Mark M's Exoplanet Transit Photometry Project

[mark.m]

How do your graph units relate to real numbers such as time and magnitude Mark?

Pete

The X axis numbers are the Julian day, so they correspond to fractions of a day. That runs from about 0.5 to about 0.75, so about 1/4 of a day (6 hours).

The Y axis is in units of "relative flux." A change from 1.00 to 1.01 (1% change in flux) is pretty close to a change of 0.01 magnitudes in brightness. So the transit depth of about 2.5% is very close to a change of 0.025 magnitudes. (And, if I remember right, this star is around mag 13.5 or so.)

[Pete]

That's pretty fine Mark. Do you recall what you were running for S/N? That's always been my bugaboo.

Pete

[mark.m]

That's pretty fine Mark. Do you recall what you were running for S/N? That's always been my bugaboo.

Pete

So I don't really know how to calculate that (anybody care to provide a good reference?), but my back-of-the-envelope calculation is right around 100:1.

[Pete]

My software (Astrometrica)) was showing S/N of around 230 and it still wasn't adequate. Supposedly one needs 250 or better to pull the small differential out of the noise. And even then you need to do a rolling average.

Pete

[mark.m]

As I get ready for observing session #2, I've been pulling together a list of the things that I learned during the prior observing run. One of the items on the list is about saturated stars.
Before I chose 3 minutes as the exposure time for the first observing run, I was convinced that I had checked to make sure that stars weren't going to be saturated with a 3-minute exposure. I was wrong, because the AstroImageJ analysis software immediately flagged four stars as either being clearly saturated or being in a probably-non-linear-zone. As I studied that, I found some really nice plots within AstroImageJ that clearly show saturation:

Radial-profiles.png (117.31 KiB) Viewed 3376 times

Each of these is a plot showing the brightness of all the pixels associated with one star, with the vertical location corresponding to brightness and the horizontal location corresponding to the distance of the pixel from the center of the star. The plot on the left shows a "medium" star in one of the images, and the plot on the right shows one of the saturated stars. I circled the areas that are relevant. On the plot on the left, you can see pixel brightness rising steadily as you get closer to the center of the star. On the plot on the right, you can see how the brightness has hit a limit and won't get any brighter than that limit even as you move closer to the center of the star.
If all I was doing with the images is doing brightness measurements, the saturated stars wouldn't particularly matter, because I'd just exclude them from the analysis. But, I was also using each image to measure focus (as part of the new "running focus" tool that I was testing). The "flat top" on the saturated star changes the estimate of how focused the star is. (Notice that the calculated widths of the two stars is quite different: the full-width-half-maximum size of the saturated star is listed as 4.67 pixels (top right), while the dimmer star shows a FWHM size of 3.28 pixels. That undoubtedly added some measurement noise to the focus tool that just made its job a little harder.

[mark.m]

My software (Astrometrica)) was showing S/N of around 230 and it still wasn't adequate. Supposedly one needs 250 or better to pull the small differential out of the noise. And even then you need to do a rolling average.

Pete

Pete:
AstroImageJ shows an SNR of 70-108 for the target star over the duration of the observing run. The SNRs for the comparison stars that I used varied from 150 to 200. At the potluck, Andy and I were talking about how the SNR calculation can be done precisely or can be done half-heartedly, depending on whether you include camera gain in the calculation. With an SNR of about 100, photometric uncertainty is around 0.01 magnitudes for each measurement. One of the nice things that AstroImageJ performs is a least-squares fit of all data points against its model of the transit. Since I had about 100 data points, this effectively further averages the error, providing a smoothing improvement of about sqrt(100), which makes detection of this particular transit pretty unambiguous (statistically).

AstroImageJ calculated my measurement noise at 0.008 magnitudes (RMS). I've been looking at the work of some other amateurs, and I've seen them achieve measurement noise as low as 0.003 magnitudes (RMS)... leaving lots of room for technique improvement.

[AndyG]

Good catch on the saturation. Hopefully that will help your focus and the overall accuracy. It's fun pushing the gear to get the most out of it!

[Pete]

I've been looking for photometric software. AstoImageJ looks good and the price is right

[mark.m]

I tried another transit last night, with much more ambiguous results than the first try. Here's the best graph I could create:

Graph-5xbin.png (27.05 KiB) Viewed 3356 times

I'm skeptical of this curve. Small changes in analysis parameters cause big changes in the ingress/egress times and the depth of the curve. Times don't exactly line up with predictions and the depth of the transit is significantly smaller than advertised. This may or may not be an actual transit.

I shifted from the 3-minute exposures that I used the first time to just 30-second exposures for this. Even though the target star was a little bit brighter for this transit, the 6x reduction in exposure time really hurt the data scatter. In fact, in order to get the graph to look as good as it does above, I had to have AstroImageJ average together 5 exposures into a single measurement, so I'm almost back to the equivalent to 3-minute exposures. Some things I'm learning:
- Differential airmass corrections can be important. I've always assumed that my small total image size of 14 arcmin was small enough that I could safely assume that atmospheric extinction would be equal at all points in the image. But what I've learned from these two observing runs is that this isn't true at all, and making airmass corrections for each star in the image may be important.
- The running focus manager is getting better. It definitely liked having over 400 images to work from. I had noticed a nasty interdependence between the focuser software and the drift guider that created problems the first night during the very first dozen images. I made some changes to that for this second run and the focuser worked much better, and has given me some more ideas for further improvement.
- More exposure time on the target star is really important. Don't trade off exposure time in order to get better time resolution. Physics is physics, and if you don't have enough photons arriving at the camera, nothing that you do will improve the data scatter. It's just pure probability theory.
- It hasn't been hard for me to work around meridian flips. Haven't needed to flip for either observing run.

[Pete]

I'm amazed that extinction is a problem with differential photometry. Unless you're working 45° or less from the horizon. Not at all surprised about the 30 second noise. S/N is sooooo critical. (I've read).

Really exceptional work Mark.