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Register a new userThe Microlensing Event Rate and Optical Depth Toward the Galactic Bulge from MOA-II
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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.
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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.
Searches for gravitational microlensing events are traditionally concentrated on the central regions of the Galactic bulge but many microlensing events are expected to occur in the Galactic plane, far from the Galactic Center. Owing to the difficulty in conducting high-cadence observations of the Galactic plane over its vast area, which are necessary for the detection of microlensing events, their global properties were hitherto unknown. Here, we present results of the first comprehensive search for microlensing events in the Galactic plane. We searched an area of almost 3000 square degrees along the Galactic plane (|b|<7, 0<l<50, 190<l<360 deg) observed by the Optical Gravitational Lensing Experiment (OGLE) during 2013-2019 and detected 630 events. We demonstrate that the mean Einstein timescales of Galactic plane microlensing events are on average three times longer than those of Galactic bulge events, with little dependence on the Galactic longitude. We also measure the microlensing optical depth and event rate as a function of Galactic longitude and demonstrate that they exponentially decrease with the angular distance from the Galactic Center (with the characteristic angular scale length of 32 deg). The average optical depth decreases from $0.5times 10^{-6}$ at l=10 deg to $1.5times 10^{-8}$ in the Galactic anticenter. We also find that the optical depth in the longitude range 240<l<330 deg is asymmetric about the Galactic equator, which we interpret as a signature of the Galactic warp.
We analyze the data of the gravitational microlensing survey carried out by by the MOA group during 2000 towards the Galactic Bulge (GB). Our observations are designed to detect efficiently high magnification events with faint source stars and short timescale events, by increasing the the sampling rate up to 6 times per night and using Difference Image Analysis (DIA). We detect 28 microlensing candidates in 12 GB fields corresponding to 16 deg^2. We use Monte Carlo simulations to estimate our microlensing event detection efficiency, where we construct the I-band extinction map of our GB fields in order to find dereddened magnitudes. We find a systematic bias and large uncertainty in the measured value of the timescale $t_{rm Eout}$ in our simulations. They are associated with blending and unresolved sources, and are allowed for in our measurements. We compute an optical depth tau = 2.59_{-0.64}^{+0.84} times 10^{-6} towards the GB for events with timescales 0.3<t_E<200 days. We consider disk-disk lensing, and obtain an optical depth tau_{bulge} = 3.36_{-0.81}^{+1.11} times 10^{-6}[0.77/(1-f_{disk})] for the bulge component assuming a 23% stellar contribution from disk stars. These observed optical depths are consistent with previous measurements by the MACHO and OGLE groups, and still higher than those predicted by existing Galactic models. We present the timescale distribution of the observed events, and find there are no significant short events of a few days, in spite of our high detection efficiency for short timescale events down to t_E = 0.3 days. We find that half of all our detected events have high magnification (>10). These events are useful for studies of extra-solar planets.
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 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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