Non-Analyticity and the van der Waals Limit

We study the analyticity properties of the free energy f_\ga(m) of the Kac model at points of first order phase transition, in the van der Waals limit \ga\searrow 0. We show that there exists an inverse temperature $\beta_0$ and \ga_0>0 such that for all $\beta\geq \beta_0$ and for all \ga\in(0,\ga_0), f_\ga(m) has no analytic continuation along the path $m\searrow m^*$ ($m^*$ denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure p_\ga(h), which is related to the free energy f_\ga(m) by a Legendre transform

Orbits Supporting Bars within Bars

High-resolution observations of the inner regions of barred disk galaxies have revealed many asymmetrical, small-scale central features, some of which are best described as secondary bars. Because orbital time-scales in the galaxy center are short, secondary bars are likely to be dynamically decoupled from the main kiloparsec-scale bars. Here, we show that regular orbits exist in such doubly-barred potentials and that they can support the bars in their motion. We find orbits in which particles remain on loops: closed curves which return to their original positions after two bars have come back to the same relative orientation. Stars trapped around stable loops could form the building blocks for a long-lived, doubly-barred galaxy. Using the loop representation, we can find which orbits support the bars in their motion, and what are the constraints on the sizes and shapes of self-consistent double bars. In particular, it appears that a long-lived secondary bar may exist only when an Inner Lindblad Resonance is present in the primary bar, and that it would not extend beyond this resonance.Comment: 18 pages, 11 figures, to appear in MNRA

Scaling Limit of the Prudent Walk

We describe the scaling limit of the nearest neighbour prudent walk on the square lattice, which performs steps uniformly in directions in which it does not see sites already visited. We show that the scaling limit is given by the process Z(u) = s_1 theta^+(3u/7) e_1 + s_2 theta^-(3u/7) e_2, where e_1, e_2 is the canonical basis, theta^+(t), resp. theta^-(t), is the time spent by a one-dimensional Brownian motion above, resp. below, 0 up to time t, and s_1, s_2 are two random signs. In particular, the asymptotic speed of the walk is well-defined in the L^1-norm and equals 3/7.Comment: Better exposition, stronger claim, simpler description of the limiting process; final version, to appear in Electr. Commun. Probab

Near-Infrared Adaptive Optics Imaging of the Central Regions of Nearby Sc Galaxies. II. NGC 247 and NGC 2403

J, H, and K' images obtained with the Canada-France-Hawaii Telescope adaptive optics system are used to investigate the star-forming histories of the central regions of the Sc galaxies NGC 247 and NGC 2403. The brightest resolved red stars within 15 arcsec of the nucleus of each galaxy are red supergiants, indicating that the central few hundred parsecs of these galaxies experienced star formation within the last ~ 0.1 Gyr. However, when averaged over Gyr time scales, the star-forming histories of the inner disks of these galaxies have been remarkably similar, as expected if the long-term evolution of disks is defined by local characteristics such as mass density. It is demonstrated that NGC 247 and NGC 2403, like M33, harbour nuclear star clusters with stellar contents that differ from the surrounding central light concentrations. The nucleus of NGC 2403 is significantly bluer than that of the other two galaxies and the K-band surface brightnesses near the centers of NGC 247 and NGC 2403 are 1 -- 2 mag per square arcsec lower than in M33. Finally, it is noted that young or intermediate-age nuclear star clusters are a common occurence in nearby spirals, indicating that nuclear star formation in these objects is either continuous or episodic on time scales of 0.1 - 1 Gyr.Comment: 27 pages of text and 14 figures; to appear in the Astronomical Journa

