About the connection between the CℓC_{\ell} power spectrum of the Cosmic Microwave Background and the Γm\Gamma_{m} Fourier spectrum of rings on the sky

In this article we present and study a scaling law of the $m\Gamma_m$ CMB Fourier spectrum on rings which allows us (i) to combine spectra corresponding to different colatitude angles (e.g. several detectors at the focal plane of a telescope), and (ii) to recover the $C_l$ power spectrum once the $\Gamma_m$ coefficients have been measured. This recovery is performed numerically below the 1% level for colatitudes $\Theta> 80^\circ$ degrees. In addition, taking advantage of the smoothness of the $C_l$ and of the $\Gamma_m$, we provide analytical expressions which allow to recover one of the spectrum at the 1% level, the other one being known.Comment: 8 pages, 8 figure

About the connection between vacuum birefringence and the light-light scattering amplitude

Birefringence phenomena stemming from vacuum polarization are revisited in the framework of coherent scattering. Based on photon-photon scattering, our analysis brings out the direct connection between this process and vacuum birefringence. We show how this procedure can be extended to the Kerr and the Cotton-Mouton birefringences in vacuum, thus providing a unified treatment of various polarization schemes, including those involving static fields

Observation of periodic variable stars towards the galactic spiral arms by EROS II

We present the results of a massive variability search based on a photometric survey of a six square degree region along the Galactic plane at ($l = 305^\circ$, $b = -0.8^\circ$) and ($l = 330^\circ$, $b = -2.5^\circ$). This survey was performed in the framework of the EROS II (Exp\'erience de Recherche d'Objets Sombres) microlensing program. The variable stars were found among 1,913,576 stars that were monitored between April and June 1998 in two passbands, with an average of 60 measurements. A new period-search technique is proposed which makes use of a statistical variable that characterizes the overall regularity of the flux versus phase diagram. This method is well suited when the photometric data are unevenly distributed in time, as is our case. 1,362 objects whose luminosity varies were selected. Among them we identified 9 Cepheids, 19 RR Lyrae, 34 Miras, 176 eclipsing binaries and 266 Semi-Regular stars. Most of them are newly identified objects. The cross-identification with known catalogues has been performed. The mean distance of the RR Lyrae is estimated to be $\sim 4.9 \pm 0.3$ kpc undergoing an average absorption of $\sim 3.4 \pm 0.2$ magnitudes. This distance is in good agreement with the one of disc stars which contribute to the microlensing source star population.Our catalogue and light curves are available electronically from the CDS, Strasbourg and from our Web site http://eros.in2p3.fr.Comment: 15 pages, 11 figures, accepted in A&A (april 2002

The EROS2 search for microlensing events towards the spiral arms: the complete seven season results

The EROS-2 project has been designed to search for microlensing events towards any dense stellar field. The densest parts of the Galactic spiral arms have been monitored to maximize the microlensing signal expected from the stars of the Galactic disk and bulge. 12.9 million stars have been monitored during 7 seasons towards 4 directions in the Galactic plane, away from the Galactic center. A total of 27 microlensing event candidates have been found. Estimates of the optical depths from the 22 best events are provided. A first order interpretation shows that simple Galactic models with a standard disk and an elongated bulge are in agreement with our observations. We find that the average microlensing optical depth towards the complete EROS-cataloged stars of the spiral arms is $\bar{\tau} =0.51\pm .13\times 10^{-6}$, a number that is stable when the selection criteria are moderately varied. As the EROS catalog is almost complete up to $I_C=18.5$, the optical depth estimated for the sub-sample of bright target stars with $I_C<18.5$ ($\bar{\tau}=0.39\pm >.11\times 10^{-6}$) is easier to interpret. The set of microlensing events that we have observed is consistent with a simple Galactic model. A more precise interpretation would require either a better knowledge of the distance distribution of the target stars, or a simulation based on a Galactic model. For this purpose, we define and discuss the concept of optical depth for a given catalog or for a limiting magnitude.Comment: 22 pages submitted to Astronomy & Astrophysic

Probing For New Physics and Detecting non linear vacuum QED effects using gravitational wave interferometer antennas

