So far in this Introduction we have considered the physics of molecular clouds and star forma- tion. The dense cores of gas seen in molecular clouds are the link between these two topics. Cores represent the densest peaks of the hierarchical density distribution within molecular clouds, and it is within them that stars are formed. Further, observations of the core mass function have shown it strongly resembles the IMF (Motte et al., 1998), leading many to pro- pose a direct link between them (eg. Alves et al., 2007). Firstly let us consider the properties of the cores:-
1.3.1
Observations of Cores
As the sites of star formation, cores have been studied in great detail; recent surveys include Motte et al. (1998); Johnstone et al. (2000, 2006); Ikeda et al. (2007); Alves et al. (2007);
1.3. The Clump Mass Function Nutter & Ward-Thompson (2007); Ward-Thompson et al. (2007); Enoch et al. (2008). From these an understanding of the key features of cores is beginning to develop.
Cores are generally sub-classified into two types. Cores containing stars already have an infrared source at their centre, meaning they are actively forming proto-stars, and so are often referred to as proto-stellar cores. Star-less cores show no evidence of a proto-star at their centre and are usually referred to as pre-stellar cores.
As regards the structure of cores, Ward-Thompson et al. (1994) found that while the densities of the outer regions of cores can be well fit by the power lawρ∝r−2, the profile is flattened at the centre. This resembles the density profile of a Bonor-Ebert sphere which was discussed in Section 1.2.1. Observations of pre-stellar cores are generally well fit by this model (e.g. Johnstone et al., 2000). Bonnor-Ebert spheres are hydrostatic and pressure confined, so does this mean that cores also share these properties?
Lada et al. (2008) make the case that the core population of the Pipe Nebula could be pressure confined. However this may not always be the case, as Tafalla et al. (2004) have observed cores within which the thermal pressure is insufficient to balance self-gravity. More worryingly, Ballesteros-Paredes et al. (2003) have shown that dynamically collapsing cores can be well fit by stable Bonnor-Ebert spheres, therefore the usefulness of this method in determining the evolutionary state of cores is as yet uncertain. Moreover, even the simple assumption of sphericity is not entirely valid. Myers et al. (1991) found cores to be elongated structures better represented as prolate or oblate spheroids, as a consequence of which their internal energy equilibrium must be imperfect.
Pre-stellar cores have temperatures of around 10K, similar to their parent molecular clouds. Temperatures will only rise above this if the core becomes unstable and begins to collapse. When densities become so high that the gas is opaque to its own cooling radiation the core will be heated. Larson (2005) proposed a simple polytropic heating and cooling law to model gas temperatures during the early stages of star formation. This will be discussed further in Chapter 2.
Unlike the velocities of the larger cloud, core velocities are generally close to thermal (Myers, 1983; Goodman et al., 1998). These largely sonic motions seem chiefly due to tur- bulence, as the contribution from rotation seems small (Goodman et al., 1993). Additionally in-fall motions are often observed; for instance Lee et al. (1999) found an overabundance of
inward velocities of 0.05−0.1 kms−1 in a sample of 220 starless cores. At least some cores, therefore, must be in a state of dynamic collapse.
1.3.2
The Core Mass Function
Since the seminal observations of Motte et al. (1998) a clear resemblance has been recognised between the core (and clump) mass functions and the stellar initial mass function (IMF). Motte et al. (1998) have shown that the core mass function (CMF) inρOph can be described by a similar power-law fit as the IMF. Above∼0.5 Mthey find d n/d m∝m−αis well-fitted by an exponent value ofα=2.5, while at lower masses they see a turn-over that can be fitted withα = 1.5. These values forα are broadly consistent with the usual fits to the (Kroupa, 2002) IMF shown in Section 1.2. Similar results have been confirmed by a number of authors for a variety of nearby star-forming regions, although the range of core masses found and the break mass of the power law fit can vary (Johnstone et al., 2000, 2006; Nutter & Ward- Thompson, 2007; Alves et al., 2007; Testi & Sargent, 1998). Clumps and cores appear to have slightly different mass functions. Larger clump measurements using CO tend to find a shallower value of the exponent α = 1.4−1.8 (Blitz, 1993; Kramer et al., 1998). This is perhaps due to gravity steepening the slope on smaller scales where structures are more bound. A more detailed account of the clump/core mass distribution can be found in Ward- Thompson et al. (2007).
There are various theories as to how a power-law CMF could be formed. Gravity, causing successive fragmentation in a collapsing gas cloud will naturally lead to a power law dis- tribution (Larson, 1973a; Elmegreen & Mathieu, 1983). Alternatively, as discussed earlier, supersonic turbulence produces a clumpy, hierarchical density structure, the density peaks of which are cores. Padoan & Nordlund (2002) have argued that a CMF with a power law resem- bling that of the IMF is a natural consequence of turbulence with a power spectrum consistent with the Larson velocity dispersion law. Recently, Hennebelle & Chabrier (2008) proposed that the CMF is a combination of a power law caused by turbulence, and a lognormal cutoff centered around the characteristic mass of gravitational mass for gravitational collapse. The Jeans mass (Jeans, 1902) at the point of fragmentation has been shown to be only weakly de- pendent on temperature, density, metallicity and radiation field in the environments in which stars form (Larson, 2005; Elmegreen et al., 2008), which means that the characteristic mass of a Jeans unstable fragment should be similar in all molecular clouds.
1.4. Outline of Thesis