In a series of papers Wilson (1972aWilson ( , b, 1973) ) has proposed a Carnot cycle to explain the cooling of a sunspot. It is the purpose of this note to point out some inconsistencies in these papers. If the cooling cycle envisaged by Wilson operates at all, it falls short of the cooling required in a spot by a factor of at least 100.
Wilson begins by assuming that a horizontal temperature gradient already exists, i.e., he assumes that the spot is already cool. Thus his cooling cycle is a secondary process which 'is more applicable to the decay phase' of a spot rather than to the initial spot cooling. Another mechanism is presumed to be operative in producing the initial cooling, but no reason is given why a new mechanism (namely, Wilson's cycle) should have to be introduced in the late phases of a spot's life. Why not assume that whatever cooled the spot initially continues to do so at a late phase?
Even supposing that Wilson's cycle is at work, he has to change drastically his initial model (Figure 2 of Paper I) in order to obtain cooling large enough to support his claim that this mechanism can explain the sunspot energy deficit (2 x 1029 erg s-1). The drastic revision (see Table I of Paper III) requires that the cycle be confined to a height of only 100 km at a depth of 5000 km. Why 5000 km is chosen is not explained, except to refer to 'depths associated with the supergranules'. Such depths are not clearly defined. But more essential is the confinement to a depth range of only 100 km. By this device, segments BC and AD of the cycle are defined to be isotherms, while a temperature gain or loss of 103K is allowed to build up along the 'adiabats' AB and CD. Now admittedly no cycle is ideally a Carnot cycle, but to use a formula for the cooling E per unit volume per cycle such as Wilson uses: In (vl/v,)