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MPC observation produced with Astrometrica by using both CMC-14 star catalog -- the circular aperture radius = 5 pixel in the program:
In the next step, I attempted to do photometry of the comet in a median-stacked final image of all the separate frames. Magnitudes enclosed by aperture radii varing from 1-pixel to 7-pixel in a step of every pixel were calculated in IDL by aper.pro with the solved optocenter pixel coordinates of the comet found by routine cntrd.pro. The inner sky annulus was set to 15-pixel, while the outer one was 25-pixel. The results are listed as follows:
DATE-OBS = 2012-08-22T20:48:05
XCEN = 1028.278, YCEN = 905.760
SKY = 0.1505 $\pm$ 0.0007 DN/s
APER (pix): 1.0 2.0 3.0 4.0 5.0 6.0 7.0
MAGNITUDE: 14.124 13.065 12.631 12.338 12.115 11.917 11.824
ERROR: 0.195 0.128 0.114 0.108 0.105 0.102 0.107
The model I used to fit the magnitude data is:
$ m\left ( r \right )=m_\infty-2.5\log \left [ 1-\exp \left ( -\left( \frac{r}{\rho} \right) ^n \right ) \right ] $ (1),
where $ r $ is the radius of some aperture, $\rho $ is the apparent radius of the coma, $n$ relates to the morphology of the comet, and $ m_\infty $ is the magnitude obtained by an infinite aperture. After several tests, $n = 1.29$ was found to best describe magnitudes in different apertures, thereby $m_\infty = 11.300 \pm 0.048$, consistent with visual observations.
The value of $n$ could have been smaller owing to the fact that the size of the coma appeared smaller with interference from city lights.
Copyright @ Man-To Hui 2012/09/08
Feel free to e-mail me with any doubts or questions.
