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The detection of microlensing has opened the way for the development of new methods in galactic astronomy. This series of papers investigates what microlensing can teach us about the structure and shape of the dark halo. In this paper we present formulas for the microlensing rate, optical depth and event duration distributions for a simple set of axisymmetric disk-halo models. The halos are based on the power--law models which have simple velocity distributions. Using these models, we show that there is a large uncertainty in the predicted microlensing rate because of uncertainty in the halo parameters. For example, models which reproduce the measured galactic observables to within their errors still differ in microlensing rate towards the Magellanic Clouds by more than a factor of ten. We find that while the more easily computed optical depth correlates well with microlensing rate, the ratio of optical depth to rate can vary by a factor of two (or greater if the disk is maximal). Comparison of microlensing rates towards the Large and Small Magellanic Clouds (LMC and SMC) and M31 can be used to aid determinations of the halo flattening and rotation curve slope. For example, the ratio of microlensing rates towards the LMC and SMC is $sim 0.7-0.8$ for E0 halos and $sim 1.0 - 1.2$ for E7 halos (c.f. Sackett & Gould 1993). Once the flattening has been established, the ratio of microlensing rates towards M31 and the LMC may help to distinguish between models with rising, flat or falling rotation curves. Comparison of rates along LMC and galactic bulge lines-of-sight gives useful information on the halo core radius, although this may not be so easy to extract in practice. Maximal disk models provide substantially smaller halo optical depths, shorter event durations and even larger model uncertainties.
Galaxy kinematics and gravitational lensing are two complementary ways to constrain the distribution of dark matter on galaxy scales. The typical dark matter density profiles adopted in dynamical studies cannot easily be adopted in lensing studies. I
The most accurate way to get information on the mass of the MACHOs (Massive Astrophysical Compact Halo Objects) is to use the method of mass moments. For the microlensing events detected so far by the EROS and the MACHO collaborations in the Large Ma
The claimed detection of large amounts of substructure in lensing flux anomalies, and in Milky Way stellar stream gaps statistics, has lead to a step change in constraints on simple warm dark matter models. In this study we compute predictions for th
We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution function for th
The next generation of axion direct detection experiments may rule out or confirm axions as the dominant source of dark matter. We develop a general likelihood-based framework for studying the time-series data at such experiments, with a focus on the