Parallel transport along Seifert manifolds and fractional monodromy

The notion of fractional monodromy was introduced by Nekhoroshev, Sadovski\'{i} and Zhilinski\'{i} as a generalization of standard (`integer') monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a general result that allows to compute fractional monodromy in various integrable Hamiltonian systems. In particular, we show that the non-triviality of fractional monodromy in 2 degrees of freedom systems with a Hamiltonian circle action is related only to the fixed points of the circle action. Our approach is based on the study of a specific notion of parallel transport along Seifert manifolds

Fractional bidromy in the vibrational spectrum of HOCl

We introduce the notion of fractional bidromy which is the combination of fractional monodromy and bidromy, two recent generalizations of Hamiltonian monodromy. We consider the vibrational spectrum of the HOCl molecule which is used as an illustrative example to show the presence of nontrivial fractional bidromy. To our knowledge, this is the first example of a molecular system where such a generalized monodromy is exhibited.Comment: 9 pages, 2 figue

Evolution of the Pairwise Peculiar Velocity Distribution Function in Lagrangian Perturbation Theory

The statistical distribution of the radial pairwise peculiar velocity of galaxies is known to have an exponential form as implied by observations and explicitly shown in N-body simulations. Here we calculate its statistical distribution function using the Zel'dovich approximation assuming that the primordial density fluctuations are Gaussian distributed. We show that the exponential distribution is realized as a transient phenomena on megaparsec scales in the standard cold-dark-matter model.Comment: 19 pages, 8 Postscript figures, AAS LaTe

Orbits in the H2O molecule

We study the forms of the orbits in a symmetric configuration of a realistic model of the H2O molecule with particular emphasis on the periodic orbits. We use an appropriate Poincar\'e surface of section (PSS) and study the distribution of the orbits on this PSS for various energies. We find both ordered and chaotic orbits. The proportion of ordered orbits is almost 100% for small energies, but decreases abruptly beyond a critical energy. When the energy exceeds the escape energy there are still non-escaping orbits around stable periodic orbits. We study in detail the forms of the various periodic orbits, and their connections, by providing appropriate stability and bifurcation diagrams.Comment: 21 pages, 14 figures, accepted for publication in CHAO

Luminosity density estimation from redshift surveys and the mass density of the Universe

In most direct estimates of the mass density (visible or dark) of the Universe, a central input parameter is the luminosity density of the Universe. Here we consider the measurement of this luminosity density from red-shift surveys, as a function of the yet undetermined characteristic scale R_H at which the spatial distribution of visible matter tends to a well defined homogeneity. Making the canonical assumption that the cluster mass to luminosity ratio M/L is the universal one, we can estimate the total mass density as a function \Omega_m(R_H,M/L). Taking the highest estimated cluster value M/L ~300h and a conservative lower limit R_H > 20 Mpc/h, we obtain the upper bound \Omega_m < 0.1 . We note that for values of the homogeneity scale R_H in the range R_H ~ (90 +/- 45) hMpc, the value of \Omega_m may be compatible with the nucleosynthesis inferred density in baryons.Comment: 16 pages, latex, no figures. To be published in Astrophysical Journal Letter

Impact of Reionization on the Stellar Populations of Nearby Dwarf Galaxies

Cold dark matter models for galaxy formation predict that low-mass systems will be the first sites of star formation. As these objects have shallow gravitational potential wells, the subsequent growth of their stellar populations may be halted by heating and gas loss due to reionization. This effect has been suggested to have profoundly influenced properties of present-day dwarf galaxies, including their stellar populations and even survival as visible galaxies. In this Letter we draw on results from quantitative studies of Local Group dwarf galaxy star formation histories, especially for Milky Way satellites, to show that no clear signature exists for a widespread evolutionary impact from reionization. All nearby dwarf galaxies studied in sufficient detail contain ancient populations indistinguishable in age from the oldest Galactic globular clusters. Ancient star formation activity proceeded over several Gyr, and some dwarf spheroidal galaxies even experienced fairly continuous star formation until just a few Gyr ago. Despite their uniformly low masses, their star formation histories differ considerably. The evolutionary histories of nearby dwarf galaxies appear to reflect influences from a variety of local processes rather than a dominant effect from reionization.Comment: Accepted by The Astrophysical Journal Letters. 5 pages, one figur

Hamiltonian Monodromy and Morse Theory

We show that Hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying Morse theory to the Hamiltonian of the system. Our proof is based on Takens's index theorem, which specifies how the energy-h Chern number changes when h passes a non-degenerate critical value, and a choice of admissible cycles in Fomenko-Zieschang theory. Connections of our result to some of the existing approaches to monodromy are discussed

Constraints on the small-scale power spectrum of density fluctuations from high-redshift gamma-ray bursts

Cosmological models that include suppression of the power spectrum of density fluctuations on small scales exhibit an exponential reduction of high-redshift, non-linear structures, including a reduction in the rate of gamma ray bursts (GRBs). Here we quantify the constraints that the detection of distant GRBs would place on structure formation models with reduced small-scale power. We compute the number of GRBs that could be detectable by the Swift satellite at high redshifts (z > 6), assuming that the GRBs trace the cosmic star formation history, which itself traces the formation of non-linear structures. We calibrate simple models of the intrinsic luminosity function of the bursts to the number and flux distribution of GRBs observed by the Burst And Transient Source Experiment (BATSE). We find that a discovery of high-z GRBs would imply strong constraints on models with reduced small-scale power. For example, a single GRB at z > 10, or 10 GRBs at z > 5, discovered by Swift during its scheduled two-year mission, would rule out an exponential suppression of the power spectrum on scales below R_c=0.09 Mpc (exemplified by warm dark matter models with a particle mass of m_x=2 keV). Models with a less sharp suppression of small-scale power, such as those with a red tilt or a running scalar index, n_s, are more difficult to constrain, because they are more degenerate with an increase in the power spectrum normalization, sigma_8, and with models in which star-formation is allowed in low-mass minihalos. We find that a tilt of \delta n_s ~ 0.1 is difficult to detect; however, an observed rate of 1 GRB/yr at z > 12 would yield an upper limit on the running of the spectral index, alpha = d(n_s)/d(ln k) > -0.05.Comment: 10 pages, 6 figures; Minor changes to match version published in Ap

Constraints on the Dark Matter Particle Mass from the Number of Milky Way Satellites

We have conducted N-body simulations of the growth of Milky Way-sized halos in cold and warm dark matter cosmologies. The number of dark matter satellites in our simulated Milky Ways decreases with decreasing mass of the dark matter particle. Assuming that the number of dark matter satellites exceeds or equals the number of observed satellites of the Milky Way we derive lower limits on the dark matter particle mass. We find with 95% confidence m_s > 13.3 keV for a sterile neutrino produced by the Dodelson and Widrow mechanism, m_s > 8.9 keV for the Shi and Fuller mechanism, m_s > 3.0 keV for the Higgs decay mechanism, and m_{WDM} > 2.3 keV for a thermal dark matter particle. The recent discovery of many new dark matter dominated satellites of the Milky Way in the Sloan Digital Sky Survey allows us to set lower limits comparable to constraints from the complementary methods of Lyman-alpha forest modeling and X-ray observations of the unresolved cosmic X-ray background and of dark matter halos from dwarf galaxy to cluster scales. Future surveys like LSST, DES, PanSTARRS, and SkyMapper have the potential to discover many more satellites and further improve constraints on the dark matter particle mass.Comment: 17 pages, 13 figures, replaced with final version published in Physical Review