Mass gap in the critical gravitational collapse of a kink

We study the gravitational collapse of a kink within spherical symmetry and the characteristic formulation of General Relativity. We explore some expected but elusive gravitational collapse issues which have not been studied before in detail, finding new features. The numerical one-parametric solution and the structure of the spacetime are calculated using finite differences, Galerkin collocation techniques, and some scripting for automated grid coverage. We study the threshold of black hole formation and confirm a mass gap in the phase transition. In the supercritical case we find a mass scaling power law $M_{BH}={M^*_{BH}}+K[\lambda-\lambda^*]^{2\gamma}+f(K[\lambda-\lambda^*]^{2\gamma})$, with $\gamma\approx 0.37$ independent of the initial data for the cases considered, and $M^*_{BH}$, $K$ and $\lambda^*$ each depending on the initial datum. The spacetime has a self-similar structure with a period of $\Delta\approx 3.4$. In the subcritical case the Bondi mass at null infinity decays in cascade with $\Delta/2$ interval as expected.Comment: 5 pages, 5 figures; to appear in Physical Review

Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure

High magnification crack-tip field characterisation under biaxial conditions

This work presents a novel methodology for characterising fatigue cracks under biaxial conditions.The methodology uses high magnification Digital Image Correlation (DIC) technique for measuringdisplacement and strain crack-tip fields. By applying micro-speckle pattern on the metal surface it is possible toachieve high magnification for DIC technique. The speckles were created by electro-spray technique. Thevalidity of this novel technique is demonstrated by direct comparison with standard extensometermeasurements, under tension-compression and torsion conditions. In order to image the correct region, thenotch effect on the fatigue life was also evaluated

Is the Cepheus E Outflow driven by a Class 0 Protostar?

New early release observations of the Cepheus E outflow and its embedded source, obtained with the Spitzer Space Telescope, are presented. We show the driving source is detected in all 4 IRAC bands, which suggests that traditional Class 0 classification, although essentially correct, needs to accommodate the new high sensitivity infrared arrays and their ability to detected deeply embedded sources. The IRAC, MIPS 24 and 70 microns new photometric points are consistent with a spectral energy distribution dominated by a cold, dense envelope surrounding the protostar. The Cep E outflow, unlike its more famous cousin the HH 46/47 outflow, displays a very similar morphology in the near and mid-infrared wavelengths, and is detected at 24 microns. The interface between the dense molecular gas (where Cep E lies) and less dense interstellar medium, is well traced by the emission at 8 and 24 microns, and is one of the most exotic features of the new IRAC and MIPS images. IRS observations of the North lobe of the flow confirm that most of the emission is due to the excitation of pure H2 rotational transitions arising from a relatively cold (Tex~700 K) and dense (N{H}~9.6E20 cm-2 molecular gas.Comment: 14 pages (pre-print format), including 6 figures. Published in ApJ Special Spitzer Issue (2004

The X-ray Luminosities of HH Objects

The recent detection of X-ray emission from HH 2 and HH 154 with the Chandra and XMM-Newton satellites (respectively) have opened up an interesting, new observational possibility in the field of Herbig-Haro objects. In order to be able to plan further X-ray observations of other HH objects, it is now of interest to be able to estimate their X-ray luminosities in order to choose which objects to observe. This paper describes a simple, analytic model for predicting the X-ray luminosity of a bow shock from the parameters of the flow (i.e., the size of the bow shock, its velocity, and the pre-shock density). The accuracy of the analytic model is analyzed through a comparison with the predictions obtained from axisymmetric, gasdynamic simulations of the leading working surface of an HH jet. We find that our analytic model reproduces the observed X-ray luminosities of HH 2 and HH 154, and we propose that HH~80/81 is a good candidate for future observations with Chandra.Comment: 10 pages (8 text, 2 figures

The precession of the giant HH34 outflow: a possible jet deceleration mechanism

The giant jets represent a fundamental trace of the historical evolution of the outflow activity over timescales which are comparable to the accretion time of the outflow sources in their main protostellar phase. The study of such huge jets provides the possibility of retrieving important elements related to the life of the outflow sources. In this paper, we study the role of precession (combined with jet velocity-variability and the resulting enhanced interaction with the surrounding environment) as a deceleration mechanism for giant jets using a numerical approach. We obtain predictions of H alpha intensity maps and position-velocity diagrams from 3D simulations of the giant HH 34 jet (including an appropriate ejection velocity time-variability and a precession of the outflow axis), and we compare them with previously published observations of this object. Our simulations represent a step forward from previous numerical studies of HH objects, in that the use of a 7-level, binary adaptive grid has allowed us to compute models which appropiately cover all relevant scales of a giant jet, from the ~ 100 AU jet radius close to the source to the ~ 1 pc length of the outflow. A good qualitative and quantitative agreement is found between the model predictions and the observations. Moreover, we show that a critical parameter for obtaining a better or worse agreement with the observations is the ratio rho_j/rho_a between the jet and the environmental densities. The implications of this result in the context of the current star formation models are discussed (ABRIDGED).Comment: 19 pages, 8 eps figs.,uses aaspp4; accepted by the Ap