pyLIMA use the following conventions.

The time given in observations is expected to be in HJD.

Following the idea of uniform notations in the field, pyLIMA is based on Gould2000.

The informations in [] represents the units \(t_{o}\) [days]:

  • \(t_o\) [days] is define as the time of the minimum impact parameter.
  • \(u_o\) [ \(\theta_E\)] is the minimum impact parameter. It is positive if the source pass on the left of the source. It is define on the center of mass of the lens system.
  • \(t_E\) [days] is the angular Einstein ring crossing time.
  • \(\rho\) [ \(\theta_E\)] is the normalised angular source radius.
  • \(s\) [ \(\theta_E\)] is the normalised angular separation between the binary lens component.
  • \(q\) [] is the binary mass ratio, with the smaller body on the right of the system.
  • \(\alpha\) [rad] is the angle between the source trajectory and the the binary lens axis, counted in trigonometric convention.
  • \(\pi_{EN}\) [ \(AU/r_E\)] is the North component of the microlensing parallax.
  • \(\pi_{EE}\) [ \(AU/r_E\)] is the East component of the microlensing parallax.

Then, the source trajectory x,y is define as :

  • \(\tau = (t-t_o)/t_E\)
  • \(x = \tau . cos(\alpha)- u_o . sin(\alpha)\)
  • \(y = \tau . sin(\alpha)+ u_o . cos(\alpha)\)