Newly discovered brown dwarfs not seen in microlensing time scale frequency distribution?

The 2-Micron All Sky Survey (2MASS) (Skrutskie et al. 1997) and the DEep Near Infrared Survey of the southern sky (DENIS) (Epchtein et al. 1997) have revealed a heretofore unknown population of free brown dwarfs that has extended the local mass function down to as small as 0.01M_sun (Reid et al. 1999). If this local proportion of brown dwarfs extends throughout the Galaxy---in particular in the Galactic bulge---one expects an increase in the predicted fraction of short time scale microlensing events in directions toward the Galactic bulge. Zhao et al.(1996) have indicated that a mass function with 30-60% of the lens mass in brown dwarfs is not consistent with empirical microlensing data. Here we show that even the much lower mass fraction (~ 10%) of brown dwarfs inferred from the new discoveries appears inconsistent with the data. The added brown dwarfs do indeed increase the expected number of short time scale events, but they appear to drive the peak in the time scale frequency distribution to time scales smaller than that observed, and do not otherwise match the observed distribution. A reasonably good match to the empirical data (Alcock et al. 1996) is obtained by increasing the fraction of stars in the range 0.08<m<0.7M_sun considerably above that deduced from several star counts. However, all inferences from microlensing about the appropriate stellar mass function must be qualified by the meagerness of the microlensing data and the uncertainties in the Galactic model.Comment: 5 pages, 1 figure. PS file using aas2pp4.sty. To appear in ApJ Letter

Probability of Detecting a Planetary Companion during a Microlensing Event

The probability of detecting a planetary companion of a lensing star during a microlensing event toward the Galactic center, averaged over all relevant event and galactic parameters, when the planet-star mass ratio $q=0.001$ has a maximum exceeding 10% at an orbit semimajor axis $a$ near 1.5 AU for a uniform distribution of impact parameters. The maximum probability is raised to more than 20% for a distribution of source-lens impact parameters that is determined by the efficiency of event detection. The averaging procedures are carefully defined, and they determinine the dependence of the detection probabilities on several properties of the Galaxy. The probabilities scale approximately as $\sqrt{q}$. A planet is assumed detectable if the perturbation of the single lens light curve exceeds $2/(S/N)$ for at least 20 consecutive photometric points sometime during the event. Two meter telescopes with 60 second integrations in I-band with high time resolution photometry throughout the duration of an ongoing event are assumed. The probabilities are derived as a function of $a$, where they remain significant for $0.6<a<10$ AU. Dependence of the detection probabilities on the lens mass function, luminosity function of the source stars as modified by extinction, distribution of source-lens impact parameters, and the line of sight to the source are also determined, and the probabilities are averaged over the distribution of the projected planet position, the lens mass function, the distribution of impact parameters, the lens and source distances as weighted by their distributions along the line of sight and over the $I$-band apparent luminosity function of the sources. The extraction of the probabilility as a function of $a$ for a particular $q$ from empirical data is indicated.Comment: 32 pages, 20 figures, In Press, ApJ, Latex format with aas2pp4 forma

New families of weighted sum formulas for multiple zeta values

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Fitting functions for dark matter density profiles

We present a unified parameterization of the fitting functions suitable for density profiles of dark matter haloes or elliptical galaxies. A notable feature is that the classical Einasto profile appears naturally as the continuous limiting case of the cored subfamily amongst the double power-law profiles of Zhao (1996). Based on this, we also argue that there is basically no qualitative difference between halo models well-fitted by the Einasto profile and the standard NFW model. This may even be the case quantitatively unless the resolutions of simulations and the precisions of fittings are sufficiently high to make meaningful distinction possible.Comment: 13 pages (6 pages main text + 5 pages appendices + 2 pages full tables) including 5 figures and 7 tables. submitted to MNRA

Investigation of split injection in a single cylinder optical diesel engine

SAE paper 2010-01-0605, Copyright © 2010 SAE International. This paper is posted on this site with permission from SAE International, and is for viewing only. Further use and distribution of this paper is not permitted without permission from SAE.Over the last decade, the diesel engine has made dramatic progress in its performance and market penetration. However, in order to meet future emissions legislations, Nitrogen Oxides (NOx) and particulate matters’ (PM) emissions will need to be reduced simultaneously. Nowadays researchers are focused on different combustion modes which can have a great potential for both low soot and low NOx. In order to achieve this, different injection strategies have been investigated. This study investigates the effects of split injection strategies with high levels of Exhaust Gas Recirculation (EGR) on combustion performance and emissions in a single cylinder direct injection optical diesel engine. The investigation is focused on the effects of injection timing of split injection strategies. A Ricardo Hydra single cylinder optical engine was used in which conventional experimental methods like cylinder pressure data, heat release analysis and exhaust emissions analysis were applied. Optical techniques like direct spray and combustion visualization were applied by means of a high speed imaging system with a copper vapor laser illumination system and a high-speed two-color system was applied to obtain in-cylinder diesel combustion temperature and soot measurements distributions

The Maximum Optical Depth Towards Bulge Stars From Axisymmetric Models of the Milky Way

It has been known that recent microlensing results towards the bulge imply mass densities that are surprisingly high given dynamical constraints on the Milky Way mass distribution. We derive the maximum optical depth towards the bulge that may be generated by axisymmetric structures in the Milky Way, and show that observations are close to surpassing these limits. This result argues in favor of a bar as a source of significantly enhanced microlensing. Several of the bar models in the literature are discussed.Comment: Latex, 6 pages, 4 figures, uses aas2pp4 and epsf style files. Accepted for publication in ApJ Letter