Gravitational energy of rotating black holes

In the teleparallel equivalent of general relativity the energy density of asymptotically flat gravitational fields can be naturaly defined as a scalar density restricted to a three-dimensional spacelike hypersurface $\Sigma$. Integration over the whole $\Sigma$ yields the standard ADM energy. After establishing the reference space with zero gravitational energy we obtain the expression of the localized energy for a Kerr black hole. The expression of the energy inside a surface of constant radius can be explicitly calculated in the limit of small $a$, the specific angular momentum. Such expression turns out to be exactly the same as the one obtained by means of the method preposed recently by Brown and York. We also calculate the energy contained within the outer horizon of the black hole for {\it any} value of $a$. The result is practically indistinguishable from $E=2M_{ir}$, where $M_{ir}$ is the irreducible mass of the black hole.Comment: 18 pages, LaTex file, one figur

Evidence for quasi-chemically homogeneous evolution of massive stars up to solar metallicity

Long soft gamma ray bursts (LGRBs) are usually associated with the death of the most massive stars. A large amount of core angular momentum in the phases preceding the explosion is required to form LGRBs. A very high initial rotational velocity can provide this angular momentum. Such a velocity strongly influences the way the star evolves: it is chemically homogeneously mixed and evolves directly towards the blue part of the HR diagram from the main sequence. We have shown that chemically homogeneous evolution (CHE) takes place in the SMC, at low metallicity. We want to see if there is a metallicity threshold above which such an evolution does not exist. We perform a spectroscopic analysis of H-rich early-type WN stars in the LMC and the Galaxy. We use the code CMFGEN to determine the fundamental properties and the surface composition of the target stars. We then place the stars in the HR diagram and determine their evolution. We show that both the LMC and Galactic WNh stars we selected cannot be explained by standard stellar evolution. They are located on the left of the main sequence but show surface abundances typical of CN equilibrium. In addition, they still contain a large amount of hydrogen. They are thus core-H burning objects. Their properties are consistent with CHE. We determine the metallicity of the Galactic stars from their position and Galactic metallicity gradients, and conclude that they have 0.6<Z<1.0. A moderate coupling between the core and the envelope is required to explain that stellar winds do not extract to much angular momentum to prevent a blueward evolution. In view of the findings that some long gamma ray bursts appear in solar environments, CHE may be a viable way to form them over a wide range of metallicities.Comment: 10 pages, 10 figures. Accepted in Astronomy and Astrophysic

The Arches cluster revisited: I. Data presentation and stellar census

Context. Located within the central region of the Galaxy, the Arches cluster appears to be one of the youngest, densest and most massive stellar aggregates within the Milky Way. As such it has the potential to be a uniquely instructive laboratory for the study of star formation in extreme environments and the physics of very massive stars. Aims. To realise this possibility, the fundamental physical properties of both cluster and constituent stars need to be robustly determined; tasks we attempt here. Methods. In order to accomplish these goals we provide and analyse new multi-epoch near-IR spectroscopic data obtained with the VLT/SINFONI and photometry from the HST/WFC3. We are able to stack multiple epochs of spectroscopy for individual stars in order to obtain the deepest view of the cluster members ever obtained. Results. We present spectral classifications for 88 cluster members, all of which are WNLh or O stars: a factor of three increase over previous studies. We find no further examples of Wolf-Rayet stars within the cluster; importantly no H-free examples were identified. The smooth and continuous progression in spectral morphologies from O super-/hypergiants through to the WNLh cohort implies a direct evolutionary connection. We identify candidate giant and main sequence O stars spectroscopically for the first time. No products of binary evolution may be unambiguously identified despite the presence of massive binaries within the Arches. Conclusions. Notwithstanding difficulties imposed by the highly uncertain (differential) reddening to the Arches, we infer a main sequence/luminosity class V turn-off mass of ∼ 30 − 38M⊙ via the distribution of spectral types. Analysis of the eclipsing binary F2 suggests current masses of ∼ 80M⊙ and ∼ 60M⊙ for the WNLh and O hypergiant cohorts, respectively; we conclude that all classified stars have masses > 20M⊙. An age of ∼ 2.0 − 3.3Myr is suggested by the turn-off between ∼O4-5 V; constraints imposed by the supergiant population and the lack of H-free WRs are consistent with this estimate. While the absence of highly evolved WC stars strongly argues against the prior occurrence of SNe within the Arches, the derived age does accommodate such events for exceptionally massive stars. Further progress will require quantitative analysis of multiple individual cluster members in addition to further spectroscopic observations to better constrain the binary and main sequence populations; nevertheless it is abundantly clear that the Arches offers an unprecedented insight into the formation, evolution and death of the most massive stars Nature allows to form

