Limb-Darkening Measured in a Bulge K Giant
Limb-Darkening Measured in a Bulge K Giant:
First posted: 10-January-1999
PLANET Observations of MACHO 97-BLG-28
In 1997, the binary microlensing event MACHO 97-BLG-28 was alerted as an
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
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
or read our journal article in the
Astrophysical Journal, 522, 1011.
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