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Register a new userTheory of Exploring the Dark Halo with Microlensing 1: Power--Law Models
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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.
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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. Ideally, a mass model should be used that has the global characteristics of realistic dark matter distributions, and that allows for an analytical calculation of the magnifications and deflection angles. A simple model with these properties, the broken-power-law (BPL) model, has very recently been introduced. We examine the dynamical structure of the family of BPL models. We derive simple closed expressions for basic dynamical properties, and study the distribution function under the assumption of velocity isotropy. We find that none of the BPL models with realistic parameters has an isotropic distribution function that is positive over the entire phase space, implying that the BPL models cannot be supported by an isotropic velocity distribution, or models with a more radially anisotropic orbital structure. This result limits the attractiveness of the BPL family as a tool for lensing studies to some degree. More generally, we find that not all members of the general family of double power-law or Zhao models, often used to model dark matter haloes, can be supported by an isotropic or radially anisotropic distribution function. In other words, the distribution function may become negative even for spherically symmetric models with a well-behaved density profile.
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 Magellanic Cloud the average mass turns out to be 0.08$M_{odot}$. Assuming a spherical standard halo model we find that MACHOs contribute about 20% to the halo dark matter. The eleven events recorded by OGLE, mainly during its first two years of operation, in the galactic bulge lead to an average mass of 0.29$M_{odot}$, whereas forty events detected by MACHO during its first year give 0.16$M_{odot}$, thus suggesting that the lens objects are faint disk stars.
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 the halo mass function both for these simple models and also for comprehensive particle physics models of sterile neutrinos and dark acoustic oscillations. We show that the mass function fit of Lovell et al. underestimates the number of haloes less massive than the half-mode mass, $M_mathrm{hm}$ by a factor of 2, relative to the extended Press-Schechter (EPS) method. The alternative approach of applying EPS to the Viel et al. matter power spectrum fit instead suggests good agreement at $M_mathrm{hm}$ relative to the comprehensive model matter power spectra results, although the number of haloes with mass $<M_mathrm{hm}$ is still suppressed due to the absence of small scale power in the fitting function. Overall, we find that the number of dark matter haloes with masses $<10^{8}M_{odot}$ predicted by competitive particle physics models is underestimated by a factor of $sim2$ when applying popular fitting functions, although careful studies that follow the stripping and destruction of subhaloes will be required in order to draw robust conclusions.
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 the gap between neighbouring particles serves to discriminate between different laws of attraction. We develop an exact Fokker-Planck approach for the infinite hierarchy of distribution functions for multiple adjacent gaps and solve it exactly, at the mean-field level, where correlations are ignored. The crucial role of correlations and their effect on the gap distribution function is explored both numerically and analytically. Finally, we analyse a random input of particles, which results in a stationary state where the effect of correlations is largely diminished.
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 role of dark-matter astrophysics, to search for signatures of the QCD axion or axion like particles. We illustrate how in the event of a detection the likelihood framework may be used to extract measures of the local dark matter phase-space distribution, accounting for effects such as annual modulation and gravitational focusing, which is the perturbation to the dark matter phase-space distribution by the gravitational field of the Sun. Moreover, we show how potential dark matter substructure, such as cold dark matter streams or a thick dark disk, could impact the signal. For example, we find that when the bulk dark matter halo is detected at 5$sigma$ global significance, the unique time-dependent features imprinted by the dark matter component of the Sagittarius stream, even if only a few percent of the local dark matter density, may be detectable at $sim$2$sigma$ significance. A co-rotating dark disk, with lag speed $sim$50 km$/$s, that is $sim$20$%$ of the local DM density could dominate the signal, while colder but as-of-yet unknown substructure may be even more important. Our likelihood formalism, and the results derived with it, are generally applicable to any time-series based approach to axion direct detection.
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