Transformer and LCL Filter Design for DPFCs

Flexible AC Transmission Systems (FACTS) can be used for power flow control in AC transmission grids, allowing simultaneous control of the bus voltage and line active and reactive power. However, due to high costs and reliability concerns, the application of this technology has been limited in such applications. Recently, the concept of Distributed FACTS (DFACTS) and Distributed Power Flow Controller (DPFC) has been introduced as a low cost high reliability alternative for power flow control. This paper presents the design of a coupling transformer and a LCL filter for DPFC devices. To extract the electromagnetic energy from the transmission line a transformer with a single turn primary is designed and optimized. A third-order LCL filter is used to guarantee high order harmonics filtering. Simulations results are presented and discussed

New results for the t-J model in ladders: Changes in the spin liquid state with applied magnetic field. Implications for the cuprates

Exact Diagonalization calculations are presented for the t-J model in the presence of a uniform magnetic field. Results for 2xL ladders (L=8,10,12) and 4x4 square clusters with 1 and 2 holes indicate that the diamagnetic response to a perpendicular magnetic field tends to induce a spin liquid state in the spin background. The zero-field spin liquid state of a two-leg ladder is reinforced by the magnetic field: a considerable increase of rung antiferromagnetic correlations is observed for J/t up to 0.6, for 1 and 2 holes. Pair-breaking is also clearly observed in the ladders and seems to be associated in part with changes promoted by the field in the spin correlations around the zero-field pair. In the 4x4 cluster, the numerical results seem to indicate that the field-induced spin liquid state competes with the zero-field antiferromagnetic short-range-order, the spin liquid state being favored by higher doping and smaller values of J/t. It is interesting to note that the field-effect can also be observed in a 2x2 plaquette with 1 and 2 holes. This opens up the possibility of gaining a qualitative understanding of the effect.Comment: 16 pages, 7 figures, latex New results adde

Qualitative understanding of the sign of t' asymmetry in the extended t-J Model and relevance for pairing properties

Numerical calculations illustrate the effect of the sign of the next nearest-neighbor hopping term t' on the 2-hole properties of the t-t'-J model. Working mainly on 2-leg ladders, in the -1.0 < t'/t < 1.0 regime, it is shown that introducing t' in the t-J model is equivalent to effectively renormalizing J, namely t' negative (positive) is equivalent to an effective t-J model with smaller (bigger) J. This effect is present even at the level of a 2x2 plaquette toy model, and was observed also in calculations on small square clusters. Analyzing the transition probabilities of a hole-pair in the plaquette toy model, it is argued that the coherent propagation of such hole-pair is enhanced by a constructive interference between both t and t' for t'>0. This interference is destructive for t'<0.Comment: 5 pages, 4 figures, to appear in PRB as a Rapid Communicatio

Properties of WNh stars in the Small Magellanic Cloud: evidence for homogeneous evolution

We derive the physical properties of three WNh stars in the SMC to constrain stellar evolution beyond the main sequence at low metallicity and to investigate the metallicity dependence of the clumping properties of massive stars. We compute atmosphere models to derive the stellar and wind properties of the three WNh targets. A FUV/UV/optical/near-infrared analysis gives access to temperatures, luminosities, mass loss rates, terminal velocities and stellar abundances. All stars still have a large hydrogen mass fraction in their atmosphere, and show clear signs of CNO processing in their surface abundances. One of the targets can be accounted for by normal stellar evolution. It is a star with initial mass around 40-50 Msun in, or close to, the core He burning phase. The other two objects must follow a peculiar evolution, governed by fast rotation. In particular, one object is likely evolving homogeneously due to its position blue-ward of the main sequence and its high H mass fraction. The clumping factor of one star is found to be 0.15+/-0.05. This is comparable to values found for Galactic Wolf-Rayet stars, indicating that within the uncertainties, the clumping factor does not seem to depend on metallicity.Comment: 16 pages. A&A accepte

Lossless Photonic Switched Networks For Metro-access

We evaluate through computer simulation the performance of Photonic switching OPS/OBS networks of various sizes and configurations, based on a lossless (amplified) photonic switching node experimentally demonstrated previously. The great advantage of photonic switching is transparency to signal rate and format. Thus we propose a basic flexible network, with low-energy consumption and high-efficiency. In simulations traffic load is varied and network parameters such as, average number of hops (ANH), network latency (delay) and packet loss fraction are evaluated. Consistent results for the various configurations are presented, analyzed and discussed; and Interesting conclusions emerge.9773Conference on Optical Metro Networks and Short-Haul Systems VIIIFEB 16-18, 2016San Francisco, C

Shelf-Ocean material exchange influencing the Atlantic chemical composition off NW Iberian margin since the last glaciation

