  Tertiary tides (TTs), or the continuous tidal distortion of the tertiary in a
hierarchical triple system, can extract energy from the inner binary, inducing
within it a proclivity to merge. Despite previous work on the subject, which
established that it is significant for certain close triple systems, it is
still not a well-understood process. A portion of our ignorance in this regard
stems from our inability to integrate a simulation of this phenomenon into
conventional stellar evolution codes, since full calculations of these tidal
interactions are computationally expensive on stellar evolution timescales.
Thus, to attain a better understanding of how these TTs act on longer
timescales, an empirical expression of its effects as a function of parameters
of the triple system involved is required. In our work, we evaluate the rate at
which TTs extract energy from the inner binary within a series of constructed
hierarchical triple systems under varying parameters, and study the rate at
which the inner binary orbital separation shrinks as a function of those
parameters. We find that this rate varies little with the absolute values of
the masses of the three component objects, but is very sensitive to the mass
ratio of the inner binary $q$, the tertiary radius $R_{\rm 3}$, the inner
binary orbital separation $a_{\rm 1}$, the outer orbital separation $a_{\rm
2}$, and the viscoelastic relaxation time of the tertiary $\tau$. More
specifically, we find that the percentage by which $a_{\rm 1}$ shrinks per unit
time can be reasonably approximated by (1/$a_{\rm 1}$)(d$a_{\rm
1}$/d$t$)=$\left(2.22{\times}10^{-8}{\rm
yrs}^{-1}\right)4q\left(1+q\right)^{-2}(R_{\rm 3}/100{\rm
R}_{\odot})^{5.2}(a_{\rm 1}/0.2{\rm AU})^{4.8}(a_{\rm 2}/2{\rm AU})^{-10.2}$
$({\tau}/0.534{\rm yrs})^{-1.0}$. We also provide tests of how precise this
fitting function is.
