Self-Consistent Response of a Galactic Disk to an Elliptical Perturbation Halo Potential

We calculate the self-consistent response of an axisymmetric galactic disk perturbed by an elliptical halo potential of harmonic number m = 2, and obtain the net disk ellipticity. Such a potential is commonly expected to arise due to a galactic tidal encounter and also during the galaxy formation process. The self-gravitational potential corresponding to the self-consistent, non-axisymmetric density response of the disk is obtained by inversion of Poisson equation for a thin disk. This response potential is shown to oppose the perturbation potential, because physically the disk self-gravity resists the imposed potential. This results in a reduction in the net ellipticity of the perturbation halo potential in the disk plane. The reduction factor denoting this decrease is independent of the strength of the perturbation potential, and has a typical minimum value of 0.75 - 0.9 for a wide range of galaxy parameters. The reduction is negligible at all radii for higher harmonics (m > or = 3) of the halo potential. (abridged).Comment: 26 pages (LaTex- aastex style), 3 .eps figures. To appear in the Astrophysical Journal, Vol. 542, Oct. 20, 200

Very Luminous Carbon Stars in the Outer Disk of the Triangulum Spiral Galaxy

Stars with masses in the range from about 1.3 to 3.5 Mo pass through an evolutionary stage where they become carbon stars. In this stage, which lasts a few Myr, these stars are extremely luminous pulsating giants. They are so luminous in the near-infrared that just a few of them can double the integrated luminosity of intermediate-age (0.6 to 2 Gyr) Magellanic Cloud clusters at 2.2 microns. Astronomers routinely use such near-infrared observations to minimize the effects of dust extinction, but it is precisely in this band that carbon stars can contribute hugely. The actual contribution of carbon stars to the outer disk light of evolving spiral galaxies has not previously been morphologically investigated. Here we report new and very deep near-IR images of the Triangulum spiral galaxy M33=NGC 598, delineating spectacular arcs of carbon stars in its outer regions. It is these arcs which dominate the near-infrared m=2 Fourier spectra of M33. We present near-infrared photometry with the Hale 5-m reflector, and propose that the arcs are the signature of accretion of low metallicity gas in the outer disk of M33.Comment: 4 pages, 4 figures. Revised version submitted to A&A Letter

The Distribution of Bar and Spiral Strengths in Disk Galaxies

The distribution of bar strengths in disk galaxies is a fundamental property of the galaxy population that has only begun to be explored. We have applied the bar/spiral separation method of Buta, Block, and Knapen to derive the distribution of maximum relative gravitational bar torques, Q_b, for 147 spiral galaxies in the statistically well-defined Ohio State University Bright Galaxy Survey (OSUBGS) sample. Our goal is to examine the properties of bars as independently as possible of their associated spirals. We find that the distribution of bar strength declines smoothly with increasing Q_b, with more than 40% of the sample having Q_b <= 0.1. In the context of recurrent bar formation, this suggests that strongly-barred states are relatively short-lived compared to weakly-barred or non-barred states. We do not find compelling evidence for a bimodal distribution of bar strengths. Instead, the distribution is fairly smooth in the range 0.0 <= Q_b < 0.8. Our analysis also provides a first look at spiral strengths Q_s in the OSU sample, based on the same torque indicator. We are able to verify a possible weak correlation between Q_s and Q_b, in the sense that galaxies with the strongest bars tend also to have strong spirals.Comment: Accepted for publication in the Astronomical Journal, August 2005 issue (LaTex, 23 pages + 11 figures, uses aastex.cls

Analytic models and forward scattering from accelerator to cosmic-ray energies

Analytic models for hadron-hadron scattering are characterized by analytical parametrizations for the forward amplitudes and the use of dispersion relation techniques to study the total cross section $\sigma_{tot}$ and the $\rho$ parameter. In this paper we investigate four aspects related to the application of the model to $pp$ and $\bar{p}p$ scattering, from accelerator to cosmic-ray energies: 1) the effect of different estimations for $\sigma_{tot}$ from cosmic-ray experiments; 2) the differences between individual and global (simultaneous) fits to $\sigma_{tot}$ and $\rho$; 3) the role of the subtraction constant in the dispersion relations; 4) the effect of distinct asymptotic inputs from different analytic models. This is done by using as a framework the single Pomeron and the maximal Odderon parametrizations for the total cross section. Our main conclusions are the following: 1) Despite the small influence from different cosmic-ray estimations, the results allow us to extract an upper bound for the soft pomeron intercept: $1 + \epsilon = 1.094$; 2) although global fits present good statistical results, in general, this procedure constrains the rise of $\sigma_{tot}$; 3) the subtraction constant as a free parameter affects the fit results at both low and high energies; 4) independently of the cosmic-ray information used and the subtraction constant, global fits with the odderon parametrization predict that, above $\sqrt s \approx 70$ GeV, $\rho_{pp}(s)$ becomes greater than $\rho_{\bar{p}p}(s)$, and this result is in complete agreement with all the data presently available. In particular, we infer $\rho_{pp} = 0.134 \pm 0.005$ at $\sqrt s = 200$ GeV and $0.151 \pm 0.007$ at 500 GeV (BNL RHIC energies).Comment: 16 pages, 7 figures, aps-revtex, wording changes, corrected typos, to appear in Physical Review

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Psi-floor diagrams and a Caporaso-Harris type recursion

Floor diagrams are combinatorial objects which organize the count of tropical plane curves satisfying point conditions. In this paper we introduce Psi-floor diagrams which count tropical curves satisfying not only point conditions but also conditions given by Psi-classes (together with points). We then generalize our definition to relative Psi-floor diagrams and prove a Caporaso-Harris type formula for the corresponding numbers. This formula is shown to coincide with the classical Caporaso-Harris formula for relative plane descendant Gromov-Witten invariants. As a consequence, we can conclude that in our case relative descendant Gromov-Witten invariants equal their tropical counterparts.Comment: minor changes to match the published versio

Variation of Galactic Bar Length with Amplitude and Density as Evidence for Bar Growth over a Hubble Time

K_s-band images of 20 barred galaxies show an increase in the peak amplitude of the normalized m=2 Fourier component with the R_25-normalized radius at this peak. This implies that longer bars have higher $m=2$ amplitudes. The long bars also correlate with an increased density in the central parts of the disks, as measured by the luminosity inside 0.25R_25 divided by the cube of this radius in kpc. Because denser galaxies evolve faster, these correlations suggest that bars grow in length and amplitude over a Hubble time with the fastest evolution occurring in the densest galaxies. All but three of the sample have early-type flat bars; there is no clear correlation between the correlated quantities and the Hubble type.Comment: ApJ Letters, 670, L97, preprint is 7 pages, 4 figure