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Register a new userPossible Solution of the long-standing discrepancy in the Microlensing Optical Depth Toward the Galactic Bulge by correcting the stellar number count
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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 $f_{rm RC}=(0.63pm0.11)-(0.052pm0.028)times b$, ranging between 1 and 0.7 at $b=-6^circsim-1.5^circ$. 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 $Gamma=[18.74pm0.91]times10^{-6}exp[(0.53pm0.05)(3-|b|)]$ star$^{-1}$ yr$^{-1}$ and $tau_{200}=[1.84pm0.14]times10^{-6}exp[(0.44pm0.07)(3-|b|)]$ for the 427 events with $t_{rm E}leq200,$days using all sources brighter than $I_sleq20$ 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 $Gamma=4.60pm0.25times10^{-5}$ 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.
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We present measurements of the microlensing optical depth and event rate toward the Galactic Bulge based on two years of the MOA-II survey. This sample contains ~1000 microlensing events, with an Einstein Radius crossing time of t_E < 200 days between -5 <l< 10 degree and -7 <b< -1 degree. Our event rate and optical depth analysis uses 474 events with well defined microlensing parameters. In the central fields with |l|< 5 degree, we find an event rates of Gamma = [2.39+/-1.1]e^{[0.60pm0.05](3-|b|)}x 10^{-5}/star/yr and an optical depth of tau_{200} = [2.35+/-0.18]e^{[0.51+/-0.07](3-|b|)}x 10^{-6} for the 427 events using all sources brighter than I_s = 20 mag centered at (l,b)=(0.38, -3.72). We find that the event rate is maximized at low latitudes and a longitude of $l~1 degree. For the 111 events in 3.2 deg^2 of the central Galactic Bulge at |b| < 3.0 degree and 0.0 < l < 2.0, centered at (l,b)=(0.97, -2.26), we find Gamma = 4.57_{-0.46}^{+0.51} x 10^{-5}/star/yr and tau_{200} = 3.64_{-0.45}^{+ 0.51} x 10^{-6}. We also consider a Red Clump Giant (RCG) star sample with I_s<17.5 mag. Our results are consistent with previous optical depth measurements. We find that the previously observed difference in optical depth measurements between all-source and RCG samples may be largely due to statistical fluctuations. These event rate measurements towards the central galactic bulge are necessary to predict the microlensing event rate and to optimize the survey fields in the future space mission such as WFIRST.
We present a measurement of the microlensing optical depth toward the Galactic Bulge based on 4 years of the OGLE-II survey using Red Clump Giant (RCG). Using 32 events we find tau=2.55_{-0.46}^{+0.57}* 10^{-6} at (l,b)=(1.16, -2.75). Taking into account the measured gradient along the Galactic latitude b, tau = [ (4.48+/- 2.37) + (0.78+/- 0.84)* b]* 10^{-6}, this value is consistent with previous measurements using RCG sources and recent theoretical predictions. We determine the microlensing parameters and select events using a model light curve with the flux blending. We find that ~38% of the OGLE-II events which appear to have RCG sources are actually due to much fainter stars blended with a bright companion. We show explicitly that model fits without blending result in similar tau estimates through partial cancellation of contributions from higher detection efficiency, underestimated time-scales and larger number of selected events. This approach, however, leads to biased time-scale distributions and event rates. Consequently, microlensing studies should carefully consider source confusion effects even for bright stars.
We examine the left-right asymmetry in the cleaned COBE/DIRBE near-infrared data of the inner Galaxy and show (i) that the Galactic bar is probably not seen very nearly end-on, and (ii) that even if it is, it is not highly elongated. The assumption of constant mass-to-light ratio is used to derive simulated terminal-velocity plots for the ISM from our model luminosity distributions. By comparing these plots with observed terminal velocities we determine the mass-to-light ratio of the near-IR bulge and disk. Assuming that all this mass contributes to gravitational microlensing we compute optical depths $tau$ for microlensing in Galactic-centre fields. For three models with bar major axis between $10deg-25deg$ from the Sun-Galactic Center line, the resulting optical depths in Baades window lie in the range $0.83times10^{-6} lta tau lta 0.89times10^{-6}$ for main-sequence stars and $1.2times10^{-6} lta tau lta 1.3times10^{-6}$ for red-clump giants. We discuss a number of uncertainties including possible variations of the near-infrared mass-to-light ratio. We conclude that, although the values predicted from analyzing the COBE and gas velocity data are inconsistent at the $2-2.5sigma$ level with recent observational determinations of $tau$, we believe they should be taken seriously.
We present a new EROS-2 measurement of the microlensing optical depth toward the Galactic Bulge. Light curves of $5.6times 10^{6}$ clump-giant stars distributed over $66 deg^2$ of the Bulge were monitored during seven Bulge seasons. 120 events were found with apparent amplifications greater than 1.6 and Einstein radius crossing times in the range $5 {rm d}<t_e <400 {rm d}$. This is the largest existing sample of clump-giant events and the first to include northern Galactic fields. In the Galactic latitude range $1.4degr<|b|<7.0degr$, we find $tau/10^{-6}=(1.62 pm 0.23)exp[-a(|b|-3 {rm deg})]$ with $a=(0.43 pm0.16)deg^{-1}$. These results are in good agreement with our previous measurement, with recent measurements of the MACHO and OGLE-II groups, and with predictions of Bulge models.
We present the microlensing optical depth towards the Galactic bulge based on the detection of 99 events found in our Difference Image Analysis (DIA) survey. This analysis encompasses three years of data, covering ~ 17 million stars in ~ 4 deg^2, to a source star baseline magnitude limit of V = 23. The DIA technique improves the quality of photometry in crowded fields, and allows us to detect more microlensing events with faint source stars. We find this method increases the number of detection events by 85% compared with the standard analysis technique. DIA light curves of the events are presented and the microlensing fit parameters are given. The total microlensing optical depth is estimated to be tau_(total)= 2.43^(+0.39/-0.38) x 10^(-6) averaged over 8 fields centered at l=2.68 and b=-3.35. For the bulge component we find tau_(bulge)=3.23^(+0.52/-0.50) x 10^(-6) assuming a 25% stellar contribution from disk sources. These optical depths are in good agreement with the past determinations of the MACHO Alcock et al. (1997) and OGLE Udalski et al. (1994) groups, and are higher than predicted by contemporary Galactic models. We show that our observed event timescale distribution is consistent with the distribution expected from normal mass stars, if we adopt the stellar mass function of Scalo (1986) as our lens mass function. However, we note that as there is still disagreement about the exact form of the stellar mass function, there is uncertainty in this conclusion. Based on our event timescale distribution we find no evidence for the existence of a large population of brown dwarfs in the direction of the Galactic bulge.
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