Formation of Molecular Clouds

As stated before, the mass spectrum of molecular clouds covers a rather wide range of masses. In addtion to intrinsic e fects like turbulence (which may disperse the gas), the range of masses is a natural consequence of the di ferent formation mechanisms. Some clouds do form by processes, which act on Galactic scales. Other clouds may form due to more localised events. Below, I will introduce possible formation mechanisms, which seem to form molecular clouds on a frequent level and which are intrinsically coupled to the dynamics of the ISM.

Parker Instability

Horizontally aligned magnetic eld lines, if slightly perturbed, can undergo buoyant oscillations, thereby building magnetic ridges and valleys (Parker,1966). A gaseous disc in initial magneto–

hydrostatic equilibrium with a vertically oriented gravitational eld will always be unstable to this kind of instability (Shu,1992). Gas settles in the disc midplane due to the in uence of the verti-cally oriented gravitational eld (here due to stars). The gas will then move along the magnetic eld lines, preferentially towards magnetic valleys, that is, towards the lowest point of a eld line.

The accumulation of gas in such valleys will in turn drag the eld along towards the central parts of the disc, which ampli es the buoyancy of the eld. AsDobbs et al.(2014) point out, the most unstable mode of this instability is proportional to2πH, whereH is the scale height and the growth rate is∼vA/H(McKee and Ostriker,2007). However, perturbations with longer wave-lengths will grow slower, but the collapse of the gas along the eld lines will be nearly at free–fall (seeShu,1992). SinceH ∼ 100−200 pc, it is in general possible to accumulate enough mass within the valleys such that clouds with massesMcloud ∼ 10⁵ −10⁶M⊙form. This is indeed con rmed by numerical simulations with an external stellar potential only (see e.g.Mouschovias et al.,2009). In addition, the authors report cloud separations ofdC ∼ 500 pcand magnetic eld strengths in the midplane ofB ∼ 4.3µGwith a slightly larger rms component, but in agreement with observations.

Figure 2.9 shows the resulting Parker instability from simulations byMouschovias et al.(2009).

The lef sub gure indicates the stage of linear growth, whereas the other sub gures depict the phase where the instability grows non–linearly. The authors point out that it takes roughly 18 Myr to reach the non–linear stage. Simulations including e fects like turbulent uctuations or Galactic rotation observe only a slight increase in gas density at the midplane of the disc (Kim et al.,1998,2001,2002). It was concluded that the Parker instability might be too ine cient to form GMCs but may trigger or amplify other instabilities (McKee and Ostriker,2007). On the other hand, more recent simulations byLee and Hong(2011) suggest that the Parker instability may indeed form GMCs, but only in combination with the Jeans instability due to self–gravity, because the latter is able to suppress the convective instability, which naturally arises from the buoyancy of the eld lines in the classical Parker instability.

Figure 2.9:Numerical simulation of the Parker instability. Colour coded is the density. Black solid lines denote the magnetic field lines. The field lines first become only slightly perturbed during the linear growth stage, but then greatly deform at later stages. FromMouschovias et al.(2009),Formation of interstellar clouds: Parker instability with phase transitions. MNRAS, 397:14–23, figure 3.

Cloud–Cloud Collisions

Frequent observations of di fuse H I clouds in the ISM have lead to the suggestion that (giant) molecular clouds form due to collisions of two or more low–mass clouds (Field and Saslaw, 1965;Kwan,1979). However, the latter authors found the time to build up clouds with masses

> 10⁵M⊙is≳ 10⁴Myr(see alsoBlitz and Shu,1980;Elmegreen,1990) and it was hence con-cluded to be a negligible formation process. But, as clouds are formed within spiral–arms or in the interarm regions they can undergo frequent collisions during one spiral arm revolution (e.g.

Tasker and Tan,2009;Tan et al.,2013;Dobbs et al.,2015). Values range from one collision every 1/4 orbit (Tasker and Tan,2009) to a collision every 1/40th of an orbit (Fujimoto et al.,2014, see alsoDobbs et al.(2015)). The latter authors included more sophisticated physics compared to the former. However, both studies highlight a revival of cloud–cloud collisions as a possible mecha-nism to form high–mass clouds.

The collisions of clouds naturally lead to either the formation of more massive clouds or to the disruption of the projectile clouds (e.g.Tasker and Tan,2009;Tasker,2011;Dobbs et al.,2014).

This depends to a large fraction on the Mach numbers of the colliders (McLeod et al.,2011;Wu et al.,2015) as well as the impact parameter between the clouds (Wu et al.,2015). The possible success of this model is its ability to account for the observed cloud–mass spectrum since a large

variety of projectile masses as the basis can form either lower–mass clouds due to destruction or subsequently ll up the high–mass tail of the spectrum (Dobbs et al.,2014). In addition, as stated inDobbs et al.(2014), the observed quasi–perdiodic spacing of GMCs can be explained by Galactic scale simulations and the in uence of the epicyclic frequency (see alsoDobbs et al.,2011).

Once, the collision was successful in the respect of forming a GMC, formation of high–mass stars might be triggered due to the large reservoir of gas (Wu et al.,2015;Balfour et al.,2015).

