The distances to which the optical flash destroys dust via sublimation , and the burst and afterglow change the size distribution of the dust via fragmentation , are functions of grain size .
Furthermore , the sublimation distance is a decreasing function of grain size , while the fragmentation distance is a decreasing function of grain size for large grains and an increasing function of grain size for small grains .
We investigate how these very different , but somewhat complementary , processes change the optical depth of the circumburst medium .
To this end , we adopt a canonical distribution of graphite and silicate grain sizes , and a simple fragmentation model , and we compute the post-burst/optical flash/afterglow optical depth of a circumburst cloud of constant density n and size R as a function of burst and afterglow isotropic-equivalent X-ray energy E and spectral index \alpha , and optical flash isotropic-equivalent peak luminosity L : This improves upon previous analyses that consider circumburst dust of a uniform grain size .
We find that circumburst clouds do not significantly extinguish ( \tau \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } % } 0.3 ) the optical afterglow if R \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 10 % L _ { 49 } ^ { 1 / 2 } pc , fairly independent of n , E , and \alpha , or if N _ { H } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } % } } 5 \times 10 ^ { 20 } cm ^ { -2 } .
On the other hand , we find that circumburst clouds do significantly extinguish ( \tau \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 3 ) the optical afterglow if R \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 10 % L _ { 49 } ^ { 1 / 2 } pc and N _ { H } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } % } } 5 \times 10 ^ { 21 } cm ^ { -2 } , creating a so-called ‘ dark burst ’ .
The majority of bursts are dark , and as circumburst extinction is probably the primary cause of this , this implies that most dark bursts occur in clouds of this size and mass M \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 3 % \times 10 ^ { 5 } L _ { 49 } M _ { \sun } .
Clouds of this size and mass are typical of giant molecular clouds , and are active regions of star formation .