Double lenses

The analysis of the shear induced by a single cluster on the images of a large number of background galaxies is all centered around the curl-free character of a well-known vector field that can be derived from the data. Such basic property breaks down when the source galaxies happen to be observed through two clusters at different redshifts, partially aligned along the line of sight. In this paper we address the study of double lenses and obtain five main results. (i) First we generalize the procedure to extract the available information, contained in the observed shear field, from the case of a single lens to that of a double lens. (ii) Then we evaluate the possibility of detecting the signature of double lensing given the known properties of the distribution of clusters of galaxies. (iii) As a different astrophysical application, we demonstrate how the method can be used to detect the presence of a dark cluster that might happen to be partially aligned with a bright cluster studied in terms of statistical lensing. (iv) In addition, we show that the redshift distribution of the source galaxies, which in principle might also contribute to break the curl-free character of the shear field, actually produces systematic effects typically two orders of magnitude smaller than the double lensing effects we are focusing on. (v) Remarkably, a discussion of relevant contributions to the noise of the shear measurement has brought up an intrinsic limitation of weak lensing analyses, since one specific contribution, associated with the presence of a non-vanishing two-galaxy correlation function, turns out not to decrease with the density of source galaxies (and thus with the depth of the observations).Comment: 40 pages, 15 figures. Accepted for publication in ApJ main journa

Larson's third law and the universality of molecular cloud structure

Larson (1981) first noted a scaling relation between masses and sizes in molecular clouds that implies that these objects have approximately constant column densities. This original claim, based upon millimeter observations of carbon monoxide lines, has been challenged by many theorists, arguing that the apparent constant column density observed is merely the result of the limited dynamic range of observations, and that in reality clouds have column density variations over two orders of magnitudes. In this letter we investigate a set of nearby molecular clouds with near-infrared excess methods, which guarantee very large dynamic ranges and robust column density measurements, to test the validity of Larson's third law. We verify that different clouds have almost identical average column densities above a given extinction threshold; this holds regardless of the extinction threshold, but the actual average surface mass density is a function of the specific threshold used. We show that a second version of Larson's third law, involving the mass-radius relation for single clouds and cores, does not hold in our sample, indicating that individual clouds are not objects that can be described by constant column density. Our results instead indicate that molecular clouds are characterized by a universal structure. Finally we point out that this universal structure can be linked to the log-normal nature of cloud column density distributions.Comment: 5 pages, 4 figures, A&A in press (letter

Hipparcos distances of Ophiuchus and Lupus cloud complexes

We combine extinction maps from the Two Micron All Sky Survey (2MASS) with Hipparcos and Tycho parallaxes to obtain reliable and high-precision estimates of the distance to the Ophiuchus and Lupus dark complexes. Our analysis, based on a rigorous maximum-likelihood approach, shows that the rho-Ophiuchi cloud is located at (119 +/- 6) pc and the Lupus complex is located at (155 +/- 8) pc; in addition, we are able to put constraints on the thickness of the clouds and on their orientation on the sky (both these effects are not included in the error estimate quoted above). For Ophiuchus, we find some evidence that the streamers are closer to us than the core. The method applied in this paper is currently limited to nearby molecular clouds, but it will find many natural applications in the GAIA-era, when it will be possible to pin down the distance and three-dimensional structure of virtually every molecular cloud in the Galaxy.Comment: A&A in press - Corrected typo (Lupus distance) in the electronic abstrac

Smoothed Particle Hydrodynamics Calculations of Stellar Interactions

Smoothed Particle Hydrodynamics is a multidimensional Lagrangian method of numerical hydrodynamics that has been used to tackle a wide variety of problems in astrophysics. Here we develop the basic equations of the SPH scheme, and we discuss some of its numerical properties and limitations. As an illustration of typical astrophysical applications, we discuss recent calculations of stellar interactions, including collisions between main sequence stars and the coalescence of compact binaries.Comment: 21 pages, invited review paper to appear in Journal of Computational and Applied Mathematics (JCAM). Fig. 2 is available from the authors in hardcopy form only. Revised, slightly abbreviated versio

Strong Lensing Reconstruction

We present a general linear algorithm for measuring the surface mass density 1-\kappa from the observable reduced shear g=\gamma/(1-\kappa) in the strong lensing regime. We show that in general, the observed polarization field can be decomposed into ``electric'' and ``magnetic'' components, which have independent and redundant solutions, but perfectly orthogonal noise properties. By combining these solutions, one can increase the signal-to-noise ratio by \sqrt{2}. The solutions allow dynamic optimization of signal and noise, both in real and Fourier space (using arbitrary smoothing windows). Boundary conditions have no effect on the reconstructions, apart from its effect on the signal-to-noise. Many existing reconstruction techniques are recovered as special cases of this framework. The magnetic solution has the added benefit of yielding the global and local parity of the reconstruction in a single step.Comment: final accepted version for ApJ

The noise of cluster mass reconstructions from a source redshift distribution

The parameter-free reconstruction of the surface-mass density of clusters of galaxies is one of the principal applications of weak gravitational lensing. From the observable ellipticities of images of background galaxies, the tidal gravitational field (shear) of the mass distribution is estimated, and the corresponding surface mass density is constructed. The noise of the resulting mass map is investigated here, generalizing previous work which included mainly the noise due to the intrinsic galaxy ellipticities. Whereas this dominates the noise budget if the lens is very weak, other sources of noise become important, or even dominant, for the medium-strong lensing regime close to the center of clusters. In particular, shot noise due to a Poisson distribution of galaxy images, and increased shot noise owing to the correlation of galaxies in angular position and redshift, can yield significantly larger levels of noise than that from the intrinsic ellipticities only. We estimate the contributions from these various effects for two widely used smoothing operations, showing that one of them effectively removes the Poisson and the correlation noises related to angular positions of galaxies. Noise sources due to the spread in redshift of galaxies are still present in the optimized estimator and are shown to be relevant in many cases. We show how (even approximate) redshift information can be profitably used to reduce the noise in the mass map. The dependence of the various noise terms on the relevant parameters (lens redshift, strength, smoothing length, redshift distribution of background galaxies) are explicitly calculated and simple estimates are provided.Comment: 18 pages, A&A in pres

Mixing in massive stellar mergers

The early evolution of dense star clusters is possibly dominated by close interactions between stars, and physical collisions between stars may occur quite frequently. Simulating a stellar collision event can be an intensive numerical task, as detailed calculations of this process require hydrodynamic simulations in three dimensions. We present a computationally inexpensive method in which we approximate the merger process, including shock heating, hydrodynamic mixing and mass loss, with a simple algorithm based on conservation laws and a basic qualitative understanding of the hydrodynamics of stellar mergers. The algorithm relies on Archimedes' principle to dictate the distribution of the fluid in the stable equilibrium situation. We calibrate and apply the method to mergers of massive stars, as these are expected to occur in young and dense star clusters. We find that without the effects of microscopic mixing, the temperature and chemical composition profiles in a collision product can become double-valued functions of enclosed mass. Such an unphysical situation is mended by simulating microscopic mixing as a post-collision effect. In this way we find that head-on collisions between stars of the same spectral type result in substantial mixing, while mergers between stars of different spectral type, such as type B and O stars ($\sim$10 and $\sim$40\msun respectively), are subject to relatively little hydrodynamic mixing.Comment: Accepted by MNRA