Fixing my mistakes… [lab 3]

When I said “by Wednesday”… I guess I didn’t specifically say WHICH Wednesday I would fix it by…
New information:
• the “ marks in the image are arcseconds, not degrees - I should have converted units to account for this!
• Keep values in radians
• Recheck what K-band really means!

SO! Now, I have 0.009 arcseconds as the value for the separation of the binaries, which I can covert to degrees:

Proceeding with this value, I know that the distance to the first airy ring should be 0.1 arcseconds, not 0.1 degrees. With this knowledge, I can convert again to degrees and then radians (for radians, see summary table way below).

Now, I also need to check the values for the wavelengths of K-band. According to Wikipeida: http://en.wikipedia.org/wiki/Photometric_system
The values of K-band in this system of measurement have a center of around 2190 nm. Using these new values, I can use the same methodology as last time, except my value for theta will be different. Theta in the equation below refers to not the distance from the center to the airy ring, but the entire distance across the diameter of the airy ring. So,



Using small angle approximation, and the fact that 2190 nm = 2.19*10^-6 meters,



This suggests that the aperture is 2.76 meters – not the 10ish meters I previously found.
NOW – which telescope could this be? …. I notice that depending on the measurement for the width of the airy ring, I get different results. This is frustrating because depending on from where I measure (the innermost and smallest distance, or from the center of the outer pixel) I get different values for the minimum angular resolution. I can get what look like equally valid measurements varying from 0.09 to 0.23 arcseconds. These correspond to apertures between roughly 2.5 and 6.5 meters. See graph below, which graphs D as a function of the diameter of the smallest airy ring, measured in arcseconds.

Choosing what telescope this image is from is difficult because of the uncertainty in my original measurement of the diameter of an airy ring. However, based on considerations of where in the sky this source would be visible (see the uncorrected post) I can say that it would be visible from Hawaii, California, or equivalent areas. Combined with my knowledge that this image came from a Caltech-affiliated source, who likely has most easy access to Palomar and Keck, I can hypothesize that the image was taken using the Hale telescope at Palomar, which has an approximately 5 meter aperture, within my error bounds.
Trying to confirm or disprove my hypothesis, I combed through the publications of the two observers listed in the FITS header and found this abstract:
http://adsabs.harvard.edu/abs/2010DPS....42.3930L
So, K-band observing was going on at Palomar April 25-26…. Looks promising! Unfortunately I can’t seem to find a copy of the entire paper – maybe because I am not on the Caltech network?
Also, I found:
http://www.palomar.caltech.edu:8000/calendar.tcl?cal_date=2010%2d04%2d25+00%3a00%3a00%2b00
Which shows that April 27 was used by a different astronomer… but the nights of the 25th and 26th were used by a consistent observer to the file. I would say that the day had just changed and this observation was from the night of the 27th, but the observation time says 11:28. This does not mean that my hypothesis was wrong; I’m not sure which time zones /sidereal time/PST time were used to mark the file; so although the observation was marked 11:29, April 27th it could possibly have been from the 26th.
Also – Knowing that Justin Crepp was the observer, (I feel like such a stalker…) how likely is it that he would, having observed all night on April 26th, then proceed to fly somewhere else and observe AGAIN the next night? I don’t think that would be very likely, and it is always possible that the nights got switched or something else unreported on the observation time website happened. Therefore I will not reject the hypothesis that this image was taken at Palomar on the Hale 200-inch telescope.


Fixing my errors: a summary

Airy ring distance from center: I used to think this was 0.09 degrees.
Now I know it's 0.000025 degrees, or 4.36332 × 10^-7 radians
K-band wavelengths: I used to think it was 7.5*10^-1 to 1.5 cm,
Now I know that it's centered at 2190 nm
Aperture: my first value was 10.48 meters,
My new value was 2.9 meters but I also realized that this number comes with some sizeable error bounds!
Telescope: I used to think it was the Keck2, NIRC2
Now I think the Hale 200 inch at Palomar was used