Gravitational microlensing

Gravitational microlensing is lensing by compact masses whose individual image splitting is unresolved, so their motion is observed through time-dependent magnification.

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- Microlensing optical depth Gravitational microlensing

Microlensing optical depth ( $τ = \int n_{l} π R_{E}^{2} d D_{l}$ )

The microlensing optical depth is the probability, when small, that a source lies within one Einstein radius of a foreground lens. For point lenses and compact-object mass density

ρ_{l}

in nearby Euclidean geometry,

τ = \frac{4 π G}{c ^{2}} \int_{0}^{D_{s}} ρ_{l} (D_{l}) \frac{D _{l} ( D _{s} - D _{l} )}{D _{s}} d D_{l} .

The individual lens mass cancels because

n_{l} = ρ_{l} / m

and

R_{E}^{2} \propto m

. Detection efficiencies and event durations still depend on individual masses and survey cadence.

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