Time evolution of the apo-galacticon Ra against peri-galacticon Rp plane for the MW1 model. A mean probability of finding an orbit within a given bin of Ra and Rp (where the mean is calculated over the indicated 1 Gyr time interval) is mapped. The bin size is 0.1 × 0.1 kpc. The probability for every bin is calculated as a sum of orbits with the bin’s Ra and Rp values, where the contribution of each orbit is divided by the total number of revolutions per orbit within the time interval (so the total contribution of each orbit to each map is equal to 1). Finally, the probability is normalized to the total number of orbits 104 and converted to %. Each column shows orbits for models including different components – axisymmetric model, model with bar, model with spiral arms, and finally bar and spiral arms combined model. Orbits are mapped within time intervals of 1 Gyr (0–1, 3–4, and 7–8 Gyr) as indicated in the left upper corner of each plot. The NGC 6791’s values of Ra and Rp with their three sigma error-bars are plotted with a red cross in each plot. The four lines in each of the plots show the lines of constant eccentricity for values 0.0 (circular orbits), 0.25, 0.5, and 0.75, respectively, with decreasing slope.
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