Frequency-Dependent Shift in the Image Centroid of the Black Hole at the Galactic Center as a Test of General Relativity

The inferred black hole in the Galactic center spans the largest angle on the sky among all known black holes. Forthcoming observational programs plan to localize or potentially resolve the image of Sgr A* to an exquisite precision, comparable to the scale of the black hole horizon. Here we show that the location of the image centroid of Sgr A* should depend on observing frequency because of relativistic and radiative transfer effects. The same effects introduce a generic dependence of the source polarization on frequency. Future detection of the predicted centroid shift and the polarization dependence on frequency can be used to determine the unknown black hole spin and verify the validity of General Relativity.Comment: Submitted to ApJ Letter

Imaging Optically-Thin Hot Spots Near the Black Hole Horizon of Sgr A* at Radio and Near-Infrared Wavelengths

Sub milli-arcsecond astrometry and imaging of the black hole Sgr A* at the Galactic centre may become possible in the near future at infrared and sub-millimetre wavelengths. Motivated by observations of short-term infrared and X-ray variability of Sgr A*, in a previous paper we computed the expected images and light curves, including polarization, associated with an compact emission region orbiting the central black hole. We extend this work, using a more realistic hot-spot model and including the effects of opacity in the underlying accretion flow. We find that at infrared wavelengths the qualitative features identified by our earlier work are present, namely it is possible to extract the black hole mass and spin from spot images and light curves of the observed flux and polarization. At radio wavelengths, disk opacity produces significant departures from the infrared behaviour, but there are still generic signatures of the black hole properties. Detailed comparison of these results with future data can be used to test general relativity and to improve existing models for the accretion flow in the immediate vicinity of the black hole.Comment: 13 pages, 26 figures, submitted to MNRA

Sectoral Employment Efkcts of Trade and ProductiviQ in a Small Open Economy

This paper assesses the impact of trade and technology on Belgian industrial employment. A framework is developed which incorporates employment effects of (i) export expansion (ii) impost competition and (iii) labour saving productivity improvements. In this context, evidence is found for the hypothesis that international trade induces adjustments in technology.

Optimal Active Control of a Wave Energy Converter

Abstract-This paper investigates optimal active control schemes applied to a point absorber wave energy converter within a receding horizon fashion. A variational formulation of the power maximization problem is adapted to solve the optimal control problem. The optimal control method is shown to be of a bang-bang type for a power take-off mechanism that incorporates both linear dampers and active control elements. We also consider a direct transcription of the optimal control problem as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard NLP solver. Since the system model is bilinear and the cost function is non-convex quadratic, the resulting optimization problem is not a convex quadratic program. Results will be compared with an optimal command latching method to demonstrate the improvement in absorbed power. Time domain simulations are generated under irregular sea conditions

Detection of Gravitational Waves from the Coalescence of Population-III Remnants with Advanced LIGO

The comoving mass density of massive black hole (MBH) remnants from pre-galactic star formation could have been similar in magnitude to the mass-density of supermassive black holes (SMBHs) in the present-day universe. We show that the fraction of MBHs that coalesce during the assembly of SMBHs can be extracted from the rate of ring-down gravitational waves that are detectable by Advanced LIGO. Based on the SMBH formation history inferred from the evolution of the quasar luminosity function, we show that an observed event rate of 1 per year will constrain the SMBH mass fraction that was contributed by MBHs coalescence down to a level of ~10^-6 for 20 solar mass MBH remnants (or ~10^-4 for 260 solar mass remnants).Comment: 4 pages, 2 figures. Submitted to ApJ Letter