On distributional and asymptotic results for exponential functional of renewal -- reward processes describing risk models

Inspired by the double-debt problem in Japan where the mortgagor has to pay the remaining loan even if their house was destroyed by a catastrophic event, we model the lender's cash flow, by an exponential functional of a renewal-reward process. We propose an insurance add-on to the loan repayments and analyse the asymptotic behavior of the distribution of the first hitting time, which represents the probability of full repayment. We show that the finite-time probability of full loan repayment converges exponentially fast to the infinite-time one. In a few concrete scenarios, we calculate the exact form of the infinite-time probability and the corresponding premiums

Properties of the cosmological filament between two clusters: A possible detection of a large-scale accretion shock by SuzakuSuzaku

We report on the results of a $Suzaku$ observation of the plasma in the filament located between the two massive clusters of galaxies Abell 399 and Abell 401. Abell 399 ($z$=0.0724) and Abell 401 ($z$=0.0737) are expected to be in the initial phase of a cluster merger. In the region between the two clusters, we find a clear enhancement in the temperature of the filament plasma from 4 keV (expected value from a typical cluster temperature profile) to $kT\sim$6.5 keV. Our analysis also shows that filament plasma is present out to a radial distance of 15' (1.3 Mpc) from a line connecting the two clusters. The temperature profile is characterized by an almost flat radial shape with $kT\sim$6-7 keV within 10' or $\sim$0.8 Mpc. Across $r$=8'~from the axis, the temperature of the filament plasma shows a drop from 6.3 keV to 5.1 keV, indicating the presence of a shock front. The Mach number based on the temperature drop is estimated to be ${\cal M}\sim$1.3. We also successfully determined the abundance profile up to 15' (1.3 Mpc), showing an almost constant value ($Z$=0.3 solar) at the cluster outskirt. We estimated the Compton $y$-parameter to be $\sim$14.5$\pm1.3\times10^{-6}$, which is in agreement with $Planck$'s results (14-17$\times10^{-6}$ on the filament). The line of sight depth of the filament is $l\sim$1.1 Mpc, indicating that the geometry of filament is likely a pancake shape rather than cylindrical. The total mass of the filamentary structure is $\sim$7.7$\times10^{13}~\rm M_{\odot}$. We discuss a possible interpretation of the drop of X-ray emission at the rim of the filament, which was pushed out by the merging activity and formed by the accretion flow induced by the gravitational force of the filament.Comment: 8 pages, 8 figures, accepted for publication in A&

Interacting Large-Scale Magnetic Fields and Ionised Gas in the W50/SS433 System

The W50/SS433 system is an unusual Galactic outflow-driven object of debatable origin. We have used the Australia Telescope Compact Array (ATCA) to observe a new 198 pointing mosaic, covering $3^\circ \times 2^\circ$, and present the highest-sensitivity full-Stokes data of W50 to date using wide-field, wide-band imaging over a 2 GHz bandwidth centred at 2.1 GHz. We also present a complementary H$\alpha$ mosaic created using the Isaac Newton Telescope Photometric H$\alpha$ Survey of the Northern Galactic Plane (IPHAS). The magnetic structure of W50 is found to be consistent with the prevailing hypothesis that the nebula is a reanimated shell-like supernova remnant (SNR), that has been re-energised by the jets from SS433. We observe strong depolarization effects that correlate with diffuse H$\alpha$ emission, likely due to spatially-varying Faraday rotation measure (RM) fluctuations of $\ge48$ to 61 rad m$^{-2}$ on scales $\le4.5$ to 6 pc. We also report the discovery of numerous, faint, H$\alpha$ filaments that are unambiguously associated with the central region of W50. These thin filaments are suggestive of a SNR's shock emission, and almost all have a radio counterpart. Furthermore, an RM-gradient is detected across the central region of W50, which we interpret as a loop magnetic field with a symmetry axis offset by $\approx90^{\circ}$ to the east-west jet-alignment axis, and implying that the evolutionary processes of both the jets and the SNR must be coupled. A separate RM-gradient is associated with the termination shock in the Eastern ear, which we interpret as a ring-like field located where the shock of the jet interacts with the circumstellar medium. Future optical observations will be able to use the new H$\alpha$ filaments to probe the kinematics of the shell of W50, potentially allowing for a definitive experiment on W50's formation history.Comment: Submitted to MNRA

Ion-by-ion Cooling efficiencies

We present ion-by-ion cooling efficiencies for low-density gas. We use Cloudy (ver. 08.00) to estimate the cooling efficiencies for each ion of the first 30 elements (H-Zn) individually. We present results for gas temperatures between 1e4 and 1e8K, assuming low densities and optically thin conditions. When nonequilibrium ionization plays a significant role the ionization states deviate from those that obtain in collisional ionization equilibrium (CIE), and the local cooling efficiency at any given temperature depends on specific non-equilibrium ion fractions. The results presented here allow for an efficient estimate of the total cooling efficiency for any ionic composition. We also list the elemental cooling efficiencies assuming CIE conditions. These can be used to construct CIE cooling efficiencies for non-solar abundance ratios, or to estimate the cooling due to elements not explicitly included in any nonequilibrium computation. All the computational results are listed in convenient online tables.Comment: Submitted to ApJS. Electronic data available at http://wise-obs.tau.ac.il/~orlyg/ion_by_ion

Stochastic integration based on simple, symmetric random walks

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, it gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not c\`adl\`ag in general.Comment: 16 pages, some typos correcte

Why Do Only Some Galaxy Clusters Have Cool Cores?

