Calculating Limb Darkening Coefficient

I calculated the Limb Darkening Coefficient from the Linear Limb Darkening law assuming a plane-parallel solar atmosphere.:

As a base, I used a picture from the solar disk taken during the recent solar eclipse with an OIII filter (500nm). Using ImageJ software I was able to plot the intensity (limb darkening) graph by retrieving the gray intensity data per pixel. Using above formule, I calculated the Linear Limb Darkening coefficient (LDC). To calculate the LDC, I took the average LDC's of the radius between 0,9 and 0,3 . This results in a LDC of 0,22 (500nm)

I put this data together in a graph which combines the intensity graph from ImageJ and the theoretical derived graph with a LDC of 0,22.

Discussion:
In the literature I found LDC's  of around 0,8 (eg. Dias-Cordoves see this link)  

Conclusion : my LDC calculation is not really near the ones published in different studies. 

See also interesting LD calculators like the one for the James Webb Telescope. See this link

Dynamic of Sunspot group AR3141 and AR3145

Picture of sunspot group AS3141 and AR3145 on November 11 and 12.

 

Sunspot AR3141 - CaK and White light

 

Sunspot AR3141, AR3140 and AR3145 observed on November 12, 2022. Sunspot AR3141 not only photographed in White Light but also with CaK filter.

Setting : TAL200K f/8.5, ND3.8 filter, CaK filter, ASI290mm, Barlow x2

Software : SharpCap4, AS3! (50% stacked), IMPPG, CS4

Sunspot AR3141 - Light Bridges

Some high clouds but still I was able to make some pictures of Sunspot AR3141 (and AR3140, AR3145). Sunpot AR3141 is a complex sunspot with an beta, gamma, delta configuration. 

The sunspot has also a couple of bright light bridges.

Setting: TAL200K f/8.5 with ASI290MM and ND3.8

Software: SharpCap 4.0, AS3! (25% stacked), IMPPG, DeNoise AI and CS4

Moon and Jupiter

Jupiter north of the Moon with Golden Handle.

Halo 22° and Circumzenithal Arc

Around midday, the sun was surrounded by a halo 22° and a faint circumzenithal arc.

Partial Solar eclipse Oct 25, 2022 - calculating max coverage using ImageJ

The partial solar eclipse of October 25, 2022 was tracked from Averbode. With some clouds, the conditions were less good than last year on June 10, 2021, but still sufficient.The solar eclipse was tracked with a TLAPO80/480 f/6 and Nikon D7500. A solar filter ND3.8 and OIII filter were used. A total of 127 photos were taken represesnting 3.56Gb of data. Several photos were edited and one timelapse of the process was created. You can visit my blog for this see this link .

I tried to determine the maximum of the solar eclipse as well as the time of the maximum. ImageJ software was used. To determine the surface of the sun, raw photos were uploaded and after selection via color contrast, the number of pixels that  which are not obscured are calculated. The “solidity” was also calculated. This is the result of dividing the area of ​​the eclipse by the convex area (smallest perimeter of a surface). To calibrate the time with my Nion D7500 photos, I used the time via the Frankfurt atomic clock.

I have shown in the top right corner the data for Averbode as obtained from www.timeanddate.com

Conclusion: the solidity gives much lower coverage values ​​than the pixel values. The traject of the eclipse and the calculations are influenced by the clouds on the photos. The time of the maximum is 2 minutes earlier than indicated on the website. The coverage value is 2% points higher than indicated on the website. 

A fun exercise that mainly shows the power of the ImageJ program.