Star Formation Time Scale

There are long-standing controversy on how fast stars are form in the molecular clouds. One idea is that the interstellar cloud is in a hydrostatic balance in which magnetic field plays an important role. That is, the cloud is magnetically subcritical. In such a cloud, the magnetic field escapes from the center in a timescale of $\tau_D \sim 10\times t_{\rm ff}$ (see §4.4). After the mass-to-flux ratio exceeds a critical value, dynamical contraction begins. The timescale of cloud lifetime is equal to the time scale of ambipolar diffusion, $\tau_D\sim 3\times 10^7{\rm yr}(\rho/10^{2}{\rm H_2 cm^{-3}})^{-1/2}$. Long lifetime of molecular clouds is necessary to explain giant molecular clouds are formed by agglomeration process of small clouds. The necessary lifetime is estimated $10^7 {\rm yr}$ - $10^8{\rm yr}$.

Another idea is that the star formation timescale is much shorter than this timescale. Table 4.1 (Hartmann 2009) shows the ages of stellar population observed for respective star forming regions. Stellar clusters and associations accompanied with molecular clouds have ages younger than 5 Myr. And clusters and associations without accompanied molecular clouds are older than 5 Myr. This means that a molecular cloud will disappear after 5 Myr since star formation begins in the cloud. Since this timescale is shorter than $\tau_D$, the clouds seem to continue to be formed and the turbulance supports the cloud, the cloud core begins dynamical contraction after the turbulance decays away within the sound crossing timescale $\sim {\rm Myr}$.