CO(1-0)
interferometer observations and numerical simulations
, M.J.Sempere , F. Combes 
,
R. Neri 
Observatorio Astronómico Nacional, Apartado
1143, E-28800 Alcalá de Henares, Spain Observatoire de Paris,
DEMIRM, 61 Av. de l'Observatoire, F-75014, France Institut de RadioAstronomie Millimétrique, 300
rue de la Piscine, F-38406 Saint Martin d'Hères, France 
) the CO(1-0) emission in the
nucleus of the doubled barred SABbc spiral M 100. Our synthesized map
includes the zero spacing flux of the single-dish 30m map (Sempere &
García-Burillo, 1997, paper I). Molecular gas is
distributed in a two spiral arm structure starting from the end points
of the nuclear bar (r=600 pc) up to r=1.2 kpc, and a central
source ( 
100 pc). The kinematics of the gas indicates the
existence of a steep rotation curve (v 
=180 km s 
at
pc) and strong streaming motions characteristic of a
trailing spiral wave inside corotation.
Interpretation of the CO observations and their relation with stellar
and gaseous tracers (K, optical, H 
, HI and radiocontinuum
maps) are made in the light of a numerical model of the clouds
hydrodynamics. Gas flow simulations analyse the gas response to a
gravitational potential derived from the K-band plate, including the
two nested bars. We develop two families of models: first, a single
pattern speed solution shared by the outer bar+spiral and by the
nuclear bar, and secondly, a two independent bars solution, where the
nuclear bar is dynamically decoupled and rotates faster than the
primary bar.
We found the best fit solution consisting of a fast pattern
( 
=160 kms kpc ) for the nuclear bar (with
corotation at R 
=1.2 kpc) decoupled from the slow pattern
of the outer bar+spiral ( =23 kms kpc ) (with
corotation at R 
=8-9 kpc). As required by non-linear
coupling of spirals (Tagger et al 1987), the corotation of the fast
pattern falls in the ILR region of the slow pattern, allowing an
efficient transfer of molecular gas towards the nuclear region.
Solutions based on a single pattern hypothesis for the whole disk
cannot fit the observed molecular gas response and fail to account for
the relation between other stellar and gaseous tracers. In the
two-bar solution, the gas morphology and kinematics are strongly
varying in the rotating frame of the slow large-scale bar, and fit the
data periodically during a short fraction (about 20%) of the relative
nuclear bar period of 46 Myr (Fig. 10).
Figure 10: We display the particle orbits for molecular clouds in the
region where the bar instability develops, as they are seen, firstly,
a(top): from the frame rotating at
=23kms kpc , for the solution of a single slow
pattern and b(bottom): from the frame rotating at
=23kms kpc for the best-fit solution of a
double pattern ( =160kms kpc (from
r=0 
to 10 ), 
=23kms kpc (for
r>10 ). The length of the arrows is proportional to the
particle speed in the rotating frame. These simulations illustrate the
efficiency of fast nuclear bars, dynamically decoupled form the outer
bar+spiral structure, in driving the gas towards the nucleus, hence
accounting for the observations.