# Mass Spectrum

We have seen that a molecular cloud consists in many molecular cloud cores. For many years, there are attempts to determine the mass spectrum of the cores.

From a radio molecular line survey, a mass of each cloud core is determined. Plotting a histogram of number of cores against the mass, we have found that a mass spectrum can be fitted by a power law as

 (1.18)

where represents the number of cores per unit mass interval. Many observation indicate that as Table 1.1.

 Paper Region Observation Mass range Loren (1989) Oph Stutzki & Guesten (1990) M17 SW CO (), SS (, ) Lada et al. (1991) L1630 CS () Nozawa et al. (1991) Oph North CO () Tatematsu et al. (1993) Orion A CS () Dobashi et al. (1996) Cygnus CO () Onish et al (1996) Taurus CO () Motte, André, & Neri (1998) Oph mm Testi & Sargent (1998) Sarpens mm Kramer et al.(1998) L1457 etc CO, CO, CO (, ) Heithausen et al. (1998) MCLD 123.5 + 24.9, Polaris Flare CO( and ) Johnstone et al. (2000) Oph Johnstone et al. (2001) Ori B Onishi et al. (2002) Taurus HCO () Ikeda, Sunada, & Kitamura (2007) Ori A HCO () Ikeda & Kitamura (2009) Ori A CO ()
MCLD126.6+24.5, NGC 1499 SW, Orion B South, S140, M17 SW, and NGC 7538

Figure 1.31(left) (André, Ward-Thomson, & Barsony 2000) shows a mass spectrum function for 59 Oph cloud prestellar cores obtained at the IRAM 30-m telescope with the MPIfR 19-channel bolometer array. Presetellar cores with a mass has a spectrum of () for . While the right panel (Motte et al 2001) shows the cumulative mass spectrum ( vs. ) of the 70 starless condensations identified in NGC 2068/2071. The mass spectrum for the 30 condensations of the NGC 2068 sub-region is very similar in shape. The best-fit power-law is above . That is, . This power derived from the dust thermal emission is different from that derived by the radio molecular emission lines. Table 1.1 summarizes the observations to calculate the power index of core mass function.

The mass fuction of newborn stars is called as initial mass fuction (IMF). IMF for field stars in the solar neighborhood has been obtained as shown in Figure 1.33. The most famous one is Salpeter's IMF as (Salpeter 1955). The low-mass end is flatter than that of as for while for (Meyer et al. 2000). The powers of stellar ( ) and prestellar () mass functions are similar. If one prestellar core forms one star, the stellar mass is proportional to the prestellar core mass as and , the mass spectrum of prestellar cores completely determines the IMF.

Figure 1.32 plots the power-law indices against the typical gas densities of respective observations, in which the critical density is taken as a typical density for molecular line studies. The power-law index is an increasing function of the typical gas densitiy (Ikeda 2007) and the cores with have the same power-law index as the IMF. This may indicates these cores are the sites of star formation or direct parents of new-born stars1.1.

Kohji Tomisaka 2009-12-10