  We analyze the effect of a heterogeneous variance on bump detection in a
Gaussian regression model. To this end we allow for a simultaneous bump in the
variance and specify its impact on the difficulty to detect the null signal
against a single bump with known signal strength. This is done by calculating
lower and upper bounds, both based on the likelihood ratio. Lower and upper
bounds together lead to explicit characterizations of the detection boundary in
several subregimes depending on the asymptotic behavior of the bump heights in
mean and variance. In particular, we explicitly identify those regimes, where
the additional information about a simultaneous bump in variance eases the
detection problem for the signal. This effect is made explicit in the constant
and / or the rate, appearing in the detection boundary. We also discuss the
case of an unknown bump height and provide an adaptive test and some upper
bounds in that case.
