Limb-Darkening Measured in a Bulge K Giant

Limb-Darkening Measured in a Bulge K Giant:
PLANET Observations of MACHO 97-BLG-28

First posted: 10-January-1999

In 1997, the binary microlensing event MACHO 97-BLG-28 was alerted as an anomalous event, and was monitored intensely by the PLANET collaboration. Analysis of our nearly 700 images of this event has shown that the foreground double lens created a caustic pattern that swept over a giant star in the Galactic Bulge, creating a large, but short-lived peak in the light curve of the background star.

The top panels in this figure show the brightness of the background star as measured by PLANET when the green V filter was placed in front of the camera detector. The bottom panels show the light curve through the very red I filter. Every mark on the bottom left indicates 20 days have elapsed; the right panels zoom in around the peak, where every mark indicates two days. PLANET observations from Chile are shown as black points, from Tasmania (Australia) as green points, and from South Africa as red points.

The PLANET measurements were continuous over the peak and were precise enough to discern the difference in light curve shape that would be caused by a background star of constant brightness and one that is fainter (limb-darkened) at the edges.

This difference is illustrated in the figure above where the solid curve on the left passes through the data points more precisely than the curve on the right. Now the light curve has been zoomed so that every mark on the bottom represents a little over an hour of elapsed time on the top frames and about 5 hours on the bottom frames. Microlensing aids the astronomer to see these differences by creating the sharp magnifying-glass effect of the caustic that sweeps over the background star, selectively magnifying first the edge (limb) of the very distant star, then its center, and then the other limb.

The effect is even more striking when looking at the differences between the data and the models (lines). This is shown in the figure below.

The differences between the data and the limb-darkened model (left) are closer to zero than the differences between the data and the uniform brightness model (right), especially in the hours between dates 896.3 and 896.4 when the caustic is passing over the edge of the background star.

By taking a spectrum of the background star (passing its light though a prism-like device and measuring the amount of light transmitted in each color), the PLANET team could identify the background star as a cool giant star called a K giant near the center of our own Galaxy. By measuring the precise shape of the light curve over the peak, the amount of limb-darkening of this star could be measured, and compared to theory.

The result compares quite well to theory. The red and blue lines show how much fainter the background star becomes at its edges in the red I filter (left) and the blue-greenish V filter (right), at least according to the PLANET team observations and modeling. If the star instead emitted a uniform amount of light across its whole stellar disk, the profile would look like the straight solid black line instead. The results agree with predictions from theory (dashed lines) for K giant stars like this one.

This is the first time that limb-darkening has been measured in a star this distant, and one of the few measurements for this type of star by any technique. The foreground lensing system itself appears to be a stellar binary composed of two low-mass stars separated by a distance comparable to the Earth-Sun distance (1-2 AU). For more technical details, download our paper astro-ph/9811479 or read our journal article in the Astrophysical Journal, 522, 1011.

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