Motivic Serre invariants, ramification, and the analytic Milnor fiber

We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce the so-called analytic Milnor fiber associated to the germ of a morphism f from a smooth complex algebraic variety X to the affine line. This analytic Milnor fiber is a smooth rigid variety over the field of Laurent series C((t)). Its etale cohomology coincides with the singular cohomology of the classical topological Milnor fiber of f; the monodromy transformation is given by the Galois action. Moreover, the points on the analytic Milnor fiber are closely related to the motivic zeta function of f, and the arc space of X. We show how the motivic zeta function can be recovered as some kind of Weil zeta function of the formal completion of X along the special fiber of f, and we establish a corresponding Grothendieck trace formula, which relates, in particular, the rational points on the analytic Milnor fiber over finite extensions of C((t)), to the Galois action on its etale cohomology. The general observation is that the arithmetic properties of the analytic Milnor fiber reflect the structure of the singularity of the germ f.Comment: Some minor errors corrected. The original publication is available at http://www.springerlink.co

The Extraordinary `Superthin' Spiral Galaxy UGC7321. I. Disk Color Gradients and Global Properties from Multiwavelength Observations

We present B- and R-band imaging and photometry, H-alpha narrow-band imaging, NIR H-band imaging, and HI 21-cm spectroscopy of the nearby Sd spiral galaxy UGC7321. UGC7321 exhibits a remarkably thin stellar disk with no bulge component. The galaxy has a very diffuse, low surface brightness disk, which appears to suffer little internal extinction in spite of its edge-on geometry. The UGC7321 disk shows significant B-R color gradients in both the radial and vertical directions. These color gradients cannot be explained solely by dust and are indicative of changes in the mix of stellar ages and/or metallicity as a function of both radius and height above the galaxy plane. The outer regions of the UGC7321 disk are too blue to be explained by low metallicity alone (B-R<0.6), and must be relatively young. However, the galaxy also contains stellar populations with B-R>1.1, indicating it is not a young or recently-formed galaxy. The disk of UGC7321 is not a simple exponential, but exhibits a light excess at small radii, as well as distinct surface brightness zones. Together the properties of UGC7321 imply that it is an under-evolved galaxy in both a dynamical and in a star-formation sense. (Abridged)Comment: Accepted to the Astronomical Journal; 28 pages, 1 table and 21 figures (GIF and postscript

The effect of metallicity on the Cepheid distance scale and its implications for the Hubble constant (H0H_0) determination

Recent HST determinations of the expansion's rate of the Universe (the Hubble constant, H_0) assumed that the Cepheid Period-Luminosity relation at V and I are independent of metallicity (Freedman, et al., 1996, Saha et al., 1996, Tanvir et al., 1995). The three groups obtain different vales for H_0. We note that most of this discrepancy stems from the asumption (by both groups) that the Period-Luminosity relation is independent of metallicity. We come to this conclusion as a result of our study of the Period-Luminosity relation of 481 Cepheids with 3 millions two colour measurements in the Large Magellanic Cloud and the Small Magellanic Cloud obtained as a by-product of the EROS microlensing survey. We find that the derived interstellar absorption corrections are particularly sensitive to the metallicity and when our result is applied to recent estimates based on HST Cepheids observations it makes the low-H_0 values higher and the high-H_0 value lower, bringing those discrepant estimates into agrement around $H_0 \approx 70 km/s Mpc^{-1}$.Comment: 4 pages, Latex, with 2 .ps accepted for publication astronomy and astrophysics Letter

Observational Limits on Machos in the Galactic Halo

We present final results from the first phase of the EROS search for gravitational microlensing of stars in the Magellanic Clouds by unseen deflectors (machos: MAssive Compact Halo Objects). The search is sensitive to events with time scales between 15 minutes and 200 days corresponding to deflector masses in the range 1.e-7 to a few solar masses. Two events were observed that are compatible with microlensing by objects of mass of about 0.1 Mo. By comparing the results with the expected number of events for various models of the Galaxy, we conclude that machos in the mass range [1.e-7, 0.02] Mo make up less than 20% (95% C.L.) of the Halo dark matter.Comment: 4 pages, 3 Postscript figures, to be published in Astronomy & Astrophysic

Fermi Large Area Telescope Bright Gamma-ray Source List

Following its launch in June 2008, the Fermi Gamma-ray Space Telescope (Fermi) began a sky survey in August. The Large Area Telescope (LAT) on Fermi in 3 months produced a deeper and better-resolved map of the gamma-ray sky than any previous space mission. We present here initial results for energies above 100 MeV for the 205 most significant (statistical significance greater than ~10-sigma) gamma-ray sources in these data. These are the best-characterized and best-localized point-like (i.e., spatially unresolved) gamma-ray sources in the early-mission data.Comment: Accepted by ApJS. Many helpful comments by referee incorporated 57 pages, 12 figure

AGAPEROS: Searches for microlensing in the LMC with the Pixel Method; 2, Selection of possible microlensing events

