The Maximum Mass of Star Clusters

When an universal untruncated star cluster initial mass function (CIMF) described by a power-law distribution is assumed, the mass of the most massive star cluster in a galaxy (M_max) is the result of the size-of-sample (SoS) effect. This implies a dependence of M_max on the total number of star clusters (N). The SoS effect also implies that M_max within a cluster population increases with equal logarithmic intervals of age. This is because the number of clusters formed in logarithmic age intervals increases (assuming a constant cluster formation rate). This effect has been observed in the SMC and LMC. Based on the maximum pressure (P_int) inside molecular clouds, it has been suggested that a physical maximum mass (M_max[phys]) should exist. The theory predicts that M_max[phys] should be observable, i.e. lower than M_max that follows from statistical arguments, in big galaxies with a high star formation rate. We compare the SoS relations in the SMC and LMC with the ones in M51 and model the integrated cluster luminosity function (CLF) for two cases: 1) M_max is determined by the SoS effect and 2) M_max=M_max[phys]=constant. The observed CLF of M51 and the comparison of the SoS relations with the SMC and LMC both suggest that there exists a M_max[phys] of 5*10^5 M_sun in M51. The CLF of M51 looks very similar to the one observed in the ``Antennae'' galaxies. A direct comparison with our model suggests that there M_max[phys]=2*10^6 M_sun.Comment: 4 pages, contribution to "Globular Clusters: Guides to Galaxies", March 6th-10th, 200

Outskirts of Nearby Disk Galaxies: Star Formation and Stellar Populations

The properties and star formation processes in the far-outer disks of nearby spiral and dwarf irregular galaxies are reviewed. The origin and structure of the generally exponential profiles in stellar disks is considered to result from cosmological infall combined with a non-linear star formation law and a history of stellar migration and scattering from spirals, bars, and random collisions with interstellar clouds. In both spirals and dwarfs, the far-outer disks tend to be older, redder and thicker than the inner disks, with the overall radial profiles suggesting inside-out star formation plus stellar scattering in spirals, and outside-in star formation with a possible contribution from scattering in dwarfs. Dwarf irregulars and the far-outer parts of spirals both tend to be gas dominated, and the gas radial profile is often non-exponential although still decreasing with radius. The ratio of H-alpha to far-UV flux tends to decrease with lower surface brightness in these regions, suggesting either a change in the initial stellar mass function or the sampling of that function, or a possible loss of H-alpha photons.Comment: 20 pages, 8 figures, Invited review, Book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion

We determine the critical exponents for the XY universality class in three dimensions, which is expected to describe the $\lambda$-transition in ${}^4$He. They are obtained from the analysis of high-temperature series computed for a two-component $\lambda\phi^4$ model. The parameter $\lambda$ is fixed such that the leading corrections to scaling vanish. We obtain $\nu = 0.67166(55)$, $\gamma = 1.3179(11)$, $\alpha=-0.0150(17)$. These estimates improve previous theoretical determinations and agree with the more precise experimental results for liquid Helium.Comment: 8 pages, revte

The starburst phenomenon from the optical/near-IR perspective

The optical/near-IR stellar continuum carries unique information about the stellar population in a galaxy, its mass function and star-formation history. Star-forming regions display rich emission-line spectra from which we can derive the dust and gas distribution, map velocity fields, metallicities and young massive stars and locate shocks and stellar winds. All this information is very useful in the dissection of the starburst phenomenon. We discuss a few of the advantages and limitations of observations in the optical/near-IR region and focus on some results. Special attention is given to the role of interactions and mergers and observations of the relatively dust-free starburst dwarfs. In the future we expect new and refined diagnostic tools to provide us with more detailed information about the IMF, strength and duration of the burst and its triggering mechanisms.Comment: 6 pages, 3 figures, to appear in "Starbursts: from 30 Doradus to Lyman Break Galaxies" 2005, eds. R. de Grijs and R. M. Gonzalez Delgado (Kluwer

