ORB is a feature detection and description pipeline like SIFT and contains Oriented FAST(oFAST) and Rotated BRIEF(rBRIEF) as its feature detector and feature descriptor respectively. In short, Oriented FAST feature detector is the FAST corner detector computed along with its orientation(which is computed as in [1] Section 3.2). Rotated BRIEF is the BRIEF feature descriptor computed by rotating the test-decision pairs along the orientation of oFAST. Refer [2] and [1].

Currently, I cannot answer this question in complete confidence, partly because I am yet to complete and test FREAK and partly because I am not aware of the data, or the kind of solar images that are going to be aligned. Can you give some examples of pairs of images that are required to be aligned in Solar Physics. Some queries that one would have about the data are like : Are the solar images that need to be aligned generated from the same camera but at different time intervals? Is the scaling or the zoom factor changing? Is it only the Sun's rotation about its axis that is generating these two different images or some other factor is also involved? Currently, ORB is the best bet, because of its speed and invariance to both scaling and rotation.

Image Registration Pipeline can be summarized as : Detect features(keypoints) --> Compute Descriptors --> Match keypoints --> Treat one image as the reference and Estimate the Geometric Transformation required to get the second image using the matches. ORB does the first three and the 4th stage is what needs to be done. These slides[3] explain it better.

[1] http://www.vision.cs.chubu.ac.jp/CV-R/pdf/Rublee_iccv2011.pdf
[2] http://cvlabwww.epfl.ch/~lepetit/papers/calonder_eccv10.pdf
[3] http://cs.haifa.ac.il/hagit/courses/CP/Lectures/CP05_FeaturesRegistX4.pdf