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Astron. Astrophys. 350, L57-L61 (1999)

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4. Multi-component model of the LMC

We model the LMC to contain several stellar populations, each associated with a different velocity dispersion [FORMULA] which has evolved according to Eq. 9.

We describe each of the ten components of our model by an ellipsoidal density profile

[EQUATION]

up to a cut-off radius [FORMULA] kpc (Aubourg et al. 1999). The multi-component model based on these profiles is self-consistent in the sense that it satisfies Poisson equation and results in a flat rotation curve with the desired [FORMULA] of 80 km s-1. We define the set of [FORMULA] so as to sample linearly the range between [FORMULA] km s-1 and [FORMULA] km s-1 (see previous section). The parameters [FORMULA] and the ellipticities [FORMULA] are determined so that the model reproduces the set of velocity dispersions [FORMULA] and surface mass densities [FORMULA] where [FORMULA] with [FORMULA] the stellar formation history of the LMC mentioned in Sect. 2. Assuming a typical M/L of 3, which is a free parameter in our model, we reproduce the observed surface brightness of the LMC.

For a given distribution of objects, one can compute the total self-lensing optical depth [FORMULA] and the event rate [FORMULA]. Both quantities are integrated on all deflectors and sources, considering that only main sequence stars brighter than [FORMULA] and red giants can be potential sources, since they are the only objects bright enough to be visible in microlensing surveys. The computation of [FORMULA] requires an estimate of the relative transverse velocity of deflector and source, for which we have assumed an horizontal velocity dispersion equal to the vertical one predicted by the model. Details of this computation can be found in (Aubourg et al. 1999).

For the model described above, one obtains [FORMULA] and [FORMULA] yr-1. This can be compared to the EROS and MACHO optical depths, respectively [FORMULA] (Ansari et al. 1996) and [FORMULA] (Alcock et al. 1997). A combination of those two results yields an average optical depth of [FORMULA] (Bennett 1998), but preliminary MACHO results from their five-year analysis (Sutherland 1999) hint to a reduced optical depth as compared to their two-year analysis. The model prediction is thus in good agreement with the results obtained so far from microlensing experiments.

Another relevant prediction of the model is the distribution of event durations, [FORMULA]. Fig. 3 illustrates this prediction for our model, along with the distribution of observed MACHO events.

[FIGURE] Fig. 3. Predicted distribution of event durations [FORMULA], superimposed with the MACHO experimental distribution. The events are those presented by MACHO at the IVth Microlensing Workshop (Cook 1998), corrected for blending and efficiency using the formulae in Alcock et al. 1997.

Our model thus reproduces both the total observed optical depth towards the LMC and the observed event duration distribution, while complying with the velocity dispersion measurements. A self-lensing interpretation of all the microlensing events observed so far towards the LMC thus appears to be a plausible explanation.

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© European Southern Observatory (ESO) 1999

Online publication: October 14, 1999
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