ner_tags: O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-CelestialObject O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O
tokens: for NOAA AR 11591. whereby t is in days and t ∈ N is at noon. X 0 is the value we are interested in and will be henceforth called offset. It is used instead of a time average ⟨ X ( t )⟩ t because it correctly accounts for missing data (most importantly the gap in the afternoon of Oct 17) and that t start and t end have a different time of day. Here we have |⟨ X ( t )⟩ t − X 0 | 0.5 G for all X ( t ) in G and 0.01° for . While X 1 and X 2 are used internally during the fitting process to guarantee numeric stability, the results are presented with parameters X 0 , X 3 , and X 4 in Table 2 . X 3 and X 4 are the amplitude and phase of the orbital artefacts. Also listed are the standard deviations of the residuals σ t = σ ( X ( t )− X fit ( t )) and the means of the standard deviations along the contours over the same range in time ⟨ σ ψ ⟩ t . Table 2. Results: fit parameters and time averages. Notes. ( a ) Excluding five snapshots due to faulty 180°-disambiguation: t = 10.22.{12 : 14, 12 : 36, 13 : 36, 14 : 00, 14 : 12}. Levels of magnetic contours. The offsets X 0 from the fits to , and for the 0.5(0.4) I qs contours are then used as contour level on the B ver , | B | and γ LRF maps, respectively. They are discussed in Sect. 3.2 and plotted in Figs. 3 and 5 and the videos. Distance between contours. To quantify how well two contours match we calculated the average distance between them ⟨ d ⟩ ψ , which we define as the area of symmetric difference divided by the length of the intensity contour, l( t ). The area of symmetric difference, Δ a ( t ), is the area surrounded by either of the contours but not both. When averaging in time we weighed by the contour length, giving These average distances between contours are listed in Table 2 in pixel. For ⟨ d ⟩ ψ ≪ 1pixel only the total ordering should be relied upon due to griding and other computational effects. Fit along each contour. For every point along a contour, a reference angle ψ = ∡(PCD) is calculated, whereby P is the point on the contour, C is the centroid of the I c = 0.5 I qs contour in the CCD frame and D is the centre of the solar disc as observed by SDO. The angles are calculated on the sphere. For every time step and every contour, is least square fitted against functions of the form Those fits are plotted in the right panels of the videos (cf. Sect. 3.2 and bottom panels of Figs. 3 and 5 ). Furthermore the time averages of the fit amplitudes are listed in Table 2 . Optimal height difference. Δ h = 465 km was chosen because it minimizes the average distance ⟨ d ⟩ ψ , t between the I c = 0.5 I qs contours after transformation with Eq. ( 1 ) and the B ver contours, whereby the contour level X 0 on the B ver map has been derived with the fit to ⟨ B ver ⟩ ψ ( t ) as described above (Eq. ( 2 )). An optimal height difference of Δ h = 465 km means that the intensity contour at the limb is shifted outwards by 465 km ⋅ r ⊙ / R ⊙ ≈ 0.65′′ ≈ 1.3 pixel. The difference of the formation heights for