The Self-gravitating Gas Fraction and The Critical Density for Star Formation

Understand

We analytically calculate the star formation efficiency and dense self-gravitating gas fraction in the presence of magneto-gravo-turbulence using the model of Burkhart (2018), which employs a piecewise lognormal and powerlaw density Probability Distribution Function (PDF).

• We show that the PDF transition density from lognormal to powerlaw forms is a mathematically motivated critical density for star formation and can be physically related to the density where the Jeans length is comparable to the sonic length, i.e.
• the post-shock critical density for collapse.
• When the PDF transition density is taken as the critical density, the instantaneous star formation efficiency ($\epsilon_{\rm inst}$) and depletion time ($\tau_{\rm depl}$) can be calculated from the dense self-gravitating gas fraction represented as the fraction of gas in the PDF powerlaw tail.