  Analyses of infrared signatures of CO$_2$ in water dominated ices in the ISM
can give information on the physical state of CO$_2$ in icy grains and on the
thermal history of the ices themselves. In many sources, CO$_2$ was found in
the `pure' crystalline form, as signatured by the splitting in the bending mode
absorption profile. To a large extent, pure CO$_2$ is likely to have formed
from segregation of CO$_2$ from a CO$_2$:H$_2$O mixture during thermal
processing. Previous laboratory studies quantified the temperature dependence
of segregation, but no systematic measurement of the concentration dependence
of segregation is available. In this study, we measured both the temperature
dependence and concentration dependence of CO$_2$ segregation in CO$_2$:H$_2$O
mixtures, and found that no pure crystalline CO$_2$ forms if the CO$_2$:H$_2$O
ratio is less than 23%. Therefore the segregation of CO$_2$ is not always a
good thermal tracer of the ice mantle. We found that the position and width of
the broad component of the asymmetric stretching vibrational mode of
$^{13}$CO$_2$ change linearly with the temperature of CO$_2$:H$_2$O mixtures,
but are insensitive to the concentration of CO$_2$. We recommend using this
mode, which will be observable towards low mass protostellar envelopes and
dense clouds with the James Webb Space Telescope, to trace the thermal history
of the ice mantle, especially when segregated CO$_2$ is unavailable. We used
the laboratory measured $^{13}$CO$_2$ profile to analyze the ISO-SWS
observations of ice mantles towards Young Stellar Objects, and the
astrophysical implications are discussed.
