Continuous star cluster formation in the spiral NGC 45

We determined ages for 52 star clusters with masses < 10^6 solar masses in the low surface brightness spiral galaxy NGC 45. Four of these candidates are old globular clusters located in the bulge. The remaining ones span a large age range. The cluster ages suggest a continuous star/cluster formation history without evidence for bursts, consistent with the galaxy being located in a relatively unperturbed environment in the outskirts of the Sculptor group.Comment: 4 pages, 3 figures. To appear in "Island Universes - Structure and Evolution of Disk Galaxies", Terschelling (Netherlands), July 200

Area products for stationary black hole horizons

Area products for multi-horizon stationary black holes often have intriguing properties, and are often (though not always) independent of the mass of the black hole itself (depending only on various charges, angular momenta, and moduli). Such products are often formulated in terms of the areas of inner (Cauchy) horizons and outer (event) horizons, and sometimes include the effects of unphysical "virtual" horizons. But the conjectured mass-independence sometimes fails. Specifically, for the Schwarzschild-de Sitter [Kottler] black hole in (3+1) dimensions it is shown by explicit exact calculation that the product of event horizon area and cosmological horizon area is not mass independent. (Including the effect of the third "virtual" horizon does not improve the situation.) Similarly, in the Reissner-Nordstrom-anti-de Sitter black hole in (3+1) dimensions the product of inner (Cauchy) horizon area and event horizon area is calculated (perturbatively), and is shown to be not mass independent. That is, the mass-independence of the product of physical horizon areas is not generic. In spherical symmetry, whenever the quasi-local mass m(r) is a Laurent polynomial in aerial radius, r=sqrt{A/4\pi}, there are significantly more complicated mass-independent quantities, the elementary symmetric polynomials built up from the complete set of horizon radii (physical and virtual). Sometimes it is possible to eliminate the unphysical virtual horizons, constructing combinations of physical horizon areas that are mass independent, but they tend to be considerably more complicated than the simple products and related constructions currently being mooted in the literature.Comment: V1: 16 pages; V2: 9 pages (now formatted in PRD style). Minor change in title. Extra introduction, background, discussion. Several additional references; other references updated. Minor typos fixed. This version accepted for publication in PRD; V3: Minor typos fixed. Published versio

Non-linear optomechanical measurement of mechanical motion

Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of non-linear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic non-linearity of the radiation pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100~pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications.Comment: 8 pages, 4 figures, extensive supplementary material available with published versio

Structure and Mass of a Young Globular Cluster in NGC 6946

Using the Wide Field Planetary Camera 2 on board the Hubble Space Telescope, we have imaged a luminous young star cluster in the nearby spiral galaxy NGC 6946. The cluster has an absolute visual magnitude M(V)=-13.2, comparable to the brightest young `super-star clusters' in the Antennae merger galaxy. UBV colors indicate an age of about 15 Myr. The cluster has a compact core (core radius = 1.3 pc), surrounded by an extended envelope. We estimate that the effective radius (Reff) = 13 pc, but this number is uncertain because the outer parts of the cluster profile gradually merge with the general field. Combined with population synthesis models, the luminosity and age of the cluster imply a mass of 8.2x10^5 Msun for a Salpeter IMF extending down to 0.1 Msun, or 5.5x10^5 Msun if the IMF is log-normal below 0.4 Msun. Depending on model assumptions, the central density of the cluster is between 5300 Msun pc^-3 and 17000 Msun pc^-3, comparable to other high-density star forming regions. We also estimate a dynamical mass for the cluster, using high-dispersion spectra from the HIRES spectrograph on the Keck I telescope. The velocity dispersion is 10.0 +/- 2.7 km/s, implying a total cluster mass within 65 pc of (1.7 +/- 0.9) x 10^6 Msun. Comparing the dynamical mass with the mass estimates based on the photometry and population synthesis models, the mass-to-light ratio is at least as high as for a Salpeter IMF extending down to 0.1 Msun, although a turn-over in the IMF at 0.4 Msun is still possible within the errors. The cluster will presumably remain bound, evolving into a globular cluster-like object.Comment: 33 pages, including 10 figures and 3 tables. Accepted for publication in the Astrophysical Journa

