Gravitational Microlensing

Participants: Dr MA Hendry, Dr N Gray, Prof JC Brown, Ms H Bryce          
Collaborations: Toulouse, Iowa, Toledo, Liverpool JMU, Luxembourg

The group has interests in the gravitational microlensing of "extended source" events (where the lensed object cannot be reasonably approximated as a point source) as a probe of both the nature of the lensing dark matter and (principally) the properties of the source star. Present research builds on pioneering work carried out at Glasgow from the mid 1990s - by Simmons, Gray, Newsam, Willis and Coleman - which established the relevance and astrophysical potential of extended source effects in microlensing. Recent and current research themes include:

Modelling the broad-band photometric signatures of extended sources

Extended sources in general display a chromatic lensing signature because - when one includes the effect of a waveband dependent non-uniform surface brightness profile - the lens "sees" a star of different effective radius at different wavelengths. We are modelling the microlensing signatures as a function of lens and stellar parameters, for realistic simulations of Galactic Bulge and LMC point lens and fold (i.e. binary) caustic events, with magnitude errors and sampling rates typical of existing monitoring programs, "alert" programs (e.g. PLANET) and proposed satellite missions (e.g. GEST). Click here to see an example of typical PLANET data.

Microlensing as a probe of stellar atmosphere models

Fold caustics are particularly suitable for this because: their magnification is very high; any transit event must be treated as an extended source event; the geometry of the caustic structure often implies a second caustic crossing, allowing intensive monitoring in response to the initial alert. Applications to real data by the microlensing community to date clearly indicate that microlensing is capable of discriminating between limb darkened and uniform source models. With Valls-Gabaud (Toulouse) e are currently extending this work to investigate the potential of point and fold caustic events for rigorous testing of the "Next Generation" stellar atmosphere models of Hauschildt et al (1999), which include a much more detailed treatment of molecular absorption lines in the atmospheres of cool giants - typical source stars in Bulge events. The figure below shows the difference in magnitude, in the V, R, I, and K bands, between the predicted microlensing light curve assuming linear limb darkening and a "NextGen" model atmosphere, for a typical bulge giant fold caustic event.

Microlensing as a probe of photospheric inhomogeneities

In addition to probing radial surface brightness variations, extended source events offer a unique means of gravitationally "imaging" the 2-d surface profile of red giant stars - about which our detailed knowledge is very limited in the optical (c.f. Alpha Orionis, shown on the left). We have developed a code to compute the multicolour signatures of  photospheric "starspots", including precise modelling of the effects of geometric foreshortening and limb darkening close to the stellar limb. Such features can produce short timescale "spikes" in the lightcurves, similar to the effects of planetary companions of the lens (although easily distinguishable from such planets because of their characteristic light curve shape and their wavelength dependence). With Valls-Gabaud (Toulouse) we are studying how point and fold caustic events can be used to constrain the surface distribution, size and temperature of starspots. An example of the light curves produced by idealised spot models is shown below.

Spectroscopic signatures of extended source events

Microlensing can be a powerful tool for diagnosing the density and velocity structure of stellar winds and the distribution of matter in circumstellar envelopes. This is because - as with photospheric observations - microlensing amplifies the flux from different parts of the source by different amounts, thus providing spatially resolved information about the source environment. As a simple illustration, with Ignace (Iowa) we have considered the microlensing signature of an emission line profile from a spherical shell of circumstellar material, either rotating or expanding, and show that microlensing can easily distinguish between these two cases. We are currently extending our treatment to more realistic wind velocity laws, and a parabolic treatment of the geometry of fold caustics - necessary because of the relatively large angular size of circumstellar envelopes compared with the characteristic lensing radius.

Polarimetric signatures of extended source events

Previous work at Glasgow by Simmons et al. showed that polarimetric observations during extended source events can provide powerful constraints on the lens and source parameters, and in particular can allow direct determination of the Einstein radius of the lens. This is because during a transit event the polarisation signature peaks strongly as the lens crosses the stellar limb, when the effect of differential amplification across the stellar disk most strongly breaks the symmetry which yields a net polarisation of zero in the absence of lensing. We are extending the earlier, point source, treatment to consider fold caustics, and to model the signature of molecular scattering - more appropriate for the limbs of late-type giant stars. We are also exploring the diagnostic potential of spectropolarimetry for mapping discrete "blobs" is stellar winds.

Optimal non-parametric methods for combining photometric, polarimetric and spectroscopic microlensing data

In recent years we have developed robust techniques for reconstructing the surface brightness profile of extended sources from microlensing data. These essentially treat the observed light curves as an integral convolution over the source, and solve for the surface brightness profile using inverse problem methods - a field in which Glasgow has world leading expertise. We have developed a non-parametric Backus-Gilbert approach to combine photometric and polarimetric data. We are currently exploring its extension to include multiband and spectroscopic data, and investigating the use of genetic algorithms as a means of "pre-conditioning" the ill-posedness of microlensing inversions.