Asymptotic geometry of negatively curved manifolds of finite volume

We study the asymptotic behaviour of simply connected, Riemannian manifolds $X$ of strictly negative curvature admitting a non-uniform lattice $\Gamma$. If the quotient manifold $\bar X= \Gamma \backslash X$ is asymptotically $1/4$-pinched, we prove that $\Gamma$ is divergent and $U\bar X$ has finite Bowen-Margulis measure (which is then ergodic and totally conservative with respect to the geodesic flow); moreover, we show that, in this case, the volume growth of balls $B(x,R)$ in $X$ is asymptotically equivalent to a purely exponential function $c(x)e^{\delta R}$, where $\delta$ is the topological entropy of the geodesic flow of $\bar X$. \linebreak This generalizes Margulis' celebrated theorem to negatively curved spaces of finite volume. In contrast, we exhibit examples of lattices $\Gamma$ in negatively curved spaces $X$ (not asymptotically $1/4$-pinched) where, depending on the critical exponent of the parabolic subgroups and on the finiteness of the Bowen-Margulis measure, the growth function is exponential, lower-exponential or even upper-exponential.Comment: 25 p. This paper replaces arXiv:1503.03971, withdrawn by the authors due to the Theorem 1.1 whose statement is far from the main subject of the paper; for the sake of clearness, this new version concentrates only on the question of volume growth (theorems 1.2, 1.3 and 1.4). Theorem 1.1 of arXiv:1503.03971 is now the subject of another paper (Signed only by 2 authors Sambusetti and Peign\'e) focused on this rigidity problem with a much better presentation of the context and another rigidity resul

Asymptotic geometry of negatively curved manifolds of finite volume

We study the asymptotic behavior of simply connected Riemannian manifolds X of strictly negative curvature admitting a non-uniform lattice Γ. If the quotient manifold X = Γ\X is asymptotically 1=4-pinched, we prove that Γ is divergent and U X has finite Bowen-Margulis measure (which is then ergodic and totally conservative with respect to the geodesic flow); moreover, we show that, in this case, the volume growth of balls B(x,R) in X is asymptotically equivalent to a purely exponential function c.x/eδR, where δ is the topological entropy of the geodesic flow of X . This generalizes Margulis' celebrated theorem to negatively curved spaces of finite volume. In contrast, we exhibit examples of lattices Γ in negatively curved spaces X (not asymptotically 1/4-pinched) where, depending on the critical exponent of the parabolic subgroups and on the finiteness of the Bowen- Margulis measure, the growth function is exponential, lower-exponential or even upper-exponential

Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio

High precision microlensing maps of the Galactic bulge

We present detailed maps of the microlensing optical depth and event density over an area of 195 sq. deg towards the Galactic bulge. The maps are computed from synthetic stellar catalogues generated from the Besancon Galaxy Model, which comprises four stellar populations and a three-dimensional extinction map calibrated against the Two-Micron All-Sky Survey. The optical depth maps have a resolution of 15 arcminutes, corresponding to the angular resolution of the extinction map. We compute optical depth and event density maps for all resolved sources above I=19, for unresolved (difference image) sources magnified above this limit, and for bright standard candle sources in the bulge. We show that the resulting optical depth contours are dominated by extinction effects, exhibiting fine structure in stark contrast to previous theoretical optical depth maps. Optical depth comparisons between Galactic models and optical microlensing survey measurements cannot safely ignore extinction or assume it to be smooth. We show how the event distribution for hypothetical J and K-band microlensing surveys, using existing ground-based facilities such as VISTA, UKIRT or CFHT, would be much less affected by extinction, especially in the K band. The near infrared provides a substantial sensitivity increase over current I-band surveys and a more faithful tracer of the underlying stellar distribution, something which upcoming variability surveys such as VVV will be able to exploit. Synthetic population models offer a promising way forward to fully exploit large microlensing datasets for Galactic structure studies.Comment: 8 pages, submitted to MNRA

The Milky Way's external disc constrained by 2MASS star counts

Context. Thanks to recent large scale surveys in the near infrared such as 2MASS, the galactic plane that most suffers from extinction is revealed and its overall structure can be studied. Aims. This work aims at constraining the structure of the Milky Way external disc as seen in 2MASS data, and in particular the warp. Methods. We use the Two Micron All Sky Survey (hereafter 2MASS) along with the Stellar Population Synthesis Model of the Galaxy, developed in Besancon, to constrain the external disc parameters such as its scale length, its cutoff radius, and the slope of the warp. In order to properly interpret the observations, the simulated stars are reddened using a three dimensional extinction map. The shape of the stellar warp is then compared with previous results and with similar structures in gas and dust. Results. We find new constraints on the stellar disc, which is shown to be asymmetrical, similar to observations of HI. The positive longitude side is found to be easily modelled with a S shape warp but with a slope significantly smaller than the slope seen in the HI warp. At negative longitudes, the disc presents peculiarities which are not well reproduced by any simple model. Finally, comparing with the warp seen in the dust, it seems to follow a slope intermediate between the gas and the stars.Comment: 9 pages. Accepted for publication in Astronomy and Astrophysic

