Alopecia areata is an autoimmune condition, where your body’s own immune system attacks some components of the hair follicle resulting in that hair to shed. Alopecia areata is very easy to identify clinically, because the areas of skin are very smooth. There is no scale or evidence of infection and the pattern that alopecia areata makes is almost a perfect circle, which is very unusual and easy to pick-up to make this diagnosis.
To treat alopecia areata we will oftentimes use an injectable cortisone to help quell some of the inflammation around those hair follicles to disperse the body's attack of that hair follicle.
Unfortunately, it is not a perfect therapy by any means and often times multiple injections are required in order to get hair to return to that spot. Eyebrows are particularly tricky, because this hair grows slower than terminal hair of your scalp and also of the beard area.
There are other topical therapies as well as oral therapies that can be used for alopecia areata that you might consider and discuss with your Board Certified Dermatologist. However, nothing can make eyebrow hair grow faster, except to find some method to suppress inflammation in that area and let it grow back at its natural, slow rate.