tokens: of SFRs and molecular gas fraction. The initial density profile of the dark matter halo in a disc galaxy is modelled using the density distribution of the NFW halo (Navarro, Frenk White 1996 ) as suggested from cold dark matter (CDM) simulations. The c -parameter ( c r vir r s , where r vir and r s are the virial radii of a dark matter halo and the scale length, respectively) and r vir are chosen appropriately by using recent predictions from cosmological simulations (Neto, Gao Bett 2007 ). We adopt the Hernquist density profile for the bulge of a disc galaxy and the bulge mass fraction ( M b M s ) is a free parameter ranging from 0 to 1. The size ( R b ) and the mass of the bulge have the following scaling relation that can reproduce the properties of the Galactic bulge: kpc. The radial ( R ) and vertical ( Z ) density profiles of the stellar disc are assumed to be proportional to exp( R R 0 ) with a scale length R 0 0.2 R s and to sech 2 ( Z Z 0 ) with a scale length Z 0 0.04 R s , respectively. The gas disc with a size of R g has the radial and vertical scale lengths of 0.2 R g and 0.02 R g , respectively. Since we investigate disc models with M h similar to that of the Galaxy (i.e. M h 10 12 M ), the exponential disc has R s 17.5kpc for all models in the present model. The initial Toomres parameter Q is set to be 1.5 for gas and stars and the vertical velocity dispersion at a given radius is set to be 0.5times as large as the radial velocity dispersion at that point so that the dynamical equilibrium in the vertical direction can be achieved. A gas particle is assumed to be converted into a new star if the local H 2 density (, where and g are the H 2 mass function and gas density, respectively) exceeds a threshold density ( th ) and we investigate the models with th 10, 30 and 100cm 3 . These are H 2 -dependent SF models, and we also investigate H-dependent one in which g should be higher than th . We adopt these values because our previous numerical simulations of galaxy evolution with dust demonstrated that the models with the above values can explain the observed SFR g relation (see fig.3 in Yozin Bekki 2014 for the case of the Magellanic Clouds). We assume that SFR ( sf 1.5) in this study. Chemical enrichment processes, dust formation and evolution in ISM and SN feedback effects are included in the same way as B13 and B15 . We investigate disc models with corotating (referred to as standard rotation and labelled as S for convenience) and counter-rotating (C) gas discs for a given set of disc parameters. By comparing between the two models, we try to understand how counter-rotating gas can influence dynamics and star formation histories of disc galaxies. We show the results for only 24 models in this study and Table 1 describes the model parameters for each of the SC pairs. The total number of particles used for a simulation is 1033400 for a fiducial model (M1 and M2) and different initial gravitational softening lengths () are
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