Young and intermediate-age massive star clusters

An overview of our current understanding of the formation and evolution of star clusters is given, with main emphasis on high-mass clusters. Clusters form deeply embedded within dense clouds of molecular gas. Left-over gas is cleared within a few million years and, depending on the efficiency of star formation, the clusters may disperse almost immediately or remain gravitationally bound. Current evidence suggests that a few percent of star formation occurs in clusters that remain bound, although it is not yet clear if this fraction is truly universal. Internal two-body relaxation and external shocks will lead to further, gradual dissolution on timescales of up to a few hundred million years for low-mass open clusters in the Milky Way, while the most massive clusters (> 10^5 Msun) have lifetimes comparable to or exceeding the age of the Universe. The low-mass end of the initial cluster mass function is well approximated by a power-law distribution, dN/dM ~ M^{-2}, but there is mounting evidence that quiescent spiral discs form relatively few clusters with masses M > 2 x 10^5 Msun. In starburst galaxies and old globular cluster systems, this limit appears to be higher, at least several x 10^6 Msun. The difference is likely related to the higher gas densities and pressures in starburst galaxies, which allow denser, more massive giant molecular clouds to form. Low-mass clusters may thus trace star formation quite universally, while the more long-lived, massive clusters appear to form preferentially in the context of violent star formation.Comment: 21 pages, 3 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 9 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. PDFLaTeX, requires rspublic.cls style fil

Time lower bounds for nonadaptive turnstile streaming algorithms

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds

WFPC2 Observations of Massive and Compact Young Star Clusters in M31

We present color magnitude diagrams of four blue massive and compact star clusters in M31: G38, G44, G94, and G293. The diagrams of the four clusters reveal a well-populated upper main sequence and various numbers of supergiants. The U-B and B-V colors of the upper main sequence stars are used to determine reddening estimates of the different lines of sight in the M31 disk. Reddening values range from E(B-V) = 0.20 +/- 0.10 to 0.31 +/- 0.11. We statistically remove field stars on the basis of completeness, magnitude and color. Isochrone fits to the field-subtracted, reddening-corrected diagrams yield age estimates ranging from 63 +/- 15 Myr to 160 +/- 60 Myr. Implications for the recent evolution of the disk near NGC 206 are discussed.Comment: 17 pages, Latex, ApJ, in Pres

ICP polishing of silicon for high quality optical resonators on a chip

Miniature concave hollows, made by wet etching silicon through a circular mask, can be used as mirror substrates for building optical micro-cavities on a chip. In this paper we investigate how ICP polishing improves both shape and roughness of the mirror substrates. We characterise the evolution of the surfaces during the ICP polishing using white-light optical profilometry and atomic force microscopy. A surface roughness of 1 nm is reached, which reduces to 0.5 nm after coating with a high reflectivity dielectric. With such smooth mirrors, the optical cavity finesse is now limited by the shape of the underlying mirror

Optimal infinite scheduling for multi-priced timed automata

This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal non-terminating schedules for such double-priced timed automata is computable. This is done by a reduction of the problem to the determination of optimal mean-cycles in finite graphs with weighted edges. This reduction is obtained by introducing the so-called corner-point abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules

Exact String Solutions in Nontrivial Backgrounds

We show how the classical string dynamics in $D$-dimensional gravity background can be reduced to the dynamics of a massless particle constrained on a certain surface whenever there exists at least one Killing vector for the background metric. We obtain a number of sufficient conditions, which ensure the existence of exact solutions to the equations of motion and constraints. These results are extended to include the Kalb-Ramond background. The $D1$-brane dynamics is also analyzed and exact solutions are found. Finally, we illustrate our considerations with several examples in different dimensions. All this also applies to the tensionless strings.Comment: 22 pages, LaTeX, no figures; V2:Comments and references added; V3:Discussion on the properties of the obtained solutions extended, a reference and acknowledgment added; V4:The references renumbered, to appear in Phys Rev.