Flux-limited X-ray samples indicate that about half of rich galaxy clusters have cool cores. Why do only some clusters have cool cores while others do not? In this paper, cosmological N-body + Eulerian hydrodynamic simulations, including radiative cooling and heating, are used to address this question as we examine the formation and evolution of cool core (CC) and non-cool core (NCC) clusters. These adaptive mesh refinement simulations produce both CC and NCC clusters in the same volume. They have a peak resolution of 15.6 h^{-1} kpc within a (256 h^{-1} Mpc)^3 box. Our simulations suggest that there are important evolutionary differences between CC clusters and their NCC counterparts. Many of the numerical CC clusters accreted mass more slowly over time and grew enhanced cool cores via hierarchical mergers; when late major mergers occurred, the CC's survived the collisions. By contrast, NCC clusters experienced major mergers early in their evolution that destroyed embryonic cool cores and produced conditions that prevented CC re-formation. As a result, our simulations predict observationally testable distinctions in the properties of CC and NCC beyond the core regions in clusters. In particular, we find differences between CC versus NCC clusters in the shapes of X-ray surface brightness profiles, between the temperatures and hardness ratios beyond the cores, between the distribution of masses, and between their supercluster environs. It also appears that CC clusters are no closer to hydrostatic equilibrium than NCC clusters, an issue important for precision cosmology measurements.Comment: 17 emulateapj pages, 17 figures, replaced with version accepted to Ap

Robust Digital Holography For Ultracold Atom Trapping

We have formulated and experimentally demonstrated an improved algorithm for design of arbitrary two-dimensional holographic traps for ultracold atoms. Our method builds on the best previously available algorithm, MRAF, and improves on it in two ways. First, it allows for creation of holographic atom traps with a well defined background potential. Second, we experimentally show that for creating trapping potentials free of fringing artifacts it is important to go beyond the Fourier approximation in modelling light propagation. To this end, we incorporate full Helmholtz propagation into our calculations.Comment: 7 pages, 4 figure

A Parameter Space Exploration of Galaxy Cluster Mergers I: Gas Mixing and the Generation of Cluster Entropy

We present a high-resolution set of adiabatic binary galaxy cluster merger simulations using FLASH. These are the highest-resolution simulations to date of such mergers using an AMR grid-based code with Eulerian hydrodynamics. In this first paper in a series we investigate the effects of merging on the entropy of the hot intracluster gas, specifically with regard to the ability of merging to heat and disrupt cluster "cool-cores." We find, in line with recent works, that the effect of fluid instabilities that are well-resolved in grid-based codes is to significantly mix the gases of the two clusters and to significantly increase the entropy of the gas of the final merger remnant. This result is characteristic of mergers over a range of initial mass ratio and impact parameter. In line with this, we find that the kinetic energy associated with random motions is higher in our merger remnants which have high entropy floors, indicating the motions have efficiently mixed the gas and heated the cluster core with gas of initially high entropy. We examine the implications of this result for the maintenance of high entropy floors in the centers of galaxy clusters and the derivation of the properties of dark matter from the thermal properties of the X-ray emitting gas.Comment: 25 pages, 23 figures, Accepted to Ap

Galaxy clusters at z~1 imaged by ALMA with the Sunyaev-Zel'dovich effect

We present high angular-resolution measurements of the thermal Sunyaev-Zel'dovich effect (SZE) toward two galaxy clusters, RCS J2319+0038 at z=0.9 and HSC J0947-0119 at z=1.1, by the Atacama Large Millimeter/submillimeter Array (ALMA) in Band 3. They are supplemented with available Chandra X-ray data, optical data taken by Hyper Suprime-Cam on Subaru, and millimeter-wave SZE data from the Atacama Cosmology Telescope. Taking into account departures from spherical symmetry, we have reconstructed non-parametrically the inner pressure profile of two clusters as well as electron temperature and density profiles for RCS J2319+0038. This is one of the first such measurements for an individual cluster at $z \gtrsim 0.9$. We find that the inner pressure profile of both clusters is much shallower than that of local cool-core clusters. Our results consistently suggest that RCS J2319+0038 hosts a weak cool core, where radiative cooling is less significant than in local cool cores. On the other hand, HSC J0947-0119 exhibits an even shallower pressure profile than RCS J2319+0038 and is more likely a non-cool-core cluster. The SZE centroid position is offset by more than 140 $h_{70}^{-1}$kpc from the peaks of galaxy distribution in HSC J0947-0119, suggesting a stronger influence of mergers in this cluster. We conclude that these distant clusters are at a very early stage of developing the cool cores typically found in clusters at lower redshifts.Comment: 26 pages, 13 figures, 8 tables, submitted to PAS