Free vibrations of an unbounded periodically reinforced elastic layer

The object of analysis is an unbounded layer made of two isotropic, linear elastic materials and periodically laminated along the Ox1 axis (cf. Fig.1). The layer is resting on the rigid base. It is assumed that the laminas are homogeneous and their number is very large. Hence we deal with a certain microstructured layer. The aim of this contribution is to propose a certain mass discretized model for the analysis of vibrations of the layer. It is shown that there exist two kinds of these vibrations which are independent of x2 and x3 coordinates

The Optical Gravitational Lensing Experiment. Catalog of stellar proper motions in the OGLE-II Galactic bulge fields

We present a proper motion (\mu) catalogue of 5,080,236 stars in 49 Optical Gravitational Lensing Experiment II (OGLE-II) Galactic bulge (GB) fields, covering a range of -11 deg. <l< 11 deg. and -6 deg. <b<3 deg., the total area close to 11 square degrees. The proper motion measurements are based on 138 - 555 I-band images taken during four observing seasons: 1997-2000. The catalogue stars are in the magnitude range 11 < I < 18 mag. In particular, the catalogue includes Red Clump Giants (RCGs) and Red Giants in the GB, and main sequence stars in the Galactic disc. The proper motions up to \mu = 500 mas/yr were measured with the mean accuracy of 0.8-3.5 mas/yr, depending on the brightness of a star. This catalogue may be useful for studying the kinematic of stars in the GB and the Galactic disk.Comment: 13 pages, 16 figures, MNRAS in pres

The OGLE View of Microlensing towards the Magellanic Clouds. III. Ruling out sub-solar MACHOs with the OGLE-III LMC data

In the third part of the series presenting the Optical Gravitational Lensing Experiment (OGLE) microlensing studies of the dark matter halo compact objects (MACHOs) we describe results of the OGLE-III monitoring of the Large Magellanic Cloud (LMC). This unprecedented data set contains almost continuous photometric coverage over 8 years of about 35 million objects spread over 40 square degrees. We report a detection of two candidate microlensing events found with the automated pipeline and an additional two, less probable, candidate events found manually. The optical depth derived for the two main candidates was calculated following a detailed blending examination and detection efficiency determination and was found to be tau=(0.16+-0.12)10^-7. If the microlensing signal we observe originates from MACHOs it means their masses are around 0.2 M_Sun and they compose only f=3+-2 per cent of the mass of the Galactic Halo. However, the more likely explanation of our detections does not involve dark matter compact objects at all and rely on natural effect of self-lensing of LMC stars by LMC lenses. In such a scenario we can almost completely rule out MACHOs in the sub-solar mass range with an upper limit at f<7 per cent reaching its minimum of f<4 per cent at M=0.1 M_Sun. For masses around M=10 M_Sun the constraints on the MACHOs are more lenient with f ~ 20 per cent. Owing to limitations of the survey there is no reasonable limit found for heavier masses, leaving only a tiny window of mass spectrum still available for dark matter compact objects.Comment: Accepted for publication in MNRAS. On-line data available on OGLE website: http://ogle.astrouw.edu.p

The quest for companions to post-common envelope binaries. II. NSVS14256825 and HS0705+6700

We report new mid-eclipse times of the two close binaries NSVS14256825 and HS0705+6700, harboring an sdB primary and a low-mass main-sequence secondary. Both objects display clear variations in the measured orbital period, which can be explained by the action of a third object orbiting the binary. If this interpretation is correct, the third object in NSVS14256825 is a giant planet with a mass of roughly 12 M_Jup. For HS0705+6700, we provide evidence that strengthens the case for the suggested periodic nature of the eclipse time variation and reduces the uncertainties in the parameters of the brown dwarf implied by that model. The derived period is 8.4 yr and the mass is 31 M_Jup, if the orbit is coplanar with the binary. This research is part of the PlanetFinders project, an ongoing collaboration between professional astronomers and student groups at high schools.Comment: Accepted by Astron. and Astrophy

Microlensing optical depth toward the Galactic Bulge using bright sources from OGLE-II

We present a measurement of the microlensing optical depth toward the Galactic Bulge based on 4 years of the OGLE-II survey using Red Clump Giant (RCG). Using 32 events we find tau=2.55_{-0.46}^{+0.57}* 10^{-6} at (l,b)=(1.16, -2.75). Taking into account the measured gradient along the Galactic latitude b, tau = [ (4.48+/- 2.37) + (0.78+/- 0.84)* b]* 10^{-6}, this value is consistent with previous measurements using RCG sources and recent theoretical predictions. We determine the microlensing parameters and select events using a model light curve with the flux blending. We find that ~38% of the OGLE-II events which appear to have RCG sources are actually due to much fainter stars blended with a bright companion. We show explicitly that model fits without blending result in similar tau estimates through partial cancellation of contributions from higher detection efficiency, underestimated time-scales and larger number of selected events. This approach, however, leads to biased time-scale distributions and event rates. Consequently, microlensing studies should carefully consider source confusion effects even for bright stars.Comment: 49 pages and 18 figures, ApJ in press, the value changed due to the systematic correctio

Microlensing of Relativistic Knots in the Quasar HE1104-1805

We present 3 years of photometry of the ``Double Hamburger'' lensed quasar, HE1104-1805, obtained on 102 separate nights using the OGLE 1.3-m telescope. Both the A and B images show variations, but with substantial differences in the lighcurves at all time delays. At the 310 day delay reported by Wisotzki and collaborators the difference lightcurve has an rms amplitude of 0.060 mag. The structure functions for the A and B images are quite different, with image A more than twice as variable as image B (a factor of 4 in structure function) on timescales of less than a month. Adopting microlensing as a working hypothesis for the uncorrelated variability, the short timescale argues for the relativistic motion of one or more components of the source. We argue that the small amplitude of the fluctuations is due to the finite size of the source with respect to the microlenses.Comment: As accepted for publication in ApJ. 22 pages. The discussion of microlensing at high optical depth has been shortened and a few minor points have been clarifie

An R- and I-Band Photometric Variability Survey of the Cygnus OB2 Association

We present a catalog of photometrically variable stars discovered within two 21'.3 X 21'.3 fields centered on the Cygnus OB2 association. There have hitherto been no deep optical variability studies of Cyg OB2 despite it being replete with early-type massive stars, perhaps due to the high and variable extinction (up to A_V ~ 20) that permeates much of the region. Here we provide results of the first variability study with this combination of spatial coverage (~ 0.5 deg) and photometric depth (R ~ 21 mag). We find 121 stars to be variable in both R- and I-band, 116 of them newly discovered. Of the 121 variables, we identify 27 eclipsing binaries (EBs) and eclipsing binary candidates, 20 potential Herbig Ae/Be stars, and 52 pulsating variables. Confirming both the status and the cluster membership of the Herbig Ae/Be stars would address the uncertainty regarding the age and star formation history of Cyg OB2. We match our catalog to known variables and binaries in the region, 2MASS near-IR (NIR) data, and Chandra X-ray observations to find counterparts to new variables in other wavelengths.Comment: 34 pages, 12 figures, submitted to Ap