The duty cycle of accretion bursts in young stellar objects
When stars are young, they gather matter from the disk and envelope that surrounds them. There is growing evidence that this accretion process is strongly variable. A favoured idea in this context is 'episodic accretion': According to this scenario, most of the material is accreted in transient episodes which are interspersed by much longer quiescent periods. This idea is supported by the fact that some - around 10 - known young stars have been observed to undergo an extreme increase in the rate of accretion, which manifests itself in an enormous increase in the brightness - the class of outbursting FU Ori variables. If this scenario is true, an important parameter in the early evolution of stars would be the duty cycle of episodic accretion - the average time difference between consecutive bursts of accretion. This quantity determines how much mass the star gains by accretion. It also puts limits on the efficiency of planet-forming processes in the disks.
In the figure I provide a crude estimate the duty cycle based on the number of known FU Ori stars. I assume that these FU Oris have been detected over the course of t=100 years and are a subset of about N=1000 stars which have been observed over this time frame. To produce the figure I calculate the probability to catch a burst for a given duty cycle, assign random numbers to each star, and check for how many of them this number is lower than the burst probability. To get a statistical estimate, this procedure was carried out 10000 times. I can then derive how probable it is to observe 10 bursts for a given duty cycle.
This gives an average duty cycle of 10000 years (easily derived: N x t / 10 FU Oris), and a 95% upper limit of 20500 years. Note that exactly the same result is obtained, as long as the product of N and t is the same. These parameters N and t, however, are not trivial to determine because the known FU Ori objects have mostly been found serendipitously, not from systematic surveys. For plausible values of these two parameters, the resulting duty cycle is in the range between 5000 and 50000 yr. This would imply that all stars experience around 20-200 episodes of strong accretion in their early evolution.
