Worksheet for MOA-2010-BLG-328L
The first discovery alert for MOA-2010-BLG-328 was issued from the MOA survey on 2010 June 16. Around 39 days later, the MOA observer first noticed a few anomalous datapoints, which were confirmed by subsequent observations. They then issued an anomaly alert to the community, who responded by obtaining high cadence follow-up data. The analysis of the event is described in Furusawa et al. 2013 ApJ 779, 91.
Use the methods outlined in estimating parameters to derive approximate values for the microlensing model parameter.
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 = Δm: | ||
| Maximum magnification = Amax: | ||
| Impact parameter = |u0|: | ||
| Magnitude at Half-Maximum = | ||
| Full Width Half Maximum = tFWHM: | ||
| Einstein Timescale = tE: |
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 = √(u02 + τ2) : | ||
| y± = ± (½) (√(u2 + 4) ± 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?