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

Collision Dynamics and Solvation of Water Molecules in a Liquid Methanol Film

Environmental molecular beam experiments are used to examine water interactions with liquid methanol films at temperatures from 170 K to 190 K. We find that water molecules with 0.32 eV incident kinetic energy are efficiently trapped by the liquid methanol. The scattering process is characterized by an efficient loss of energy to surface modes with a minor component of the incident beam that is inelastically scattered. Thermal desorption of water molecules has a well characterized Arrhenius form with an activation energy of 0.47{\pm}0.11 eV and pre-exponential factor of 4.6 {\times} 10^(15{\pm}3) s^(-1). We also observe a temperature dependent incorporation of incident water into the methanol layer. The implication for fundamental studies and environmental applications is that even an alcohol as simple as methanol can exhibit complex and temperature dependent surfactant behavior.Comment: 8 pages, 5 figure

Tracing the long bar with red-clump giants

Over the last decade a series of results have lent support to the hypothesis of the existence of a long thin bar in the Milky Way with a half-length of 4.5 kpc and a position angle of around 45 deg. This is apparently a very different structure from the triaxial bulge of the Galaxy. In this paper, we analyse the stellar distribution in the inner 4 kpc of the Galaxy to see if there is clear evidence for two triaxial or barlike structures, or whether there is only one. By using the red-clump population as a tracer of the structure of the inner Galaxy we determine the apparent morphology of the inner Galaxy. Star counts from 2MASS are used to provide additional support for this analysis. We show that there are two very different large-scale triaxial structures coexisting in the inner Galaxy: a long thin stellar bar constrained to the Galactic plane (|b|<2 deg) with a position angle of 43.1 +- 1.8 deg, and a distinct triaxial bulge that extends to at least |b|<7.5 deg with a position angle of 12.6 +- 3.2 deg. The scale height of the bar source distribution is around 100 pc, whereas for the bulge the value of this parameter is five times larger.Comment: 16 pages, 35 figures, accepted for publication in A&

PRIMA subretinal wireless photovoltaic microchip implantation in non-human primate and feline models

PURPOSE: To evaluate the surgical technique for subretinal implantation of two sizes of PRIMA photovoltaic wireless microchip in two animal models, and refine these surgical procedures for human trials. METHODS: Cats and Macaca fascicularis primates with healthy retina underwent vitrectomy surgery and were implanted with subretinal wireless photovoltaic microchip at the macula/central retina. The 1.5mm PRIMA chip was initially studied in feline eyes. PRIMA implant (2mm,1.5mm sizes) arrays were studied in primates. Feasibility of subretinal chip implantation was evaluated with a newly-developed surgical technique, with surgical complications and adverse events recorded. RESULTS: The 1.5mm implant was placed in the central retina of 11 feline eyes, with implantation duration 43-106 days. The 1.5mm implant was correctly positioned into central macula of 11 primate eyes, with follow-up periods of minimum 6 weeks (n = 11), 2 years (n = 2), and one eye for 3 years. One primate eye underwent multi-chip 1.5mm implantation using two 1.5mm chips. The 2mm implant was delivered to 4 primate eyes. Optical coherence tomography confirmed correct surgical placement of photovoltaic arrays in the subretinal space in all 26 eyes. Intraoperative complications in primate eyes included retinal tear, macular hole, retinal detachment, and vitreous hemorrhage that resolved spontaneously. Postoperatively, there was no case of significant ocular inflammation in the 1.5mm implant group. CONCLUSIONS: We report subretinal implantation of 1.5mm and 2mm photovoltaic arrays in the central retina of feline and central macula of primate eyes with a low rate of device-related complications. The in vivo PRIMA implantation technique has been developed and refined for use for a 2mm PRIMA implant in ongoing human trials

Microlensing as a probe of the Galactic structure; 20 years of microlensing optical depth studies

Microlensing is now a very popular observational astronomical technique. The investigations accessible through this effect range from the dark matter problem to the search for extra-solar planets. In this review, the techniques to search for microlensing effects and to determine optical depths through the monitoring of large samples of stars will be described. The consequences of the published results on the knowledge of the Milky-Way structure and its dark matter component will be discussed. The difficulties and limitations of the ongoing programs and the perspectives of the microlensing optical depth technique as a probe of the Galaxy structure will also be detailed.Comment: Accepted for publication in General Relativity and Gravitation. General Relativity and Gravitation in press (2010) 0