Limb darkening in this image of today’s Sun

I was given a proper solar filter for my birthday about 1,5 month ago and I hadn’t taken a single photograph through it. Until today. Today, around noon, I took this (pretty awesome) picture of the Sun:

40 frame stack of the Sun at 12.00 GMT+1, as seen from Enschede

40 frame stack of the Sun at the 21st of nov. 2014, 12.00 GMT+1, as seen from Enschede

In this image (which I colored yellow-orange-ish because you probably feel more familiar with a yellow sun than a white one), the outer regions of the Sun appear clearly less bright than near the center. This is a well studied effect and is called ‘limb darkening’. In the Eddington approximation, the intensity depends on the angle between the outgoing light and the axis perpendicular to the surface. The equation that describes this intensity is not more difficult than one cosine and 2 fractions:

limb_darkening

In the figure below, I have added 3 blue bars on the Sun’s disk, with their corresponding angles. The intensities given by measuring the mean pixel values that my DSLR gives me, are probably not the most accurate, but they are the best I can do (the intensity gradient is probably altered by the used solar filter and the DSLR settings). I have normalized the mean values with the maximum pixel value of 255 so that my measured values become 0.72 in the center, 0.60 at 71% of the radius and 0.28 at the edge of the Sun.

Measured intensities at different angles

Measured intensities at different angles

In the table below I have listed the measured values and those given by the equation I showed you. The fact that the value for theta=0 is the same was to be expected since I used this as the center intensity. The fact that the other 2 values correspond very good however, comes as quite a surprise. I didn’t really expect it to be this accurate, but the changes in contrast caused by the equipment and software seem to balance out pretty good.

table of measured and calculated values

Anyway, I just wanted to show you that the predicted limb darkening is apparent in the photo I made 🙂

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Beautiful sunset and different types of nebulosity

After I finished my exams, I grabbed the first opportunity to get my camera out and shoot some pretty pictures. The icy sky in combination with the low sun friday evening, provided beautiful views. I tried to photograph them as best as I could:

Sun dog due to icy skies

Sun dog due to icy skies

Sunset over Enschede

Sunset over Enschede

The Enschede sky, shortly after sunset

The Enschede sky, shortly after sunset

Later that evening, I took my telescope out, including new mount, motors and feedback-loop guiding system. I never had the chance to use it before and I couldn’t wait to give it a try. The skies were definately not clear (a thin layer of clouds was still blocking light from the lower magnitude stars), but nontheless my guidecamera (my DIY xbox camera) managed to pick up some stars after playing with the settings for a while.

Modded xbox cam from side

Modded xbox cam from side

The idea is, to have two telescope tubes aligned and both fitted with cameras. One camera functions as a guide camera and has the sole purpose of showing stars on the computer screen. The computer then sends signals to the motorized telescope to keep a selected star exactly at the same place on the computer screen. Since the two tubes are aligned, the second telescope – fitted with a proper imaging camera – has a perfectly steady image to photograph at long exposure times.

As a first star to try the system on, I chose Betelgeuse, a very bright, red supergiant. The system picked up the star and kept it in place for about 15 seconds. After that, it seemed to make one misstep and then lose the star. I will have a look at the settings and lower the step size to prevent overshooting while making corrections.

Luckily, I seemed to have aligned the telescope pretty well, so that the error was small enough for 10-15 second exposures without trailing. So without the feedback system, I could still make some reasonable photos. The first image is a single 10 second exposure of Betelgeuse and the stars around it.

First long exposure telescope image. The bright red supergiant Betelgeuse was my first target.

First long exposure telescope image. The bright red supergiant Betelgeuse was my first target.

After that, I spend some time trying to find the Orion Nebula. This was quite a hastle since I couldn’t really see it, or the surrounding stars and I had to guess its exact location. Yes it was that clouded. Eventually, I found it and took a large amount of 10 second photos which looked like this:

Jpeg of raw 10 second image

Jpeg of raw 10 second image

Using 16 of those frames and stacking them together with 8 dark frames (photos with the lens cap on, to measure the noise induced by the camera temperature), I got the following result, which I’m quite pleased with 🙂

M42; Great Nebula in Orion. A stack of 16 10sec frames at iso 6400

M42; Great Nebula in Orion. A stack of 16 10sec frames at iso 6400

I sure have seen much better images, but considering that my guiding wasn’t working yet, the orion nebula being very low above the horizon and the layer of clouds present, this image is very acceptable. Because by then, it was already late and the skies weren’t that clear anyway, I decided to try one last target and call it a night. The target I chose was M45; the Pleiades open cluster with its blue glowing stars. The image below is a single 20 second frame which I processed a little. The glow if visible due the the gas that surrounds the stars and reflects the blue light. This type of ‘nebulosity’ is called a reflextion nebula. In contrast, the Orion nebula is an emission nebula, that gets its glow from very hot gas that actually emits light.

M45; Pleiades open cluster. A single 10 second frame at iso 6400

M45; Pleiades open cluster. A single 20 second frame at iso 6400

All in all, this was a rather large post. I do intend to post more frequently the upcoming months, but as always, it really depends on the weather 🙂