Constraining the Location of Microlensing Objects by using the Finite Source Effect in EAGLE events

We propose a new method to constrain the location of microlensing objects using EAGLE (Extremely Amplified Gravitational LEnsing) events. We have estimated the rate of EAGLE events by taking the finite-source effect in to account. We found that the EAGLE event rate for using a 1-m class telescope w hose limiting magnitude is $V \sim 21$ is the same as or higher than that of the ordinary microlensing events which have been found to date. We have also found that the fraction of transit EAGLE events is large enough to detect: between $4 \sim 80$ depending on the lens location. Since the lens proper motion can be measured for a transit event, one can distinguish whether the lens is a MACHO (MAssive Compact Halo Object) in our hal o or one of the known stars in the Large Magellanic Cloud (LMC) from the proper motion measurement for each transit EAGLE event. Moreover, we show that the fraction of transit EAGLEs in all EAGLE events signif icantly depends on the lensing locations: the transit EAGLE fraction for the sel f-lensing case is $2 \sim 15$ times larger than that for halo MACHOs. Thus, one can constrain the location of lens objects by the statistics of the tr ansit events fraction. We show that we can reasonably expect $0 \sim 6$ transit events out of 21 EAGLE events in 3 years. We can also constrain the lens population properties at a gre ater than 99% confidence level depending on the number of transit events de tected. We also present the duration of EAGLE events, and show how an hourly ob servational mode is more suitable for an EAGLE event search program.Comment: 18 pages, 4 figures, accepted for publication in Ap

Renormalized transport of inertial particles in surface flows

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)), which is valid in the case the deflections induced on the particle trajectories by the fluid flow can be considered small. We consider a class of compressible random velocity fields, in which the effect of recirculations is modelled by an oscillatory component in the Eulerian time correlation profile. The main issue we address here is whether fluid velocity fluctuations, in particular the effect of recirculation, may produce nontrivial corrections to the streaming particle velocity. Our result is that a small (large) degree of recirculation is associated with a decrease (increase) of streaming with respect to a quiescent fluid. The presence of this effect is confirmed numerically, away from the perturbative limit. Our approach also allows us to calculate the explicit expression for the eddy diffusivity, and to compare the efficiency of diffusive and ballistic transport.Comment: 18 pages, 13 figures, submitted to JF

Observation of Microlensing towards the Galactic Spiral Arms. EROS II 2 year survey

We present the analysis of the light curves of 8.5 million stars observed during two seasons by EROS (Experience de Recherche d'Objets Sombres), in the galactic plane away from the bulge. Three stars have been found that exhibit luminosity variations compatible with gravitational microlensing effects due to unseen objects. The corresponding optical depth, averaged over four directions, is 0.38 (+0.53, -0.15) 10^{-6}. All three candidates have long Einstein radius crossing times ($\sim$ 70 to 100 days). For one of them, the lack of evidence for a parallax or a source size effect enabled us to constrain the lens-source % geometric configuration. Another candidate displays a modulation of the magnification, which is compatible with the lensing of a binary source. The interpretation of the optical depths inferred from these observations is hindered by the imperfect knowledge of the distance to the target stars. Our measurements are compatible with expectations from simple galactic models under reasonable assumptions on the target distances.Comment: 11 pages, 13 figures, accepted by A&A in Aug 9

Labour productivity in state-owned enterprises

In the aftermath of the Global and Financial Crisis (GFC), between 2013 and 2015, the Portuguese government revoked four holidays for both public sector and private employees. We test whether the revocation had an effect on labour productivity in State-Owned Enterprises (SOEs) in Portugal. Moreover, we also study whether such effects are different taking into account the SOEs managed by the Central Government or the Local and Regional Governments. Our results show that revocation of holidays did not impact labour productivity for either central or local and regional government managed SOEs. Though revocation of holidays espoused to improve productivity, the policy seems to have served a ceremonial purpose, but not an economic oneinfo:eu-repo/semantics/publishedVersio

MACHO Mass Determination Based on Space Telescope Observation

We investigate the possibility of lens mass determination for a caustic crossing microlensing event based on a space telescope observation. We demonstrate that the parallax due to the orbital motion of a space telescope causes a periodic fluctuation of the light curve, from which the lens distance can be derived. Since the proper motion of the lens relative to the source is also measurable for a caustic crossing event, one can find a full solution for microlensing properties of the event, including the lens mass. To determine the lens mass with sufficient accuracy, the light curve near the caustic crossing should be observed within uncertainty of $\sim$ 1%. We argue that the Hubble Space Telescope observation of the caustic crossing supplied with ground-based observations of the full light curve will enable us to determine the mass of MACHOs, which is crucial for understanding the nature of MACHOs.Comment: 9 pages + 3 figures, accepted for publication in ApJ Letter

Astrometric Resolution of Severely Degenerate Binary Microlensing Events

We investigate whether the "close/wide" class of degeneracies in caustic-crossing binary microlensing events can be broken astrometrically. Dominik showed that these degeneracies are particularly severe because they arise from a degeneracy in the lens equation itself rather than a mere "accidental" mimicking of one light curve by another. A massive observing campaign of five microlensing collaborations was unable to break this degeneracy photometrically in the case of the binary lensing event MACHO 98-SMC-1. We show that this degeneracy indeed causes the image centroids of the wide and close solutions to follow an extremely similar pattern of motion during the time when the source is in or near the caustic. Nevertheless, the two image centroids are displaced from one another and this displacement is detectable by observing the event at late times. Photometric degeneracies therefore can be resolved astrometrically, even for these most severe cases.Comment: 11 pages, including 4 figures. Submitted to Ap

Microjansky sources at 1.4 GHz

We present a deep 1.4 GHz survey made with the Australia Telescope Compact Array (ATCA), having a background RMS of 9 microJy near the image phase centre, up to 25 microJy at the edge of a 50' field of view. Over 770 radio sources brighter than 45 microJy have been catalogued in the field. The differential source counts in the deep field provide tentative support for the growing evidence that the microjansky radio population exhibits significantly higher clustering than found at higher flux density cutoffs. The optical identification rate on CCD images is approximately 50% to R=22.5, and the optical counterparts of the faintest radio sources appear to be mainly single galaxies close to this optical magnitude limit.Comment: 6 pages, 4 figures, accepted by ApJ Letters 4 May 199