Colliding Warm Neutral Medium Streams

Ballesteros-Paredes et al.(1999) suggested that molecular clouds can form in the collision plane of two converging streams of warm H I. Their intention was to bring up a solution to the small spread in stellar ages of only 1–3 Myr observed in the Taurus–Auriga complex.

In this scenario, to oppositely directed WNM streams form a shock–compressed layer in between (see gure 3.3 for a schematic). The density and temperature are increased, which is su cient to induce runaway cooling due to thermal instability (e.g.Field,1965;Vázquez-Semadeni et al., 2007). In addition, the WNM streams are turbulent. The turbulent uctuations yield regions within the shocked slab between the ows where the thermal pressure of the slab is not opposite to the external ram–pressure of the ows. Instead, the thermal pressure gradient within the slab will induce motions perpendicular to the ows, thereby increasing the pressure support in nearby regions. As a result, other regions in the slab will break up due to the lack of support and be-come unstable. Beside this non–linear thin–shell instability (NTSI,Vishniac,1994;Heitsch et al., 2007) the slab is prone to Kelvin–Helmholtz instabilities because of the strong shearing motions (seeHeitsch et al.,2008b,a). The combined action of turbulence and thermal and dynamical in-stabilities then leads to the formation of a lamentary network. These laments are cold density enhancements that are immersed in a warm, di fuse medium (Hennebelle et al.,2008;Banerjee et al.,2009;Vázquez-Semadeni et al.,2011;André et al.,2014a,b).

The ISM is also magnetised (Beck,2001;Crutcher et al.,2009). Hence, the ows might be aligned with the ambient background magnetic eld. In the contrary case of motion perpendicular to the magnetic eld, magnetic pressure and magnetic tension are able to either delay or completely sup-press the formation ofmolecularclouds (Heitsch et al.,2009).Inoue and Inutsuka(2009) argue that an inclination between the ow velocity and the magnetic eld, which is too large, will only result in H I clouds without any further evolution towards molecular states. This has also been inferred from one–dimensional simulations ofHennebelle and Pérault(1999).

The advantage of this kind of formation model is its ability to explain e.g. the observed sheet–

like morphologies of nearby clouds (Dobbs et al.,2014) as well as the small stellar age–spread (Ballesteros-Paredes et al.,1999). The former is due to gas motion along magnetic eld lines and the con nement of the resulting cloud by the external ram pressure (e.g.Vázquez-Semadeni et al., 2009). The latter can be explained by the following:

Gravitational energy has to exceed (in absolute values) the opposing thermal (and magnetic) en-ergy. The lower limit is then given by an equilibrium of energies. The necessary column density for the gas to a ford gravitational collapse is then (Franco and Cox,1986;Hartmann et al.,2001)

N_grav ∼1.07×10²⁰ ( T

10 K )1/2

( n 1 cm⁻³

)1/2

cm⁻². (2.18)

If a magnetic eld is taken into account, the above equation is modi ed by including a term

∝ √β.In a magnetised uid, the gas also has to besupercritical. Fromµ = µcritfollows (e.g.

Hartmann et al.,2001;Vázquez-Semadeni et al.,2011)

Ncrit ∼2.92×10²⁰ ( B

1µG )

cm⁻², (2.19)

where the critical mass–to–magnetic ux ratioµcrit = 0.16/√

GfromNakano and Nakamura (1978) was utilised. Furthermore, the gas becomesmolecularat

Nmol ∼(1−2)×10²¹cm⁻², (2.20)

as was shown byFranco and Cox(1986) andvan Dishoeck and Black(1988). Hence, the gas in the ISM becomes gravitationally unstable, magnetically supercritical, and molecular at the same time, which then implies rapid onset of star formation in a globally collapsing molecular cloud (Ballesteros-Paredes et al.,1999;Elmegreen,2007;Vázquez-Semadeni et al.,2011).

It should be noted that converging streams do not have a unique origin. In fact, large scale gravi-tational instabilities or the above mentioned Parker instability induce converging gas motions (Hennebelle and Falgarone,2012). On the other hand, expanding supernova shells may collide and form a molecular cloud (Inoue and Inutsuka,2008,2009,2012;Ntormousi et al.,2011,2014).

The latter was actually observed most recently byDawson et al.(2015). In addition, asHennebelle and Falgarone(2012) point out, converging gas motions are also observed at the junctions of la-ments within molecular clouds (see alsoHacar and Tafalla,2011).

One constraint of this approach, however, is the inability to form GMCs with massesMGMC ≥ 10⁵M⊙(Dobbs et al.,2014). The typical masses of clouds formed by converging WNM ows are of the order of10⁴M⊙(e.g.Vázquez-Semadeni et al.,2007;Banerjee et al.,2009; Vázquez-Semadeni et al.,2011;Hennebelle and Falgarone,2012;Körtgen and Banerjee,2015). This mass limit is linked to the spatial extent of the WNM streams. Thus, the larger the coherent ows the greater the nal mass of the cloud. However, the coherence of the ows might be destroyed by turbulence in the ISM (Carroll-Nellenback et al.,2014). Furthermore, accumulation of gas in the ISM is primarily guided by the magnetic eld. AsMcKee and Ostriker(2007) point out this implies a form of accretion that is very ine cient since it is along one dimension only. But, as stated inVázquez-Semadeni et al.(2011) the accretion becomes three dimensional and much more e cient as soon as the gas has become dense, cold and gravitationally unstable.