solutions with pressure are then discussed in detail; these share many of the characteristics of the dust solutions but they also exhibit new features.Comment: 63 pages. To appear in Physical Review

Spatially self-similar spherically symmetric perfect-fluid models

Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively with the theory of dynamical systems.Comment: 21 pages, 6 eps-figure

Magnetic fields in cluster cores: Faraday rotation in A400 and A2634

We present Faraday rotation data for radio sources in the centers of the Abell clusters A400 and A2634. These clusters contain large (> 100 kpc), tailed radio sources, each attached to the central cD galaxy. These clusters do not have strong cooling cores. Our data extend previous work on rotation measure in cluster centers to larger scales and non-cooling clusters. The rotation measure, and thus the magnetic field, is ordered on scales 10-20 kpc in both clusters. The geometry of the rotation measure appears to be determined by the distribution of the X-ray emitting gas, rather than by the radio tails themselves. We combine our data with previously published X-ray and radio data in order to analyze the magnetic fields in all 12 clusters whose central radio sources have been imaged in rotation measure. We find that the fields are dynamically significant in most clusters. We argue that the Faraday data measure fields in the intracluster medium, rather than in a skin of the radio source. Finally, we consider the nature and maintenance of the magnetic fields in these clusters, and conclude that either the cluster-wide field exists at similar levels, or that a weaker cluster-wide field is amplified by effects in the core.Comment: Accepted for ApJ. 43 pages including 10 embedded figures. Higher resolution versions of the figures available at http://www.aoc.nrao.edu/~jeilek/pubs/Eilekpub.htm