Double Bars, Inner Disks, and Nuclear Rings in Early-Type Disk Galaxies

We present results from an imaging survey of an unbiased sample of thirty-eight early-type (S0--Sa), low-inclination, optically barred galaxies in the field. Our goal was to find and characterize central stellar and gaseous structures: secondary bars, inner disks, and nuclear rings. Bars inside bars are surprisingly common: at least one quarter of the sample galaxies (possibly as many as 40%) are double-barred, with no preference for Hubble type or the strength of the primary bar. A typical secondary bar is ~12% of the size of its primary bar and 240--750 pc in radius. We see no significant effect of secondary bars on nuclear activity. We also find kiloparsec-scale inner disks in at least 20% of our sample, almost exclusively in S0 galaxies. These disks are on average 20% the size of their host bar, and show a wider range of relative sizes than do secondary bars. Nuclear rings are present in about a third of our sample. Most are dusty, sites of current or recent star formation, or both; such rings are preferentially found in Sa galaxies. Three S0 galaxies (15% of the S0's) appear to have purely stellar nuclear rings, with no evidence for dust or recent star formation. The fact that these central stellar structures are so common indicates that the inner regions of early-type barred galaxies typically contain dynamically cool and disklike structures. This is especially true for S0 galaxies, where secondary bars, inner disks, and/or stellar nuclear rings are present at least two thirds of the time. (abridged)Comment: LaTeX, 15 pages, 7 EPS figures; to appear in The Astronomical Journal (July 2002

A Constant Bar Fraction out to Redshift z~1 in the Advanced Camera for Surveys Field of the Tadpole Galaxy

Bar-like structures were investigated in a sample of 186 disk galaxies larger than 0.5 arcsec that are in the I-band image of the Tadpole galaxy taken with the HST ACS. We found 22 clear cases of barred galaxies, 21 galaxies with small bars that appear primarily as isophotal twists in a contour plot, and 11 cases of peculiar bars in clump-cluster galaxies, which are face-on versions of chain galaxies. The latter bars are probably young, as the galaxies contain only weak interclump emission. Four of the clearly barred galaxies at z~0.8-1.2 have grand design spirals. The bar fraction was determined as a function of galaxy inclination and compared with the analogous distribution in the local Universe. The bar fraction was also determined as a function of galaxy angular size. These distributions suggest that inclination and resolution effects obscure nearly half of the bars in our sample. The bar fraction was also determined as a function of redshift. We found a nearly constant bar fraction of 0.23+-0.03 from z~0 to z=1.1. When corrected for inclination and size effects, this fraction is comparable to the bar fraction in the local Universe, ~0.4, as tabulated for all bar and Hubble types in the Third Reference Catalogue of Galaxies. The average major axis of a barred galaxy in our sample is ~10 kpc after correcting for redshift with a LambdaCDM cosmology. Galaxy bars were present in normal abundance at least ~8 Gy ago (z~1); bar dissolution cannot be common during a Hubble time unless the bar formation rate is comparable to the dissolution rate.Comment: to appear in ApJ, Sept 1, 2004, Vol 612, 18 pg, 12 figure

The Molecular Gas in the Circumnuclear Region of Seyfert Galaxies

Sub-arcsecond IRAM Plateau de Bure mm-interferometric observations of the 12CO (2-1) line emission in the Seyfert~1 NGC 3227 and the Seyfert~2 NGC 1068 have revealed complex kinematic systems in the inner 100 pc to 300 pc that are not consistent with pure circular motion in the host galaxies. Modeling of these kinematic systems with elliptical orbits in the plane of the host galaxy (representing gas motion in a bar potential) is a possible solution but does not reproduce all features observed. A better description of the complex kinematics is achieved by circular orbits which are tilted out of the plane of the host galaxy. This could indicate that the thin circumnuclear gas disk is warped. In the case of NGC 1068 the warp model suggests that at a radius of about 70 pc, the gas disk is oriented edge-on providing material for the obscuration of the AGN nucleus. The position-velocity diagrams show rising rotation curves at r 2 x 10^7 M_solar for NGC 3227 and > 10^8 M_solar for NGC 1068 within the central 25 pc.Comment: 14 pages, Ap.J. letter, accepte