Gravitational lensing of type Ia supernovae by galaxy clusters

We propose a method to remove the mass sheet degeneracy that arises when the mass of galaxy clusters is inferred from gravitational shear. The method utilizes high-redshift standard candles that undergo weak lensing. Natural candidates for such standard candles are type Ia supernovae (SN Ia). When corrected with the light-curve shape (LCS), the peak magnitude of SN Ia provides a standard candle with an uncertainty in apparent magnitude of $\Delta m\simeq 0.1-0.2$. Gravitational magnification of a background SN Ia by an intervening cluster would cause a mismatch between the observed SN Ia peak magnitude compared to that expected from its LCS and redshift. The average detection rate for SN Ia with a significant mismatch of $\ge2\Delta m$ behind a cluster at $z\simeq0.05-0.15$ is about $1-2$ supernovae per cluster per year at $J,I,R\lesssim25-26$. Since SNe are point-like sources for a limited period, they can experience significant microlensing by MACHOs in the intracluster medium. Microlensing events caused by MACHOs of $\sim10^{-4} M_\odot$ are expected to have time scales similar to that of the SN light curve. Both the magnification curve by a MACHO and the light curve of a SN Ia have characteristic shapes that allow to separate them. Microlensing events due to MACHOs of smaller mass can unambiguously be identified in the SN light curve if the latter is continuously monitored. The average number of identifiable microlensing events per nearby cluster ($z\lesssim0.05$) per year is $\sim 0.02 (f/0.01)$, where $f$ is the fraction of the cluster mass in MACHOs of masses $10^{-7} < M_{macho}/M_\odot < 10^{-4}$.Comment: Accepted for publication in the MNRA

How to Plant a Merger Tree

We investigate several approaches for constructing Monte Carlo realizations of the merging history of virialized dark matter halos (``merger trees'') using the extended Press-Schechter formalism. We describe several unsuccessful methods in order to illustrate some of the difficult aspects of this problem. We develop a practical method that leads to the reconstruction of mean quantities such as the conditional and overall mass functions as given by the Press-Schechter model. This method is convenient, computationally efficient, and works for any power spectrum or background cosmology. In addition, we investigate statistics that describe the distribution of the number of progenitors and their masses as a function of redshift.Comment: 13 pages, LaTeX, 10 postscript figures. To appear in MNRAS. Changed to MNRAS format with inlined figures. Minor changes in text and figures to match published version. No significant changes in conten

Provisioning Spot Market Cloud Resources to Create Cost-effective Virtual Clusters

Infrastructure-as-a-Service providers are offering their unused resources in the form of variable-priced virtual machines (VMs), known as "spot instances", at prices significantly lower than their standard fixed-priced resources. To lease spot instances, users specify a maximum price they are willing to pay per hour and VMs will run only when the current price is lower than the user's bid. This paper proposes a resource allocation policy that addresses the problem of running deadline-constrained compute-intensive jobs on a pool of composed solely of spot instances, while exploiting variations in price and performance to run applications in a fast and economical way. Our policy relies on job runtime estimations to decide what are the best types of VMs to run each job and when jobs should run. Several estimation methods are evaluated and compared, using trace-based simulations, which take real price variation traces obtained from Amazon Web Services as input, as well as an application trace from the Parallel Workload Archive. Results demonstrate the effectiveness of running computational jobs on spot instances, at a fraction (up to 60% lower) of the price that would normally cost on fixed priced resources.Comment: 14 pages, 4 figures, 11th International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP-11); Lecture Notes in Computer Science, Vol. 7016, 201

Strong Evolution in the Luminosity-Velocity Relation at z>1?

We present a method for constraining the evolution of the galaxy luminosity-velocity (LV) relation in hierarchical scenarios of structure formation. The comoving number density of dark-matter halos with circular velocity of 200 km/s is predicted in favored CDM cosmologies to be nearly constant over the redshift range 0<z<5. Any observed evolution in the density of bright galaxies implies in turn a corresponding evolution in the LV relation. We consider several possible forms of evolution for the zero-point of the LV relation and predict the corresponding evolution in galaxy number density. The Hubble Deep Field suggests a large deficit of bright (M_V < -19) galaxies at 1.4 < z < 2. If taken at face value, this implies a dimming of the LV zero-point by roughly 2 magnitudes. Deep, wide-field, near-IR selected surveys will provide more secure measurements to compare with our predictions.Comment: 4 pages, 2 figures. Submitted to ApJ Letter

Lensing by Lyman Limit Systems: Determining the Mass to Gas Ratio

We present a new method to determine the total mass-to-neutral gas ratio in Lyman-limits systems. The method exploits the relation between the neutral hydrogen column density and the magnification of background sources due to the weak gravitational lensing that these systems induce. Because weak lensing does not provide a direct measure of mass, one must use this relation in a statistical sense to solve for the average mass-to-gas ratio and its distribution. We use a detailed mock catalog of quasars (sources) and Lyman-limit systems (lenses) to demonstrate the applicability of this approach through our ability to recover the parameter. This mock catalog also allows us to check for systematics in the method and to sketch its limitations. For a universal constant mass-to-gas ratio and a sample of N quasars, we obtain an unbiased estimate of its value with 95% confidence limits (independent of its actual value) of +/- 140 {10^5/N)^0.5.Comment: 20 pages, 11 figures submitted to Ap