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tokens: where and are two cylindrical coordinates; is the axial ratio, is a structure parameter, and is a function of , such that becomes the density at radius , which defines a volume containing half of the total mass of the component (for details, see Tamm et al. 2012 ). The gravitational potential derivative of a component, necessary for calculating epicyclic frequencies, can in this case be expressed in a convenient form (see e.g. Tenjes et al. 2001 ) where is eccentricity and . The formula is general, but the epicyclic frequencies were calculated within the galactic plane only. While the mass distribution parameters of the spheroidal components and the main stellar disc can be used as presented in Tamm et al. (2012) , the flat young disc needs to be split further into main subsystems. At this stage we do not yet know the relative contributions of different flat components to the overall galaxy stability, thus we have to analyse each one of them. First we separated gas and stars by taking the mass of young stars to be and the gas mass to be ( Tamm et al. 2012 ). Thus we now had two stellar discs, one containing old and intermediate-age stars, and the other containing young stars. The parameters of these flat stellar components are given in Table 1 . Several subcomponents can also be distinguished in the gas disc. Although four to five different phases can be distinguished in the interstellar medium ( McKee Ostriker 1977 ; Chemin et al. 2009 ), here we have considered the neutral gas (including both the atomic and the molecular component) to consist of two main phases, the cold neutral medium (CNM) and the warm neutral medium (WNM; see Brinks Burton 1984 ; Wolfire et al. 2003 ; Kalberla Kerp 2009 ). For M 31 Dickey Brinks (1993) estimated that the mass of WNM is about 60 per cent and the mass of CNM is 40 per cent of the total neutral gas mass. These proportions have been found to also be valid in the Milky Way: according to Heiles Troland (2003) , the mass of WNM is 60 per cent of the total neutral gas mass. Thus we took the masses and . Unfortunately, direct measurements of the thickness of these two gas components in M 31 do not exist. Brinks Burton (1984) estimated from their gas velocity dispersion measurements that CNM has . In addition, taking into account the broad similarity between M 31 and the Milky Way, we have applied here the estimate by Kalberla (2003) that at the solar distance, the WNM disc of the Milky Way is about three times thicker than the CNM disc. Thus we take and . However, to consider the impact of uncertainties, we also performed calculations for some other flatnesses. All the other structure parameters and effective radii were kept unchanged. The parameters of the two gas discs are given in Table 1 . To complete the set of input parameters for stability calculations, we also needed to know velocity dispersions and the speed of sound in the disc components. Following Dorman et al. (2015) , we took velocity dispersions of