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 2.13 \mu m observations of NML Cyg with 73 mas 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 \sim 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 2.13 \mu m visibility function .
Additionally , mid-infrared visibility functions at 11 \mu m 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 6.2 R _ { \ast } , a close embedded superwind shell extending from 15.5 R _ { \ast } to 21.7 R _ { \ast } with an amplitude ( factor of density enhancement ) of 10 , and a far-out density enhancement at 186 R _ { \ast } with an amplitude of 5 .
The angular diameters of the central star and of the inner rim of the dust shell amount to 16.2 mas and 105 mas , resp .
The diameter of the embedded close superwind region extends from 263 mas to 368 mas , and the inner boundary of the distant superwind region has a diameter of 3 \aas@@fstack { \prime \prime } 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 ) \sim a ^ { -3.5 } , with a ranging between a _ { min } = 0.005 \mu m and a _ { max } = 0.15 \mu m. The bolometric flux amounts to F _ { bol } = 3.63 \cdot 10 ^ { -9 } Wm ^ { -2 } corresponding to a central-star luminosity of L / L _ { \odot } = 1.13 \cdot 10 ^ { 5 } \cdot ( d / { kpc } ) ^ { 2 } .
Within the various parts of the dust shell , 1 / r ^ { 2 } 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 \rho \sim 1 / r ^ { 1.7 } is considered in the distant superwind region .
The present-day mass-loss rate was determined to be \dot { M } = 1.2 \cdot 10 ^ { -4 } M _ { \odot } /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 59 yr ago and lasted for \sim 18 yr .
Correspondingly , the outer superwind region is due to to a high mass-loss period ( amplitude 5 ) which terminated 529 yr ago .