Efficiency of the dynamical mechanism

The most extreme starbursts occur in galaxy mergers, and it is now acknowledged that dynamical triggering has a primary importance in star formation. This triggering is due partly to the enhanced velocity dispersion provided by gravitational instabilities, such as density waves and bars, but mainly to the radial gas flows they drive, allowing large amounts of gas to condense towards nuclear regions in a small time scale. Numerical simulations with several gas phases, taking into account the feedback to regulate star formation, have explored the various processes, using recipes like the Schmidt law, moderated by the gas instability criterion. May be the most fundamental parameter in starbursts is the availability of gas: this sheds light on the amount of external gas accretion in galaxy evolution. The detailed mechanisms governing gas infall in the inner parts of galaxy disks are discussed.Comment: 6 pages, 3 figures, to be published in "Starbursts - From 30 Doradus to Lyman break galaxies", ed. R. de Grijs and R. Gonzalez-Delgad

Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation length exponent we get $\nu=0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $\gamma=1.2373(2)$, $\nu=0.63012(16)$, $\alpha=0.1096(5)$, $\eta=0.03639(15)$, $\beta=0.32653(10)$, $\delta=4.7893(8)$. Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $\Delta=0.52(3)$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.Comment: 40 pages, 15 figure

Star Formation on Galactic Scales: Empirical Laws

Empirical star formation laws from the last 20 years are reviewed with a comparison to simulations. The current form in main galaxy disks has a linear relationship between the star formation rate per unit area and the molecular cloud mass per unit area with a timescale for molecular gas conversion of about 2 Gyr. The local ratio of molecular mass to atomic mass scales nearly linearly with pressure, as determined from the weight of the gas layer in the galaxy. In the outer parts of galaxies and in dwarf irregular galaxies, the disk can be dominated by atomic hydrogen and the star formation rate per unit area becomes directly proportional to the total gas mass per unit area, with a consumption time of about 100 Gyr. The importance of a threshold for gravitational instabilities is not clear. Observations suggest such a threshold is not always important, while simulations generally show that it is. The threshold is difficult to evaluate because it is sensitive to magnetic and viscous forces, the presence of spiral waves and other local effects, and the equation of state.Comment: 16 pages, 2 figures, Ecole Evry Schatzman 2010: Star Formation in the Local Universe. Lecture 1 of

Post-Newtonian Gravitational Radiation

1 Introduction 2 Multipole Decomposition 3 Source Multipole Moments 4 Post-Minkowskian Approximation 5 Radiative Multipole Moments 6 Post-Newtonian Approximation 7 Point-Particles 8 ConclusionComment: 46 pages, in Einstein's Field Equations and Their Physical Implications, B. Schmidt (Ed.), Lecture Notes in Physics, Springe

Variation of the IMF

(abridged) The {stellar IMF} has been found to be essentially invariant. While some apparent differences are seen, the uncertainties inherent to this game do not allow a firm conclusion to be made that the IMF varies systematically with conditions. The IMF integrated over entire galaxies, however, is another matter. Chemical and photometric properties of various galaxies do hint at {galaxial IMFs} being steeper than the stellar IMF, as is also deduced from direct star-count analysis in the MW. These results are sensitive to the modelling of stellar populations and to corrections for stellar evolution, and are thus also uncertain. However, by realising that galaxies are made from dissolving star clusters, star clusters being viewed as {the fundamental building blocks of galaxies}, the result is found that galaxial IMFs must be significantly steeper than the stellar IMF, because the former results from a folding of the latter with the star-cluster mass function. Furthermore, this notion leads to the important insight that galaxial IMFs must vary with galaxy mass, and that the galaxial IMF is a strongly varying function of the star-formation history for galaxies that have assembled only a small mass in stars. Cosmological implications of this are discussed.Comment: 13 pages, to appear in IMFat50: The Initial Mass Function 50 years later, ed: E. Corbelli, F. Palla, and H. Zinnecker, Kluwer Academic Publishers; a meeting held at the Abbazia di Spineto, Tuscany, Italy -- May 16-20, 200