Doppler shift narrowing in accelerated binary systems Steps:

• Rotation rate increase implies orbital angular velocity ω rises, shrinking separation a via Kepler's law (a ∝ ω^{-2/3}).
• Radial velocity amplitude K ∝ ω^{1/3} initially rises but stabilizes or decreases if tidal synchronization reduces relative motion.
• Doppler formula: observed f = f_rest (1 ± K/c); reduced K range shifts f_min upward and f_max downward.
• Net effect: spectral line extremes narrow toward rest frequency.

Why C is correct:

• Increased rotation synchronizes spins to orbit, reducing effective radial velocity spread per conservation of angular momentum, narrowing frequency range (f_min up, f_max down).

Why the others are wrong:

• A: Both decreasing ignores range narrowing; shift is asymmetric.
• B: f_min decreasing assumes larger K, but synchronization counters this.
• D: Both increasing would require blue-shifted center, violating rest frame.

Not enough information on synchronization context. Final answer: C