We apply the pixel method of analysis (sometimes called ``pixel lensing'') to a small subset of the EROS-1 microlensing observations of the bar of the Large Magellanic Cloud (LMC). The pixel method is designed to find microlensing events of unresolved source stars and had heretofore been applied only to M31 where essentially all sources are unresolved. With our analysis optimised for the detection of long-duration microlensing events due to 0.01-1 Mo Machos, we detect no microlensing events and compute the corresponding detection efficiencies. We show that the pixel method should detect 10 to 20 times more microlensing events for M>0.05 Mo Machos compared to a classical analysis of the same data which latter monitors only resolved stars. In particular, we show that for a full halo of Machos in the mass range 0.1 -- 0.5 Mo, a pixel analysis of the three-year EROS-1 data set covering 0.39 deg^2 would yield 4 events.We apply the pixel method of analysis (sometimes called ''pixel lensing'') to a small subset of the EROS-1 microlensing observations of the bar of the Large Magellanic Cloud (LMC). The pixel method is designed to find microlensing events of unresolved source stars and had heretofore been applied only to M31 where essentially all sources are unresolved. With our analysis optimised for the detection of long-duration microlensing events due to 0.01-1 Mo Machos, we detect no microlensing events and compute the corresponding detection efficiencies. We show that the pixel method, applied to crowded fields, should detect 10 to 20 times more microlensing events for M>0.05 Mo Machos compared to a classical analysis of the same data which latter monitors only resolved stars. In particular, we show that for a full halo of Machos in the mass range 0.1-0.5 M $\bigodot$, a pixel analysis of the three-year EROS-1 data set covering $0.39deg^{2}$ would yield $\simeq 4$ events

Metallicity Effects on the Cepheid Extragalactic Distance Scale from EROS photometry in LMC and SMC

This is an investigation of the period-luminosity relation of classical Cepheids in samples of different metallicity. It is based on 481 Cepheids in the Large and Small Magellanic Clouds from the blue and red filter CCD observations (most similar to V_J & R_J) of the French EROS microlensing project. The data-set is complete and provides an excellent basis for a differential analysis between LMC and SMC. In comparison to previous studies of effects on the PL-relation, the EROS data-set offers extremely well-sampled light curves and well-filled instability strips. This allows reliable separation of Cepheids pulsating in the fundamental and the first overtone mode and derivation of differential reddening. Our main result concerns the determination of distances to galaxies which are inferred by using the LMC as a base and using two color photometry to establish the amount of reddening. We find a zero-point offset between SMC and LMC which amounts to a difference between inferred and true distance modulus of 0.14 \pm 0.06 mag in the VI_c system. The offset is exactly the same in both sets of PL-relations - of the fundamental and of the first overtone mode Cepheids. No effect is seen on the slopes of the PL-relations, although the fundamental and the first overtone mode Cepheids have different PL slopes. We attribute the color and the zero-point offset to the difference in metallicity between the SMC and LMC Cepheids. A metallicity effect of that small magnitude still has important consequencies for the inferred Cepheid distances and the determination of H_0. When applied to recent estimates based on HST Cepheid observations, our metallicity dependence makes the low-H_0 values (Sandage et al. 1994) higher and the high-H_0 values (Freedman et al. 1994b) lower, thus bringing thoseComment: 14 pages, Latex, with 8 .ps accepted for publication in astronomy and astrophysic

AGAPEROS: Searches for microlensing in the LMC with the Pixel Method; 1, Data treatment and pixel light curves production

The presence and abundance of MAssive Compact Halo Objects (MACHOs) towards the Large Magellanic Cloud (LMC) can be studied with microlensing searches. The 10 events detected by the EROS and MACHO groups suggest that objects with 0.5 Mo could fill 50% of the dark halo. This preferred mass is quite surprising, and increasing the presently small statistics is a crucial issue. Additional microlensing of stars too dim to be resolved in crowded fields should be detectable using the Pixel Method. We present here an application of this method to the EROS 91-92 data (one tenth of the whole existing data set). We emphasize the data treatment required for monitoring pixel fluxes. Geometric and photometric alignments are performed on each image. Seeing correction and error estimates are discussed. 3.6" x 3.6" super-pixel light curves, thus produced, are very stable over the 120 days time-span. Fluctuations at a level of 1.8% of the flux in blue and 1.3% in red are measured on the pixel light curves. This level of stability is comparable with previous estimates. The data analysis dedicated to the search of possible microlensing events together with refined simulations will be presented in a companion paper.Recent surveys monitoring millions of light curves of resolved stars in the LMC have discovered several microlensing events. Unresolved stars could however significantly contribute to the microlensing rate towards the LMC. Monitoring pixels, as opposed to individual stars, should be able to detect stellar variability as a variation of the pixel flux. We present a first application of this new type of analysis (Pixel Method) to the LMC Bar. We describe the complete procedure applied to the EROS 91-92 data (one tenth of the existing CCD data set) in order to monitor pixel fluxes. First, geometric and photometric alignments are applied to each images. Averaging the images of each night reduces significantly the noise level. Second, one light curve for each of the 2.1 10^6 pixels is built and pixels are lumped into 3.6"x3.6" super-pixels, one for each elementary pixel. An empirical correction is then applied to account for seeing variations. We find that the final super-pixel light curves fluctuate at a level of 1.8% of the flux in blue and 1.3% in red. We show that this noise level corresponds to about twice the expected photon noise and confirms previous assumptions used for the estimation of the contribution of unresolved stars. We also demonstrate our ability to correct very efficiently for seeing variations affecting each pixel flux. The technical results emphasised here show the efficacy of the Pixel Method and allow us to study luminosity variations due to possible microlensing events and variable stars in two companion papers