HAT-P-1 Transit _ 2006/12/12

Fig 001. Finder Chart

Fig 002. Raw Data, Magnitude versus Time

Red = Magenta circled star [195253]
Yellow = Red circled Companion of transit star [194699]
Green = Yellow circled Transit star [194776]
Cyan = Blue circled star (Left) [208918]
Blue = Blue circled star (Right) [187026]
Note the changes in transparency, reaching 1.8 mag on a time scale under one minute
(ADU ratio = 524 %) for an expected change of 1.5%
See also how the darkblue and green curve, initially superimposed,
diverge as the air mass grows, due to the difference in their color.
The Curves are inverted relative to the convention used by photometrists
Although the magnitudes may appear close to the real values,
the Zero point was not determined

Fig 003. Provisional Result
Red = Simplified expected value (see text)
Blue = processed difference between the transit star and its companion
with an offset applied equal to out of transit difference
The Curves are inverted relative to the convention used by photometrists
X Scale = UT hours
Y Scale in millimagnitude
No point was rejected, the gap around 3.7 h is due to the loss of the guide star
Rejecting outliers may improve the results

How the red dotted curve was built:
From the ephemerid, four times were computed:
- 1st contact (t1)
- 2nd contact (t2)
- 3rd contact (t3)
- 4th contact (t4)

Then, for each measure performed at time t (pseudo code):
If ((t <= t1) Or (t > t4)) then output = 0.
If ((t >= t2) And Or (t <= t3)) then output = 0.016 mag.
else, linear interpolation, providing the slope.
No edge darkening is taken into account, and the linear slope is only a coarse approximation of the real shape.

How was determined the impact of the change in air mass due to the difference in color between the measured star and the reference star.
We tried 2 methods and they provided similar results: The curves were rebuilt with the air mass as the X axis. In a first method, we masked the data corresponding to the two slopes. This provided 3 segments of data (one before the ingress, one between the second and the third contact, and one after the ingress). In a perfect world, the first and the third are aligned, and the second, with the same slope (dmag versus air mass) shifted by the change in magnitude while in mid transit. In the second method, we first subtracted from the whole curve the red curve (in the same airmass referential), keeping all the data points. This provided a nice slope, and a linear regression provided the differential magnitude versus airmass. We kept the second method, because it uses more data points and provide a pleasant residual. Then, for each data point, from the airmass, we computed the differential extinction, and compensated for.

Fig 004. Air Mass versus Time
Red = AirMass
For the future, one more digit after decimal point must be used.

Fig 005. Guiding
Blue = Y
One square = 1 pixel (9)
Notice the temporary loss of the guide star.

Fig 006. Sky BackGround
Red = Companion of transit star
Green = Transit star
Blue = Blue circled star (right) (see Fig 001)
Although each star has a close bright companion, the measure of
the local background is barely perturbed.
Compared to the background around the blue circled star on the right,
the difference accounts for 20 millimag and may be explained,
a least in part, by a faint gradient along the image.
One minor tick on the Y axis is 1 millimagnitude.
The peak in brightness around 3.7 h is when the guide star was lost.