A quasar microlensing light-curve generator for LSST

ABSTRACT We present a tool to generate mock quasar microlensing light curves and sample them according to any observing strategy. An updated treatment of the fixed and random velocity components of observer, lens, and source is used, together with a proper alignment with the external shear defining the magnification map caustic orientation. Our tool produces quantitative results on high magnification events and caustic crossings, which we use to study three lensed quasars known to display microlensing, viz. RX J1131–1231, HE 0230–2130, and Q 2237+0305, as they would be monitored by The Rubin Observatory Legacy Survey of Space and Time (LSST). We conclude that depending on the location on the sky, the lens and source redshift, and the caustic network density, the microlensing variability may deviate significantly than the expected ∼20-yr average time-scale (Mosquera & Kochanek 2011). We estimate that ∼300 high magnification events with Δmag>1 mag could potentially be observed by LSST each year. The duration of the majority of high magnification events is between 10 and 100 d, requiring a very high cadence to capture and resolve them. Uniform LSST observing strategies perform the best in recovering microlensing high magnification events. Our web tool can be extended to any instrument and observing strategy, and is freely available as a service at http://gerlumph.swin.edu.au/tools/lsst_generator/, along with all the related code.

The diffusion of CO2-brine storage based on stochastic partial differential equations

The migration of CO2 is stochastic in heterogeneous porous media. This paper considers the CO2 diffusion with the case of steady flow in heterogeneous porous media. The partial differential equations of CO2 diffusion in random velocity field are established based on the mass conservation equations of CO2- brine two-phase flow with the change of time scale and spatial scale under the influence of heterogeneity such as permeability and porosity. The random travel process of CO2 is quantified by joint probability distributions and joint statistical moments (mean and variance), and the diffusion model of CO2 particle in random velocity field is established under the condition of non-linear and immiscibility in heterogeneous porous media. The micro mechanism of diffusion in heterogeneous porous media is revealed by numerical simulation. The general conclusion of steady state flow of CO2 diffusion in heterogeneous porous media was verified by simulating Sleipner CO2-brine storage in Norway.

Isotropic scattering coefficient of the solid earth

SUMMARY The isotropic scattering model is a simple mathematical model of the radiative transfer theory (RTT) for the propagation of the wave energy density in random media. There have been many measurements of the isotropic scattering coefficient of the heterogeneous solid earth medium, where the target region varies from the lower and upper mantle, the crust, sediments, volcanoes, mines, rock samples and also the crust and the upper mantle of the moon. Reported isotropic scattering coefficients increase according to some power of frequency with some scatter. We know that the RTT is well approximated by the diffusion equation in the multiple scattering regime, where the equipartition is established. Then, the transport scattering coefficient effectively functions as an isotropic scattering coefficient even if the scattering coefficient derived by the Born approximation for the random velocity fluctuation is anisotropic. Recent review of the power spectral density functions of random velocity fluctuations in the solid earth revealed from various kinds of measurements shows that their spectral envelope is well approximated by the inverse cube of wavenumber for a wide range of wavenumbers (Sato, 2019). The transport scattering coefficient derived from the spectral envelope linearly increases with frequency, which well explains the observed isotropic scattering coefficients for a wide range of frequencies. However, some reported isotropic scattering coefficients show unusual behaviour: the isotropic scattering coefficient increases as depth decreases in the crust and the upper mantle of the earth and the moon, those beneath volcanoes are larger than those in the lithosphere, and that in a sandstone sample with a large porosity is larger than that in a gabbro sample with little porosity. Those differences may suggest possible scattering contribution of pores and cracks widely distributed in addition to the scattering by random velocity fluctuations.