We present an analytical model for the density variations of interstel
lar pickup ions in the solar wind due to a time-dependent variation in
the photoionization rate of the interstellar atoms. Following a sudde
n increase in the photoionization rate, our model predicts a pickup io
n density enhancement lasting for a time of the order of the duration
of the increase plus the solar wind convection time to the observation
point. If the photoionization rate returns to its initial value, this
enhancement is followed by a decreased pickup ion density resulting f
rom a depleted interstellar neutral particle density. In the absence o
f further variations in the photoionization rate, the pickup ion densi
ty recovers on a time which scales as the radial position of the obser
vation point divided by the inflow speed of the neutral particles. Gra
dual variations in the photoionization rate result in a pickup ion den
sity which tends to track the ionization rate, though the density vari
ations are smoothed and delayed in time due to the solar wind convecti
on of ions picked up at points closer to the Sun.