  Dynamical friction (DF) against stars and gas is thought to be an important
mechanism for orbital evolution of massive black holes (MBHs) in merger remnant
galaxies. Recent theoretical investigations however show that DF does not
always lead to MBH inspiral. For MBHs evolving in gas-rich backgrounds, the
ionizing radiation that emerges from the innermost parts of their accretion
flow can affect the surrounding gas in such a way to cause the MBHs to
accelerate and gain orbital energy. This effect was dubbed "negative DF". We
use a semi-analytic model to study the impact of negative DF on pairs of MBHs
in merger remnant galaxies evolving under the combined influence of stellar and
gaseous DF. Our results show that for a wide range of merger galaxy and MBH
properties negative DF reduces the MBH pairing probability by $\sim 46\%$. The
suppression of MBH pairing is most severe in galaxies with one or more of these
properties: (1) a gas fraction of $f_g \geq 0.1$; (2) a galactic gas disk
rotating close to the circular velocity; (3) MBH pairs in prograde, low
eccentricity orbits, and (4) MBH pairs with mass $< 10^8\,$M$_\odot$. The last
point is of importance because MBH pairs in this mass range are direct
progenitors of merging binaries targeted by the future space-based
gravitational wave observatory LISA.
