Infrared variability of the symbiotic Mira V407 Cygni and the structure ofits dust envelope

We perform an in-depth analysis of the infrared variability of the symbioti c Mira V407 Cyg resulting both from its pulsations and from a secular trend in its mean brightness. The two effects are shown to be similar in nature and are attributable to a change in the bolometric luminosity of the Mira i n combination with a change in its temperature and/or in the optical depth of its dust envelope. In the last fourteen years, the mean bolometric lumin osity has risen by similar to 30%, which must have been reflected in an inc rease of the pulsation period by Delta P/P greater than or equal to 0.1. Th e optical depth tau(J) of the dust envelope decreased by similar to 0.06, o r the temperature of the Mira rose by similar to 100 K. Both of these effec ts result in approximately the same displacement of the star in the (J-L, K ) diagram, which is most suitable for estimating variations in the paramete rs (L, T, tau). The changes in the shape of the energy distribution observe d during pulsations of the Mira can be explained in terms of the dust-envel ope model in which a new dust layer condenses during the pulsation minimum at a distance of similar to 3.5 R*. It consists of a mixture of silicate an d graphite grains with a total mass of similar to 7 x 10(-9) M.. At this ti me, more than half of the optical depth of the entire dust envelope is conc entrated in this layer, which changes by a factor of similar to 2 in half t he pulsation period (similar to 745(d)). Near the pulsation maximum, tau(J) approximate to 0.25 and the inner radius of the dust envelope is R-in appr oximate to 5 R*. Over the past similar to 10(4) years, the Mira has lost it s mass at an approximately constant rate of similar to 5 x 10(-7) M. yr(-1) for M-gas/M-dust approximate to 200. The dust envelope may be composed eit her of small (similar to 0.01 mu m) or large (similar to 0.1 mu m) grains. In the latter case, it should be kept in mind that these grains rather than medium-sized (similar to 0.05 mu m) ones determine its optical depth. We a nalyze the dust-envelope models in detail in terms of their possible observ ational verification.