Rivers are the main conduit of sediment to the shelf. The basin geology, the drainage area and the discharge rate are the major factors that determine their sediment load (Milliman and Syvistski, 1992). Besides suspended particles, dissolved components may also give some information on the eroded crust. Sr isotopes in carbonate shells of biological organisms have been used to study, in the geological record, the influence exerted by the chemical weathering of the continental crust on the seawater composition (Macdougall, 1991). In this work, Sr isotope ratios obtained in tests of foraminifera representing the last 40 ka are presented and discussed in the scope of the palaeogeographical evolution of NW Iberia. This work aims to present and discuss the results of Sr isotope analyses (performed, by TIMS, in the Isotope Geology Laboratory of the University of Aveiro) of tests of two species of foraminifera, from nine samples taken along the OMEX core KC 024-19 (181 cm; 42°08’98’’N, 10°29´96’’W, and 2765m), collected in the Galicia Bank area, off Galicia. Taking into account that Sr contained in the carbonate tests is usually considered as preserving the signature of the contemporaneous seawater, one planktonic species (Globigerina bulloides) and one benthic species (Cibicides wuellerstorfi) were selected in order to try to detect Sr isotope variations both through time and between two different levels of the water column. The core age model, which records the last 40 ka, is based on a combination of oxygen isotope stratigraphy, eight AMS 14C datings and the synchronisation of the last four Heinrich Events in the Iberian Margin sedimentary records. As a whole, the obtained 87Sr/86Sr ratios vary between 0.709209 and 0.709108, with a mean 2σ error of 0.000025. These values lie within the range of modern marine Sr isotope ratios (0.70910-0.70922), as previously defined using analyses of both seawater and marine carbonates (see compilation by Faure and Mensing, 2005). Despite their small variation, the 87Sr/86Sr ratios obtained in G. bulloides seem to indicate that Sr dissolved in seawater at the KC 024-19 core site became slightly less radiogenic after the Last Glacial Maximum (LGM). This decrease is concomitant with diminishing amounts of the detrital components in the sediments (Fig. 1). Therefore, both the composition of dissolved Sr, as revealed by results on tests of planktonic foraminifera, and the proportions of suspended terrigenous particulate material arriving at the KC 024-19 site point to a decreasing importance of the contribution of the erosion of the Iberian Variscan crust since the Last Glacial Maximum and in the Holocene. The 87Sr/86Sr ratios measured in tests of benthic foraminifera (C. wuellerstorfi) are more erratic and no correlation can be established with palaeogeographical/palaeoclimatic constraints. The difference between the behaviour of Sr compositions in G. bulloides and C. wuellerstorfi may indicate that whilst the planktonic foraminifera should reproduce very closely the seawater composition, the benthic organisms should, in addition to the major role of seawater, also be affected by some sort of interaction with the sediments. As such, planktonic foraminifera are probably more reliable indicators of seawater composition in studies involving very small periods and corresponding very slight variations of the 87Sr/86Sr ratios. Taking into account that G. bulloides is a common planktonic species (living mostly in the first 50m of the water column), whose tests seem to be in equilibrium with sea water composition, variations in its 87Sr/86Sr ratios can be related with changes in the chemical composition of the water of the Atlantic Ocean off NW Iberian Margin. The highest 87Sr/86Sr values are contemporaneous with a period of low sea level (about -140 m; Dias et al., 2000) during the LGM. According to Dias et al. (2000) at 18 ka BP the shoreline was close to the shelf break. The summital parts of the Gerês and Estrela mountains were covered by local glaciers and close to the coast freezing occurred frequently. The river catchments, which extended far to the shelf, received more rainfall due to a longer, compared to present day conditions, wet season, which promoted both physical and chemical weathering. Higher pluviosity combined with the effect of spring ice melting maintained high river discharge and consequently caused very important sediment supply to the coastal zone. The extremely narrow shelf was a very energetic environment due to sea bottom inclination and very limited long wave refraction. Therefore, at that time, a long wet season and very competent rivers should have caused important erosion of the Variscan basement in NW Iberia. Additionally, then, the shoreline was much closer to the KC 024-19 site. The combination of all these factors favoured an important deposition of terrigenous sediments and the local slight enrichment in radiogenic Sr of the seawater. With sea level rise, after the deglaciation and during the Holocene, the river estuaries became progressively far away from the shelf break. Their competence of transport also became progressively reduced and the offshore transport of detrital sediments became progressively lower. Conversely the biogenic carbonate proportion in the sediments increased, due to lower dilution by the terrigenous particles. Simultaneously, the values of 87Sr/86Sr in the seawater at the KC 024-19 site became lower, as a consequence of a complete homogenization with the ocean global composition, which was now more effective with the increasing distance towards shoreline