We report interferometric observations of nine class II methanol maser cand
idate lines toward W3(OH). Narrow maser emission spikes at v(LSR) = -43.1 k
m s(-1) are present in three of the lines: 3(1)-4(o) A(+) 7(2)-6(3) A(+), a
nd 7(2)-6(3) A(-). For all three lines the maser position is near the north
ern edge of the W3(OH) ultracompact H II region (maser emission is also see
n near the southern edge in the 3(1)-4(o) A(+) line). For the remaining six
lines there is no obvious counterpart to the narrow maser spike at -43.1 k
m s(-1). Additional spatially extended emission is present in all nine line
s over the range from -41 to -48 km s(-1) By comparing our observed flux de
nsities with an extensive set of model calculations, we infer physical char
acteristics of the maser region. In these calculations the methanol is exci
ted by infrared radiation from warm dust, and this excited gas amplifies th
e free-free background emission from the ultracompact H II region. The gas
forming the narrow maser spikes appears to have both high kinetic temperatu
re, T-kin greater than or equal to 110 K, and high density, n(H2) approxima
te to 10(7) cm(-3). Low-temperature solutions are ruled out by the observed
line ratios and low-density solutions by the unphysically large path lengt
h that would be required. The gas is rich in methanol (2N(M) = N-A + N-E gr
eater than or similar to 10(-6) N-H2), and the methanol column density in t
he tangential direction for each symmetry species (divided by line width) i
s N-M/DeltaV approximate to 10(12) cm(-3) s. Somewhat lower values of n(H2)
and N-M/DeltaV are also acceptable. The size of the region emitting the ma
ser spike is of order 100 x 1000 AU. In most of the lines the broad emissio
n from -41 to -48 km s(-1) can also be attributed to weak maser action, pro
duced in gas with similar physical conditions thigh density and temperature
). It differs from the narrow spike emission mainly through a beaming facto
r that can be interpreted as an elongation factor for clumps of maser gas.
The combination of narrow and broad emission can arise naturally from an en
semble of clumps of different elongations and orientations. In this unified
picture the best fit to the data is provided by n(H2) approximate to 2 x 1
0(6) cm(-3) and N-M/DeltaV approximate to 4 x 10(11) cm(-3) s, somewhat low
er than the values obtained for just the spike component. The methanol mase
r clumps may be present in an expanding shell surrounding the H II region,
similar to the material producing OH maser emission in this source.