Possible Solution of the long-standing discrepancy in the Microlensing Optical Depth Toward the Galactic Bulge by correcting the stellar number count

We find that significant incompleteness in stellar number counts results in a significant overestimate of the microlensing optical depth $\tau$ and event rate per star per year $\Gamma$ toward the Galactic bulge from the first two years of the MOA-II survey. We find that the completeness in Red Clump Giant (RCG) counts $f_{\rm RC}$ decreases proportional to the galactic latitude $b$, as $f_{\rm RC}=(0.63\pm0.11)-(0.052\pm0.028)\times b$, ranging between 1 and 0.7 at $b=-6^\circ\sim-1.5^\circ$. The previous measurements using all sources by Difference Image Analysis (DIA) by MACHO and MOA-I suffer the same bias. On the other hand, the measurements using a RCG sample by OGLE-II, MACHO and EROS were free from this bias because they selected only the events associated with the resolved stars. Thus, the incompleteness both in the number of events and stellar number count cancel out. We estimate $\tau$ and $\Gamma$ by correcting this incompleteness. In the central fields with $|l|<5^\circ$, we find $\Gamma=[18.74\pm0.91]\times10^{-6}\exp[(0.53\pm0.05)(3-|b|)]$ star$^{-1}$ yr$^{-1}$ and $\tau_{200}=[1.84\pm0.14]\times10^{-6}\exp[(0.44\pm0.07)(3-|b|)]$ for the 427 events with $t_{\rm E}\leq200\,$days using all sources brighter than $I_s\leq20$ mag. Our revised all-source $\tau$ measurements are about 2-$\sigma$ smaller than the other all-source measurements and are consistent with the RCG measurements within 1-$\sigma$. We conclude that the long-standing problem on discrepancy between the high $\tau$ with all-source samples by DIA and low $\tau$ with RCG samples can probably be explained by the incompleteness of the stellar number count. A model fit to these measurements predicts $\Gamma=4.60\pm0.25\times10^{-5}$ star$^{-1}$ yr$^{-1}$ at $|b|\sim-1^\circ.4$ and $-2^\circ.25<l<3^\circ.75$ for sources with $I<20$, where the future space mission WFIRST will observe.Comment: 39 pages, 15 figures, 5 tables, accepted for publication in ApJ. arXiv admin note: substantial text overlap with arXiv:1305.018

Measurements of streaming motions of the Galactic bar with Red Clump Giants

We report a measurement of the streaming motion of the stars in the Galactic bar with the Red Clump Giants (RCGs) using the data of the Optical Gravitational Lensing Experiment II (OGLE-II). We measure the proper motion of 46,961 stars and divide RCGs into bright and faint sub-samples which on average will be closer to the near and far side of the bar, respectively. We find that the far-side RCGs (4,979 stars) have a proper motion of \Delta ~ 1.5 +- 0.11 mas yr^{-1} toward the negative l relative to the near-side RCGs (3,610 stars). This result can be explained by stars in the bar rotating around the Galactic center in the same direction as the Sun with v_b ~ 100 km s^{-1}. In the Disc Star (DS) and Red Giant (RG) samples, we do not find significant difference between bright and faint sub-samples. For those samples \Delta \~ 0.3 +- 0.14 mas yr^{-1} and ~ 0.03 +- 0.14 mas yr^{-1}, respectively. It is likely that the average proper motion of RG stars is the same as that of the Galactic center. The proper motion of DSs with respect to RGs is ~ 3.3 mas yr^{-1} toward positive l. This value is consistent with the expectations for a flat rotation curve and Solar motion with respect to local standard of rest. RGs have proper motion approzimately equal to the average of bright and faint RCGs, which implies that they are on average near the center of the bar. This pilot project demonstrates that OGLE-II data may be used to study streaming motions of stars in the Galactic bar. We intend to extend this work to all 49 OGLE-II fields in the Galactic bulge region.Comment: 7 pages, 9 figures, submitted to MNRA

Possibility to sound the atmospheric ozone by a radiosonde equipped with two temperature sensors, sensitive and non-sensitive to the long wave radiation

The sensitiveness of white coated thermistor sensors and non-sensitiveness of the gold coated over white thermistor sensors (which have been manufactured by a vacuum evaporation process) to long wave radiation were ascertained by some simple experiments in-room and also by analyses of some results of experimental soundings. From results of analyses on the temperature discrepancies caused by long wave radiation, the possibility to sound the atmospheric ozone partial pressure by a radiosonde equipped with two kinds of sensors, sensitive and non-sensitive to the long wave radiation was suggested, and the test results of the newly developed software for the deduction of ozone partial pressure in upper layers was also shown. However, it was found that the following is the necessary condition to realize the purpose. The sounding should be made by a radiosonde equipped with three sensors, instead of two, one being non-sensitive to the long wave radiation perfectly, and the other two also non-sensitive partially to the downward one, with two different angles of exposure upward. It is essential for the realization of the purpose to get two different values of temperature discrepancies simultaneously observed by the three sensors mentioned above and to avoid the troublesome effects of the upward long wave radiation

Large Magellanic Cloud Microlensing Optical Depth with Imperfect Event Selection

I present a new analysis of the MACHO Project 5.7 year Large Magellanic Cloud (LMC) microlensing data set that incorporates the effects of contamination of the microlensing event sample by variable stars. Photometric monitoring of MACHO LMC microlensing event candidates by the EROS and OGLE groups has revealed that one of these events is likely to be a variable star, while additional data has confirmed that many of the other events are very likely to be microlensing. This additional data on the nature of the MACHO microlensing candidates is incorporated into a simple likelihood analysis to derive a probability distribution for the number of MACHO microlens candidates that are true microlensing events. This analysis shows that 10-12 of the 13 events that passed the MACHO selection criteria are likely to be microlensing events, with the other 1-3 being variable stars. This likelihood analysis is also used to show that the main conclusions of the MACHO LMC analysis are unchanged by the variable star contamination. The microlensing optical depth toward the LMC is = 1.0 +/- 0.3 * 10^{-7}. If this is due to microlensing by known stellar populations, plus an additional population of lens objects in the Galactic halo, then the new halo population would account for 16% of the mass of a standard Galactic halo. The MACHO detection exceeds the expected background of 2 events expected from ordinary stars in standard models of the Milky Way and LMC at the 99.98% confidence level. The background prediction is increased to 3 events if maximal disk models are assumed for both the MilkyWay and LMC, but this model fails to account for the full signal seen by MACHO at the 99.8% confidence level.Comment: 20 pages, 2 postscript figues, accepted by Ap

About the maximal rank of 3-tensors over the real and the complex number field

High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and Atkinson-Lloyd(1980). They treated the problem in the complex field, and we will present various bounds over the real field by proving several lemmas and propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen

Circadian patterns of Wikipedia editorial activity: A demographic analysis

Wikipedia (WP) as a collaborative, dynamical system of humans is an appropriate subject of social studies. Each single action of the members of this society, i.e. editors, is well recorded and accessible. Using the cumulative data of 34 Wikipedias in different languages, we try to characterize and find the universalities and differences in temporal activity patterns of editors. Based on this data, we estimate the geographical distribution of editors for each WP in the globe. Furthermore we also clarify the differences among different groups of WPs, which originate in the variance of cultural and social features of the communities of editors

Impacts of sediment flushing on channel evolution and morphological processes: Case study of the Kurobe River, Japan

River morphodynamics and sediment transportSedimentation in reservoir