First Detection of CO in a Low Surface Brightness Galaxy

We report on the first attempts at searching for CO in red low surface brightness galaxies, and the first detection of molecular gas in a low surface brightness (mu_B(0)_{obs} > 23 mag arcsec^{-2}) galaxy. Using the IRAM 30m telescope, CO(1-0) and CO(2-1) lines were searched for in four galaxies -- P06-1, P05-5, C05-3, & C04-2. In three of the galaxies no CO was detected, to T_{MB} ~ 1.8mK (at the 3 sigma level). In the fourth galaxy, P06-1, both lines were detected. Comparing our findings with previous studies shows P06-1 to have a molecular-to-atomic mass ratio considerably lower than is predicted using theoretical models based on high surface brightness galaxy studies. This indicates the N(H_2)/(int{T(CO)dv}) conversion factor for low surface brightness galaxies may currently be consistently underestimated by a factor of 3 - 20.Comment: 8 pages, 2 figures, accepted by the ApJ

Optical microrheology using rotating laser-trapped particles

We demonstrate an optical system that can apply and accurately measure the torque exerted by the trapping beam on a rotating birefringent probe particle. This allows the viscosity and surface effects within liquid media to be measured quantitatively on a micron-size scale using a trapped rotating spherical probe particle. We use the system to measure the viscosity inside a prototype cellular structure.Comment: 5 pages, 4 figures. v2: bibliographic details, minor text correction

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

An estimate for the Morse index of a Stokes wave

Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler-Lagrange equation of a certain functional. This allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.Comment: This version contains an additional reference and some minor change

Further Discoveries of 12CO in Low Surface Brightness Galaxies

Using the IRAM 30m telescope we have obtained seven new, deep CO J(1-0) and J(2-1) observations of low surface brightness (LSB) galaxies. Five of the galaxies have no CO detected to extremely low limits (0.1-0.4 K km/s at J(1-0)), while two of the galaxies, UGC 01922 and UGC 12289, have clear detections in both line transitions. When these observations are combined with all previous CO observations taken of LSB systems, we compile a total of 34 observations, in which only 3 galaxies have had detections of their molecular gas. Comparing the LSB galaxies with and without CO detections to a sample of high surface brightness (HSB) galaxies with CO observations indicates that it is primarily the low density of baryonic matter within LSB galaxies which is causing their low CO fluxes. Finally, we note that one of the massive LSB galaxies studied in this project, UGC 06968 (a Malin-1 `cousin'), has upper limits placed on both M_H2 and M_H2/M_HI which are 10-20 times lower than the lowest values found for any galaxy (LSB or HSB) with similar global properties. This may be due to an extremely low temperature and metallicity within UGC 06968, or simply due to the CO distribution within the galaxy being too diffuse to be detected by the IRAM beam.Comment: 18 pages, 8 figures, 4 tables. Accepted by Ap

Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model

The influence of the finite number N of particles coupled to a monochromatic wave in a collisionless plasma is investigated. For growth as well as damping of the wave, discrete particle numerical simulations show an N-dependent long time behavior resulting from the dynamics of individual particles. This behavior differs from the one due to the numerical errors incurred by Vlasov approaches. Trapping oscillations are crucial to long time dynamics, as the wave oscillations are controlled by the particle distribution inhomogeneities and the pulsating separatrix crossings drive the relaxation towards thermal equilibrium.Comment: 11 pages incl. 13 figs. Phys. Rev. E, in pres

CO Detection and Millimeter Continuum Emission from Low Surface Brightness Galaxies

We present BIMA and IRAM CO(1--0) observations of seven low surface brightness (LSB) galaxies, including three large spirals with faint disks but prominent bulges, and four relatively small LSB galaxies with irregular disks. The giant LSB galaxies are UGC 5709, UGC 6614 and F568-6 (Malin2). The smaller LSB galaxies are NGC 5585, UGC 4115, UGC 5209 and F583-1. The galaxies were selected based on their relatively high metallicity and apparent signs of star formation in their disks. The BIMA maps suggested the presence of molecular gas in 2 of the giant LSB galaxies, F568-6 and UGC 6614. Using the 30m IRAM telescope we detected CO (1--0) emission in the disks of both galaxies and in the nucleus of F568-6. The molecular gas in these galaxies is clearly offset from the nucleus and definitely associated with the LSB disk. In addition we also detected a millimeter continuum source in the center of UGC 6614. When compared with VLA 1.5 GHz observations of the galaxy, the emission was found to have a flat spectrum indicating that the millimeter continuum emission is most likely due to an active galactic nucleus (AGN) in the galaxy. Our results show that giant LSB spirals may contain significant quantities of molecular gas in their disks and also harbor radio bright AGN in their centers

Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics

Optical application and measurement of torque on microparticles of isotropic nonabsorbing material

We show how it is possible to controllably rotate or align microscopic particles of isotropic nonabsorbing material in a TEM00 Gaussian beam trap, with simultaneous measurement of the applied torque using purely optical means. This is a simple and general method of rotation, requiring only that the particle is elongated along one direction. Thus, this method can be used to rotate or align a wide range of naturally occurring particles. The ability to measure the applied torque enables the use of this method as a quantitative tool--the rotational equivalent of optical tweezers based force measurement. As well as being of particular value for the rotation of biological specimens, this method is also suitable for the development of optically-driven micromachines.Comment: 8 pages, 6 figure

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page