Step 1: Understanding water activity.
Water activity (\(a_w\)) is a measure of the available water in a food that supports microbial growth. Staphylococcus aureus is known to grow at low water activity, and the growth of this bacterium typically occurs at a \(a_w\) of around 0.86 under aerobic conditions.
Step 2: Analyzing the options.
- (A) Incorrect, 0.98 is above the threshold for microbial growth, and Staphylococcus aureus can grow at higher water activities.
- (B) Incorrect, while 0.91 is low, it is still above the value supporting growth in aerobic conditions.
- (C) Incorrect, 0.89 is still above the threshold.
- (D) Correct, 0.86 is the water activity below which Staphylococcus aureus can grow in aerobic conditions.
Step 3: Conclusion.
Thus, the correct answer is (D) 0.86.