Answer Happy

2. Fragmentation During Cloud Collapse Now let's see if we can find a characteristic mass where fragmentation stops and thus a lower limit to the mass of stars formed. This is, at best, an order of magnitude scaling argument, and, at worst a misleading interpretation of what truly happens. (a) Roughly what is the luminosity from the cloud during the optically-thin, nearly isothermal, dynam- ical collapse? (b) Presume that the cloud loses energy as a black-body once it becomes optically thick. How much energy must it emit per unit time so that dynamical collapse and fragmentation can continue? If the cloud at that instant is just marginally stable, find the minimum mass it can have (in terms of the temperature, scale to T 104 K) so that cooling can continue and thus fragmentation. How does this minimum mass compare to the Sun? Jupiter? Earth?