Cold Gas Density Distribution

In §4.2, the results show that the N-body simulation develops a very rich structure whereas

the spiral potential simulation does not. Because of the self-gravity, gas in the arms tends to form clouds in a “beads on a strin” fashion. A similar behaviour is observed in the simulations of Renaud et al. (2013). The gas tends to follow well the spiral structure of the galaxy, which is consistent with otherN-body with hydrodynamics simulations such as Clarke & Gittins (2006);

Baba et al. (2009); Wada et al. (2011); Grand et al. (2012); Mata-Chávez et al. (2014); Baba et al. (2017).

The spiral potential simulation does not develop much structure after the first_≈40 Myr. However, after approximately 100 Myr, many different structures appear in the inner regions of the galaxy (see Figure 4.2). The morphological features are qualitatively similar to those re- ported in Dobbs & Bonnell (2006); Bonnell et al. (2013); Smith et al. (2014). These works use a similar potential and SPH and can be compared to the simulations in this work. These fea- tures have also been studied in simulations using mesh codes with spiral potentials (e. g. Kim & Ostriker 2002, 2006; Shetty & Ostriker 2006). However, they only develop mostly within 2−3 kpc from the galaxy’s centre. The orbital period atR=3 kpc is_≈ 108 Myr. Given the

angular frequency relative to the spiral pattern atR = 3 kpc, the crossing time of the inter-

arm region is approximately 46.5 Myr, which means that the gas has had enough time to pass through about two arms. This may explain the richer structure within 3 kpc, the first arm pas- sage leads to the formation of some dense gas structures and quickly reaches a second arm, where it interacts with more dense gas in the arm.

In both models, most of the dense gas structures form within 5 kpc (corotation is around 4.5 kpc). Because of the exponential gas profile, the inner regions have higher densities, thus higher cooling rates and shorter cooling timescales. This explains why the cold dense gas starts to form from the inner to the outer galaxy. The spiral arms also drive the formation of dense gas.

As described in Chapter 3, observations show that the molecular gas tends to have a steep profile whereas the warm gas tends to have a flatter profile. It is interesting that both sim- ulations also show this behaviour. As shown in Figure 4.4, the dense gas is concentrated in

4.5. Discussion

the inner regions and has a quickly decaying profile whereas the warm gas has a nearly flat profile. The surface density values are consistent with the typical values reported in Bigiel & Blitz (2012). It is interesting that the spiral potential simulation gives a cold gas central density close to the value reported for M33 in Druard et al. (2014).

4.5.2

Gas Dynamics in Spiral Arms

§4.3 presented the density, velocity, and velocity dispersion profiles as a function of azimuth. Roberts (1969) presented a solution for the density and velocity profiles of shocks in spiral arms. In this solution, the density is predicted to jump at the shock and then gradually de- crease; the velocity normal to the arm shows the jump due to the shock; the tangent velocity decreases to a minimum near the shock point and then increases. A key point is that Roberts (1969) predicts that as gas enters the arm, the shock occurs before the potential minimum. This has been a subject of discussion in the literature (e. g. Dobbs & Baba 2014).

In theN-body simulation, the gas density behaves in a similar fashion. It increases sharply

and decreases gradually after the jump, but this behaviour is less evident at radii larger than

≈5 kpc. In several arms, the density peak is located slightly before the arm’s density peak, but

in some cases it occurs at a different position. This result agrees with the simulations of Clarke & Gittins (2006), although a direct comparison is difficult since they assumed an isothermal and non-gravitating gas. The N-body simulation also agrees with the results of Wada et al.

(2011) and Baba et al. (2016). These works do include cooling and self-gravity, although they have less resolution than the simulations of this work.

In the spiral potential simulation, a similar behaviour is seen at smaller radii but without such a strong shock. It is interesting to note that in this simulation the density peak is forming after the potential minimum with respect to the point of inflow. Near the corotation radius, the density peak is close to the minimum. Outside corotation, the position of the peak is reversed. However, in this region, the arm rotates faster than the gas. With respect to the arm, the gas now enters from the opposite direction so the density profile is reversed. The density peak, however, is forming after the potential minimum with respect to the direction of the flow (see Figure 4.7). These results are slightly different to that of Roberts (1969), which predicts that the shock forms before the potential minimum as gas flows into the arm. However, the spiral potential parameters of this thesis are not identical to those of Roberts (1969).

Using a spiral potential, Gittins & Clarke (2004) analysed the behaviour of the gas around the corotation radius using m= 2 and m = 4 potentials. They find that the shock is offset

from the potential minimum and this offset has some dependence with the number of arms. They use semi-analytic as well as numerical codes to model the flow through the potential. Some of their simulations use the SPH method, which can be compared to the spiral potential simulation. For them=4 potential, Gittins & Clarke (2004) find that the shock forms after the

gas passes the potential, which agrees with this simulation. Gittins & Clarke (2004) measure this offset as a function of radius for their models. The spiral potential simulation in this work agrees with their results in the sense that, seen face-on, the offset tends to zero near corotation. A recent study by Sormani et al. (2017) of flow properties around a spiral arm, shows that it is possible to produce shocks forming after passing the minimum when the base flow is supersonic. The result of this section support the idea behind the method proposed by Gittins & Clarke (2004) to constrain the corotation radius by measuring the offset between the shock and the stellar arms. This has been applied in observations by Kendall et al. (2011, 2015).

In terms of the velocity profile, both simulations show a sharp jump in radial velocity where the shock is forming. Where v_R is maximum, the azimuthal velocity is minimum. The pitch

angle of the arms is small, so the normal and tangent components are not very different to the v_R and vφ components. The behaviour in the simulations is consistent with the velocity

profiles of Roberts (1969). The velocity profiles in our simulations are also consistent with the behaviour of those in the simulations of Baba et al. (2016), which also analyse gas flows in spiral arms.

In terms of the velocity dispersion, the results show that the spiral arms play a significant role in injecting a velocity dispersion to the arm. However, the dispersion may be rather low due to the lack of feedback and other injection mechanisms. The high velocity dispersion regions tend to be associated with the spiral arm regions in both models.