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Table 3:

Observed and predicted microlensing statistics.
  $\theta \ {\rm Mus} $ $\gamma \ {\rm Nor} $ $\gamma \ {\rm Sct} $ $\beta \ {\rm Sct} $  
$\bar{b^\circ}$ -1.46 -2.42 -2.09 -2.15  
$\bar{l^\circ}$ 306.56 331.09 18.51 26.60  
  Observations All
$\tau\times 10^6$ $.67^{\rm +.63}_{-.52}$ $.49^{\rm +.21}_{-.18}$ $.72^{\rm +.41}_{-.28}$ $.30^{\rm +.23}_{-.20}$ $.51^{\rm +.13}_{-.13}$
$N_{\rm events}$ 3 10 6 3 22
$\bar{t_{\rm E}}$ (days) $97\pm 47$ $57\pm 10$ $47\pm 6$ $59\pm 6$ $60\pm 9$
$\sigma_{t_{\rm E}}$ (days) 80 29 13 10 40
$\epsilon$ corrected $\bar{t_{\rm E}}$ $65\pm 45$ $43\pm 10$ $45\pm 6$ $58\pm 6$ $48\pm 9$
$\epsilon$ corrected $\sigma_{t_{\rm E}}$ 75 31 13 9 38
$median\ t_{\rm E}$ 74.2 64. 47.2 55. 56.5
  $\tau\ (\times 10^6)$ from models $\chi^2_{\rm model}$
A 0.32 0.48 0.79 0.60 2.3
+spiral 0.56 0.69 1.07 0.83 7.9
B 0.34 0.51 0.85 0.64 2.9
+spiral 0.61 0.72 1.13 0.90 10.2
C 0.47 0.78 1.11 0.95 12.5
+spiral 0.71 1.18 1.43 1.23 36.1
D 0.32 0.56 0.41 0.38 1.4
model 1 0.42 0.52 0.71 0.57 1.8
model 2 0.54 0.68 0.90 0.74 5.4
  Predictions from model 1  
$N_{\rm events}$ 2.8 9.9 7.1 6.3  
$\bar{t_{\rm E}}$ (days) 73.8 67.9 37.9 60.2  
$\sigma_{t_{\rm E}}$ (days) 63 54 36 48  
$median\ t_{\rm E}$ 54.5 52.5 28.0 46.5  
  $\bar{t_{\rm E}}$ from published models  
C (no effic.) 45 28 25 27  
C+spiral 38 38 44 40  
D 80.9 86.5 76.9 77.4  
First panel: observed optical depth $\tau$, number of events $N_{\rm events}$, average $\bar{t_{\rm E}}$, dispersion $\sigma_{t_{\rm E}}$, efficiency corrected $\bar{t_{\rm E}}$ and $\sigma_{t_{\rm E}}$and median time scale for each monitored direction. Here, we consider only the events used for the optical depth estimates (i.e. with u0<0.7). Second panel: optical depth predictions from models A, B, C, including or not a spiral structure (see text), and from model D, and estimates up to 7 kpc from the two simple Galactic models described in Table 4. The $\chi^2$'s quantify the adequacy with the observations (see Sect. 8). Third panel: expected numbers of events and duration distribution parameters from model 1 and from models C and D. $\bar{t_{\rm E}}$ from model C do not take into account the detection efficiency.

Source LaTeX | All tables | In the text

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