Context :

Aims : Bipolarity in proto-planetary and planetary nebulae is associated with events occurring in or around their cores .
Past infrared observations have revealed the presence of dusty structures around the cores , many in the form of disks .
Characterising those dusty disks provides invaluable constraints on the physical processes that govern the final mass expulsion of intermediate-mass stars .
We focus this study on the famous M2-9 bipolar nebula , where the moving lighthouse beam pattern indicates the presence of a wide binary .
The compact and dense dusty core in the center of the nebula can be studied by means of optical interferometry .

Methods : M2-9 was observed with VLTI/MIDI at 39-47 m baselines with the UT2-UT3 and UT3-UT4 baseline configurations .
These observations are interpreted using a dust radiative transfer Monte Carlo code .

Results : A disk-like structure is detected perpendicular to the lobes and a good fit is found with a stratified disk model composed of amorphous silicates .
The disk is compact , 25 \times 35 mas at 8 \mu m , and 37 \times 46 mas at 13 \mu m .
For the adopted distance of 1.2 kpc , the inner rim of the disk is \sim 15 AU .
The mass represents a few percent of the mass found in the lobes .
The compactness of the disk puts strong constraints on the binary content of the system , given an estimated orbital period 90-120yr .
We derive masses of the binary components between 0.6–1.0M _ { \sun } for a white dwarf and 0.6–1.4M _ { \sun } for an evolved star .
We present different scenarios on the geometric structure of the disk accounting for the interactions of the binary system , which includes an accretion disk as well .

Conclusions :