Event MOA-2009-BLG-226L was first detected on 2009 June 1 by the Microlensing Observations in Astrophysics (MOA) survey, using the 1.8m telescope at Mt. John University Observatory in New Zealand. It was then observed intensively by a worldwide collaboration of follow-up telescopes. As a result, the lightcurve was densely sampled which allowed a very short-lived planetary anomaly to be detected.
Analysis of the combined data was published by Muraki, Y. et al. (2011), ApJ, 741, 22.

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

Lightcurve of MOA-2009-BLG-226L
Lightcurve of MOA-2009-BLG-226L [Muraki et al.(2011)]

Determine 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 $$\Delta m$$
Maximum magnification = Amax:
Impact parameter = |u0|:
Magnitude at Half-Maximum =
Full Width Half Maximum = tFWHM:
Einstein Timescale = tE:





Determine Parameters of the Planetary Event

Step 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 = $$u = \sqrt(u_0^2 + \tau^2)$$
$$y_{\pm} = \pm (1/2) (\sqrt(u^2 + 4) \pm u)$$
Is the perturbation a major image (+) or minor image (-) perturbation?
Location of the planet = s :






Step 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?

Hint: \(\Delta m = -2.5 log10 [(A*f_s + f_{blend})/(f_s + f_{blend})]\)