Testing the star formation scaling relations in the clumps of the North
  American and Pelican cloud complexes
  The processes which regulate the star-formation within molecular clouds are
still not well understood. Various star-formation scaling relations have been
proposed to explain this issue by formulating a relation between star-formation
rate surface density ($\rm \Sigma_{SFR}$) and the underlying gas surface
density ($\rm \Sigma_{gas}$). In this work, we test various star formation
scaling relations, such as Kennicutt-Schmidt relation, volumetric
star-formation relation, orbital time model, crossing time model, and multi
free-fall time scale model towards the North American and Pelican Nebulae
complexes and in cold clumps associated with them. Measuring stellar-mass from
young stellar objects and gaseous mass from CO measurements, we estimated mean
$\rm \Sigma_{SFR}$, star formation rate per free-fall time, and star formation
efficiency (SFE) for clumps to be 1.5 $\rm M{_\odot}~yr^{-1}~kpc^{-2}$, 0.009,
2.0$\%$, respectively, while for the entire NAN complex the values are 0.6 $\rm
M{_\odot}~yr^{-1}~kpc^{-2}$, 0.0003, and 1.6$\%$, respectively. For clumps, we
notice that the observed properties are in line with the correlation obtained
between $\rm \Sigma_{SFR}$ and $\rm \Sigma_{gas}$, and between $\rm
\Sigma_{SFR}$ and $\rm \Sigma_{gas}$ per free-fall time and orbital time for
Galactic clouds. At the same time, we do not observe any correlation with $\rm
\Sigma_{gas}$ per crossing time and multi free-fall time. Even though we see
correlations in former cases, however, all models agree with each other within
a factor of 0.5 dex, and discriminating between these models is not possible
due to the current uncertainties in the input observables. We also test the
variation of $\rm \Sigma_{SFR}$ versus the dense gas, but due to low
statistics, a weak correlation is seen in our analysis.
