Alert system / Microlensing events

This page summarizes the results of a detailed study of the gravitational microlensing signal available for Gaia. For the most up-to-date version see Chapter 6 of Vasily's thesis.

Also see the microlensing information sheet (pdf) from the Gaia web-site.

Numbers of events | Gaia performance

Gaia can measure microlensing by the small excursions of the light centroid that occur during microlensing. We use a stringent definition of an astrometric microlensing event as one with a significant variation ($5 \sqrt{2} \sigmaa$) of the centroid shift, together with a closest approach during the lifetime of the Gaia mission (see Dominik and Sahu 2000). The all-sky averaged astrometric microlensing optical depth is $\sim 1.5 \times 10^{-5}$. This means that $\sim 15000$ sources will exhibit astrometric microlensing events with such characteristics during the course of the mission. Gaia can also measure microlensing by the photometric brightening that accompanies low impact parameter events. The all-sky averaged photometric optical depth is $\sim 5 \times 10^{-7}$, so there are $\sim 7500$ photometric microlensing events during the five year mission lifetime, most of which have only a few datapoints because of the poor sampling. However, these measurements are of a great importance.

The most valuable events are those for which the Einstein crossing time $\tE$, the angular Einstein radius $\thetaE$ and the relative parallax of the source with respect to the lens $\pi_{\rm rel}$ can all be inferred from Gaia's datastream. The mass of the lens then follows directly. If the source distance is known -- for example, if Gaia itself measures the source parallax -- then a complete solution of the microlensing parameters is available. Of these quantities, it is the relative parallax that is the hardest to obtain accurately. A covariance analysis is used to follow the propagation of errors and establish the conditions for recovery of the relative parallax. This happens if the angular Einstein radius $\thetaE$ is large and the Einstein radius projected onto the observer plane $\rtE \sim 1$ au so that the Earth's motion about the Sun gives a substantial distortion. It is also aided if the source is bright so that Gaia's astrometric accuracy is high and if the duration of the astrometric event is long so that Gaia has time to sample it fully. These conditions favour still further lensing populations that are very close.

Gaia measurements alone will provide a sample of at least $500$ stars with accurately determined masses. However, the numbers can be improved still further if Gaia observations are supplemented with ground-based photometry. The total of $1000$ masses will be measured with the help of dedicated telescopes on the ground.

Monte Carlo simulations are used to establish the characteristics of the $\sim 7 \%$ of events for which Gaia can recover the mass of the lens to good accuracy. The typical lens distance is $< 2$ kpc and the typical source distance is $\sim 6$ kpc. The highest quality events seen by Gaia are dominated by local lenses.

We conclude that one of the major scientific contributions of microlensing studies with Gaia will be the determination of the mass function in the solar neighbourhood. Of course, direct mass measurements are presently possible just for binary stars with well-determined orbits. Microlensing is the only technique which can measure the masses of individual stars. Gaia is the first instrument with the ability to survey the astrometric microlensing signal provided by nearby lenses. We have used Monte Carlo simulations to show that Gaia can reconstruct the mass function in the solar neighbourhood from the sample of its highest quality events. This works particularly well for masses exceeding $\sim 0.3 \msun$. Below $0.3 \msun$, the reconstructed mass function tends to underestimate the numbers of objects, as the highest quality events are biased towards larger angular Einstein radii.

If there are local populations of low mass black holes, or very cool halo and disk white dwarfs or very old brown dwarfs, then they will have easily eluded detection with available technology. However, the astrometric microlensing signal seen by Gaia will be sensitive to local populations of even the dimmest of these stars and the darkest of these objects. Gaia is the first instrument that has the potential to map out and survey our darkest neighbours.

Bibliography (ADS)

Last modified on January 29 2009 12:22:09 PM