Low energy non linear QED effects in vacuum have been predicted since 1936 and have been subject of research for many decades. Two main schemes have been proposed for such a 'first' detection: measurements of ellipticity acquired by a linearly polarized beam of light passing through a magnetic field and direct light-light scattering. The study of the propagation of light through an external field can also be used to probe for new physics such as the existence of axion-like particles and millicharged particles. Their existence in nature would cause the index of refraction of vacuum to be different from unity in the presence of an external field and dependent of the polarization direction of the light propagating. The major achievement of reaching the project sensitivities in gravitational wave interferometers such as LIGO an VIRGO has opened the possibility of using such instruments for the detection of QED corrections in electrodynamics and for probing new physics at very low energies. In this paper we discuss the difference between direct birefringence measurements and index of refraction measurements. We propose an almost parasitic implementation of an external magnetic field along the arms of the VIRGO interferometer and discuss the advantage of this choice in comparison to a previously proposed configuration based on shorter prototype interferometers which we believe is inadequate. Considering the design sensitivity in the strain, for the near future VIRGO+ interferometer, of $h<2\cdot10^{-23} \frac{1}{\sqrt{\rm Hz}}$ in the range 40 Hz $- 400$ Hz leads to a variable dipole magnet configuration at a frequency above 20 Hz such that $B^{2}D \ge 13000$ T$^{2}$m/$\sqrt{\rm Hz}$ for a `first' vacuum non linear QED detection

EROS 2 intensive observation of the caustic crossing of microlensing event MACHO SMC-98-1

We report on intensive photometric monitoring on 18 June 1998 of MACHO SMC-98-1, a binary-lens microlensing event seen toward the Small Magellanic Cloud (SMC). The observations cover 5.3 hours (UT 5:17 -- 10:37), and show a sharp drop of 1.8 mag during the first 1.8 hours, followed by an abrupt flattening at UT 7:08 +- 0:02. We interpret the kink at 7:08 as the end of the second caustic crossing (when the source first moved completely outside the caustic). These results indicate that mu sin(phi) <~ 1.5 km/s/kpc at the 2 sigma level, where mu is the proper motion of the lens (relative to the line of sight to the source), and phi is the unknown (and so random) angle of the caustic crossing. Hence, the source probably does not lie in either the Galactic halo or disk and so is most likely in the SMC itself. Our data can be combined with those of other groups to give more precise constraints on the proper motion (and hence the nature) of the lens

Observation of Microlensing towards the Galactic Spiral Arms: EROS II 3 year survey

We present an analysis of the light curves of 9.1 million stars observed during three seasons by EROS (Experience de Recherche d'Objets Sombres), in the Galactic plane away from the bulge. Seven stars exhibit luminosity variations compatible with gravitational microlensing effects due to unseen objects. The corresponding optical depth, averaged over four directions, is tau = 0.45 +0.24 -0.11 x 10^-6. While this value is compatible with expectations from simple galactic models under reasonable assumptions on the target distances, we find an excess of events with short timescale towards the direction closest to the Galactic Centre

Photometric Constraints on Microlens Spectroscopy of EROS-BLG-2000-5

We apply EROS photometric data to interpret previously published Keck and VLT spectra of the binary-microlens caustic-crossing event EROS-BLG-2000-5. We show that the VLT data imply that the outer 4 % of the limb of the K3-giant source is strongly in emission in Halpha, in contradiction to available models of the photosphere. This conflict could be resolved if the integrated Halpha emission from the chromosphere were equal to 8 % of the integrated Halpha absorption from the source as a whole. These conclusions regarding the extreme limb are almost completely model-independent. We also present a general method for using the photometric data to facilitate direct comparison between the atmospheric model and the spectroscopic data. While this method has some model-dependent features, it is fairly robust and can serve to guide the analysis of spectra while more detailed models of the lens geometry are being developed. In addition, we find that the color of the limb of the source (outer 5.5 % by radius) is Delta(V-I) = 0.37 redder than the source as a whole, so that it has the color of a M0 giant.Comment: 7 figures, 1 tabl