3 Data analysis

The analysis of the five-year data set is similar to those of the first year ( SM98) and of the first two years (Afonso et al. 1999) of data where details can be found.

A first set of cuts is designed to select light curves that exhibit a single significant fluctuation. This already excludes 99.8% of the stars, most of which exhibit flat light curves.

A second set of cuts rejects stars that are a priori likely to be variable, based upon their position in a color-magnitude diagram: bright blue stars in the upper main sequence with low-amplitude variations and stars much brighter and redder than those of the red clump are rejected. These stars are contained in two thinly populated regions of the color-magnitude diagram, so rejecting them does not reduce much the number of light curves on which we can search for microlensing. Stars exhibiting a strong correlation between the red and the blue light curves outside the period containing the main fluctuation are also rejected. Supernovae are rejected by the comparison of the rising and falling times of the variation. Half of the light curves surviving the first set of cuts are rejected at this stage, leaving about 5000 light curves.

A third set of cuts improves the signal-to-noise ratio of the set of selected candidates by comparing the measurements with the best-fit point-source point-lens microlensing light curve. These criteria are sufficiently loose not to reject light curves affected by blending, parallax and most cases of binary lenses or sources. The remaining sample consists of about 30 light curves exhibiting a clean and unique fluctuation with a smooth time variation.

A fourth set of cuts constrains the time coverage of the event, excluding in particular all events with Einstein radius crossing times $t_{\rm E}$ exceeding 1200 days.

The final criterion is as follows: if blending significantly improves the fit, then the fitted blending should be physical, i.e. indeed correspond to the amplification of only a fraction of the total flux recovered.

To limit contamination of the set of selected candidates by spurious events, the levels of the above cuts are set such that most variable stars are rejected by at least two of them. The tuning of each cut and the estimation of the efficiency of the analysis is done with Monte Carlo simulated light curves, as described in  SM98. Microlensing parameters are drawn uniformly in the following intervals: time of maximum magnification t₀ within the observing period $\pm$300 days, impact parameter normalized to the Einstein radius $u_0 \in [0,1.5]$ and time-scale $t_{\rm E} \in [0,1200]$ days.

Four candidates ( SMC-1 to  SMC-4) pass all the cuts. Their light curves are shown in Fig. 1, their coordinates are given in Table 1 and the microlensing fit parameters (point-source, point-lens and no-blending) in Table 2.

Figure 1: Red light curves of the microlensing candidates detected towards the SMC.

 

 

Table 1: Coordinates (J2000) and baseline photometry of the candidates.

	$\alpha$	$\delta$	VJ	IC
SMC-1	01:00:05.73	-72:15:02.33	17.9	17.9
SMC-2	00:48:20.16	-74:12:35.31	20.4	19.5
SMC-3	00:49:38.68	-74:14:06.77	20.2	19.3
SMC-4	01:05:36.56	-72:15:02.39	19.9	19.4

 

 

Table 2: Results of microlensing fits to the SMC candidates. u₀ is the impact parameter and $t_{\rm E}$ the Einstein radius crossing time in days.

	u0	$t_{\rm E}$	$\chi^2/{\rm d.o.f.}$
SMC-1	0.52	101	1026/706
SMC-2	0.82	390	1526/990
SMC-3	0.66	612	2316/968
SMC-4	0.80	243	2923/951

 

 

Table 3: Detection efficiency $\epsilon$ in % as a function of the timescale $t_{\rm E}$ in days for events with u₀<1.5 and normalized to $T_{\rm obs}=5~{\rm yr}$.

$t_{\rm E}$	5	15	50	125	325	500	900	1100	1300
$\epsilon$	2.1	6.3	11.1	13.8	11.8	10.1	7.5	5.9	2.7

Candidate SMC-1 is the one already present in the previous analyses (one year and two years of SMC data) done by EROS. Further analysis of its light curve indicated that it was probably a self-lensing event ( SM98). It was also detected as a possible microlensing candidate by the online trigger system of the MACHO experiment (Alcock et al. 1997b). Candidates  SMC-2, SMC-3 and  SMC-4 have very long durations, with few points outside the amplified region of the light curve. The $\chi^2/{\rm d.o.f.}$ of candidate SMC-4 is large, yet far from the cut level (which is set at 5.0 in the peak region). All three candidates, however, exhibit features in their baseline that are reminiscent of variable stars. These features appear clearly on the light curves plotted in 25-day bins (see Fig. 2). To allow a direct comparison of the red and blue fluxes, all fluxes have been normalized so that they would have a mean of zero and a variance of unity. Candidates SMC-2 and SMC-4 clearly look like irregular variables, while SMC-3 has an irregular light curve and seems to be rising at the end. These candidates will need to be monitored for several more years to be either confirmed but most probably ruled out as microlensing candidates. They are not in the $\sim$3 square degrees of the SMC on which the MACHO project took data.

Figure 2: Red and blue light curves of the microlensing candidates detected towards the SMC, in 25-day bins.

The efficiency of the analysis for events with (Monte-Carlo) u₀<1.5 normalized to an observing period  $T_{\rm obs}$ of five years is summarized in Table 3.