2001A&A...369..142B

object{NML Cyg} is a highly evolved OH/IR supergiant, one of the most prominent infrared objects due to its strong obscuration by dust, and supposed to be among the most luminous supergiants in the galaxy. We present the first diffraction-limited 2.13µm observations of NML Cyg with 73mas resolution. The speckle interferograms were obtained with the 6 m telescope at the Special Astrophysical Observatory, and the image reconstruction is based on the bispectrum speckle-interferometry method. The visibility function declines towards the diffraction limit to ∼0.6. Radiative transfer calculations have been carried out to model the spectral energy distribution, given by ground-based photometry and ISO spectroscopy, and our 2.13µm visibility function. Additionally, mid-infrared visibility functions at 11µm were considered. The observed dust shell properties do not appear to be in accordance with standard single-shell (uniform outflow) models but seem to require multiple components. Considering previous periods of enhanced mass-loss, various density enhancements in the dust shell were taken into account. An extensive grid of models was calculated for different locations and strenghts of such superwind regions in the dust shell. To match the observations from the optical to the sub-mm domain requires at least two superwind regions embedded in the shell. The best model includes a dust shell with a temperature of 1000 K at its inner radius of 6.2R_*, a close embedded superwind shell extending from 15.5R_* to 21.7R_* with an amplitude (factor of density enhancement) of 10, and a far-out density enhancement at 186R_* with an amplitude of 5. The angular diameters of the central star and of the inner rim of the dust shell amount to 16.2mas and 105mas, resp. The diameter of the embedded close superwind region extends from 263mas to 368mas, and the inner boundary of the distant superwind region has a diameter of 3.15." In the near-infrared the dust condensation zone is limb-brightened leading to a corresponding ring-like intensity distribution. The grain sizes, a, were found to be in accordance with a standard distribution function, n(a)∼a^–3.5, with a ranging between a_min=0.005µm and a_max=0.15µm. The bolometric flux amounts to F_bol=3.63x10^–9W/m² corresponding to a central-star luminosity of L/L_☉=1.13x10⁵(d/kpc)². Within the various parts of the dust shell, 1/r² density distributions could be maintained differing only in their amplitude A. A slight improvement of the far-infrared properties can be obtained if a shallower density distribution of ρ∼1/r^1.7 is considered in the distant superwind region. The present-day mass-loss rate was determined to be {dot}(M)=1.2x10^–4M_☉/yr. The inner embedded superwind shell corresponds to a phase of enhanced mass-loss (with amplitude 10) in the immediate history of NML Cyg which began 59yr ago and lasted for ∼18yr. Correspondingly, the outer superwind region is due to to a high mass-loss period (amplitude 5) which terminated 529yr ago.