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Virial parameters

In order to search for a possible reason for these findings, it may be a reasonable idea to look at the relative importance of the kinetic and gravitational energy of the cores. This can be done using the (dimensionless) virial parameter (see, e.g., Bertoldi & McKee 1992)

vir = 5 2 R/GM =~ 2 T/|W|

where is the velocity dispersion of the core (= v/(8ln2)½ for a Gaussian line profile with v the measured FWHM of the line), R and M are the radius and mass of a core, G the gravitational constant, T is the total kinetic energy of the core, and W its gravitational energy (W = -3/5 a GM2/R; a is a dimensionless parameter of order unity which measures the effects of a nonuniform or nonspherical mass distribution on the gravitational energy). A value of vir <= 1 means that the gravitational binding energy is more important than the kinetic energy, the core is gravitationally bound (but possibly still supported by magnetic fields). vir > 1 means that the kinetic energy is more important than gravity; such a core has to be confined by external pressure (otherwise it would disperse) and is unlikely to form stars.

 Virial parameter alpha_vir of cores with/without jets Figure 38  Virial parameter alpha_vir of cores with/without jets sorted by survey subregions Figure 39

In Fig. 38 the distributions of the virial parameter vir are shown for cores associated with jets (solid line) and for cores not associated with jets (dotted line). Cores with multiple jets are shown as the hashed histograms. It is evident that jets are found preferentially in cores with lower values of vir, i.e., in cores with a relatively large importance of gravitational energy compared to kinetic energy. Furthermore, among the cores associated with jets, the cores associated with multiple jets again tend to have systematically lower values of vir. The trend for jets to be found in cores with low vir is also evident if the three survey subregions are considered separately (Fig. 39); note also the general trend for vir to increase when going from region I southwards to region III footnote 3.

 Core mass - virial parameter alpha_vir relation Figure 40

Figure 40 shows a plot of the virial parameter vir against the core masses. Cores associated with jets are indicated with filled symbols (the bigger symbols mark cores with multiple jets), and cores without jets are marked by open symbols. Obviously there is a tendency for vir to increase with decreasing core mass. From this plot it becomes clear, why jets are found preferentially in more massive cores: these are the cores with smaller values of vir, i.e., they are stronger gravitationally bound and thus more prone to star formation.

T93 guessed that (given the uncertainties of the mass estimates) all cores are likely in virial equilibrium, although they found evidence for a power law relation between core mass Mcore and the ratio of the virial mass of a core to its actual mass, Mvir/Mcore, which is equivalent to vir. However, the tendency for star formation to occur more likely in cores with lower vir as observed here shows that the cores with lower vir indeed seem to be gravitationally bound (or at least more likely to be gravitationally bound). The rarity of star formation in the cores with high vir then might indicate that these are predominantly not gravitationally bound. Further support for this idea comes from the finding that vir and the core mass may be related by a power law of the form vir = 0 (M/), as is indicated in Fig. 40. A fit to the CS data gives a power law exponent of about -0.4. Similar power laws, albeit with generally smaller exponent , are also known from other clouds on larger scales for molecular clumps (see, e.g., Loren 1989; Bertoldi & McKee 1992; Williams et al. 1994). Bertoldi & McKee argue that such a power law relation (for vir reasonably greater than 1; see footnote 3) is expected for pressure-confined clumps, with a power law exponent  ~ -2/3. The findings that star formation in Orion A occurs more likely in the cores with low vir and high mass, and that vir seems to be related to the core mass by a power law with an exponent  ~ -0.4 may thus imply that pressure-confinement governs the low-mass cloud cores in Orion A.


next up previous contents
Next: Linewidths Up: 6.2 Properties of cores with and without H2 jets Previous: Core masses

Thomas Stanke

Mon Aug 14 17:51:08 CEST 2000
Last modified Wed Jul 18 19:09 CEST 2001