Models of microlensing events have quite a number of parameters which makes for a complex parameter space. In addition there are several degeneracies, meaning that models with different parameters can create a very similar lightcurves. For some events this can make it difficult to conclusively infer the nature of the lensing system. Follow-up observations like high-resolution imaging can help to detect or place constraints on the flux from the lens, which can be decisive in determining the mass of the lensing system. MOA-2013-BLG-605L is a good example of such a case. See Sumi et al. 2016 ApJ 825, 112 for a full description.

Use the methods outlined in estimating parameters to derive approximate values for the microlensing model parameter.

Lightcurve of MOA-2013-BLG-605L
Lightcurve of MOA-2013-BLG-605L [Sumi et al.(2016)]

Parameters of the Underlying Stellar Event

Based on the microlensing light curve, figure out the following properties of the microlensing event

Your answers
Time of the peak of the event = t0:
Change in magnitude = &#916m:
Maximum magnification = Amax:
Impact parameter = |u0|:
Magnitude at Half-Maximum =
Full Width Half Maximum = tFWHM:
Einstein Timescale = tE:





Parameters of the Planetary Event

1. Where is the planet?

Your answers
Time of the the planet perturbation = tplanet :
Time scaled to the Einstein timescale = τ = |tplanet - t0|/tE :
Source-lens separation = u = &#8730(u02 + τ2) :
y&#177 = &#177 (½) (&#8730(u2 + 4) &#177 u) :
Is the perturbation a major image (+) or minor image (-) perturbation?
Location of the planet = s :






2. What is the mass ratio between the planet and the star?

Your answers
Planet Einstein Timescale = tp,E ~ tFWHM :
Mass Ratio = q = (tp,E / tE)2:


Planet      q = Planet Mass/Sun's Mass 
   Jupiter      10-3 
   Neptune      5 x 10-5 
   Earth      3x 10-6 
Your answer
Is the planet more similar to Earth, Neptune, or Jupiter?


How well did you do?

Remember that these methods are approximate - they are used to find a good starting point for analysis. It’s important to remember that the approximation works less well as s–> 1.

IF the light curve is in magnitudes (rather than magnification): We’re assuming zero blending, i.e. that all the light that you see is from the source star. If there is some other (non-lensed) light blended with the light curve, then the true magnification is higher. How do your answers change if you assume that half of the baseline flux is due to a blend? What if 90% is due to a blend?