6 Comparison of LMC and SMC results

Another way to gauge the present results on microlensing towards the SMC is to compare them directly to the result of the MACHO collaboration towards the LMC (Alcock et al. 2000). Such a comparison is made easier by the fact that the expected $t_{\rm E}$ distributions of halo microlenses towards the SMC and LMC are very similar: their averages and widths differ by only a few percent, and these differences are much smaller than the widths themselves. The ratio of the optical depths towards the SMC and LMC is more uncertain; for a spherical isothermal halo, it is expected to be about $\tau_{\rm SMC} / \tau_{\rm LMC} \simeq 1.4$, but this value can be lower for flattened halos. Actually, it was proposed to use observations towards the SMC to evaluate the galactic dark halo flattening (Sackett & Gould 1993).

In their analysis A, the MACHO group has listed 13 microlens candidates with an average duration $<t_{\rm E}> ~ = 36$ days and a width of the $t_{\rm E}$ distribution compatible with all microlenses having the same mass. From this, they compute an optical depth $\tau = 1.2 \times 10^{-7}$, of which about $1.0 \times 10^{-7}$ is attributed to halo lenses. This translates into an expected number of events for the present EROS SMC data set of

$$N_{\rm evts} = N_* \frac{T_{\rm obs}}{<t_{\rm E}>} \frac{2}{\pi} <\epsilon> \tau_{\rm SMC} ~ ,$$

where $N_* = 5.2 \times 10^6$ is the number of SMC stars monitored by EROS, $T_{\rm obs} = 5$ yrs is the total duration of the observations, and $<\epsilon>~ = 0.146$ is the average EROS detection efficiency for microlensing events of duration $<t_{\rm E}>~ \simeq 0.1$ yr. (This average efficiency is obtained by interpolating the values in Table 3, and is normalized to u₀ < 1.) Substituting these numerical values leads to $N_{\rm evts} = 2.4 \times (\tau_{\rm SMC} / 10^{-7})$.

There are, however, no EROS SMC microlensing candidates that are compatible with the $t_{\rm E}$ distribution observed by the MACHO group towards the LMC: candidate SMC-1, the shortest of all, is very likely due to a lens in the SMC (see parallax analysis and the discussion that follows in SM98); the other 3 candidates all have durations longer than 240 days, clearly incompatible with an average of 36 days. From this absence of microlensing candidates with the required duration, EROS can exclude $\tau_{\rm SMC} > 10^{-7}$ for events similar to those in MACHO sample A, at better than 90% C.L. The value corresponding to the spherical isothermal halo model, $\tau_{\rm SMC} = 1.4 \times \tau_{\rm LMC} \simeq 1.4 \times10^{-7}$ is excluded at better than 96% C.L.