ConventionsΒΆ

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 :

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

In case the parallax is used, the angle \(\beta\) between the East components and the trajectory at t0par is ( Gould2004):

  • \(\beta = arctan(\pi_{EN}/\pi_{EE})\)

\(\beta\) is accessible with:

piEN = 0.8
piEE = -0.5

beta = pyLIMA.microlparallax.EN_trajectory_angle(piEN,piEE)
print(beta) #2.12939564...