  We show that the definition of the city boundaries can have a dramatic
influence on the scaling behavior of the night-time light (NTL) as a function
of population (POP) in the US. Precisely, our results show that the arbitrary
geopolitical definition based on the Metropolitan/Consolidated Metropolitan
Statistical Areas (MSA/CMSA) leads to a sublinear power-law growth of NTL with
POP. On the other hand, when cities are defined according to a more natural
agglomeration criteria, namely, the City Clustering Algorithm (CCA), an
isometric relation emerges between NTL and population. This discrepancy is
compatible with results from previous works showing that the scaling behaviors
of various urban indicators with population can be substantially different for
distinct definitions of city boundaries. Moreover, considering the CCA
definition as more adequate than the MSA/CMSA one because the former does not
violate the expected extensivity between land population and area of their
generated clusters, we conclude that, without loss of generality, the CCA
measures of light pollution and population could be interchangeably utilized in
future studies.
